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Can the Sun lose enough mass that Saturn's current velocity becomes escape velocity?
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Imagine that, through some cosmic phenomena not yet understood, the Sun 'burps' and ejects a vast amount of its mass into the cosmic void. A huge coronal discharge, perhaps. A pressure bubble inside that bursts. A mega internal explosion. The loss of mass is sudden and dramatic, but in a trajectory that does not traverse the planetary plane, and thus does not destroy any planets. Perhaps it occurs along the axis of the planetary plane. That is, the Sun does not 'burn out', go nova, or any other destructive end-of-life process, it just loses a substantial amount of mass. No other destructive radiation or other event that would immediately destroy the planets.
This loss of mass would result in a dramatic decrease in the gravitational pull of the Sun. This would affect all of the planetary orbits, as their escape velocity from the Solar System would decrease. If they kept their current velocity, I presume they would move further from the Sun.
A. How much mass would the Sun have to lose, in order for Saturn's current velocity to become its escape velocity from the Solar System? This is a tricky calculation and equation, as it has to account for the diminishing gravity of the Sun, not an increased velocity of Saturn. That is, it does not ask for the new velocity of Saturn sufficient to reach the escape velocity of Saturn from the existing Sun, but asks for the the maximum reduced mass of the Sun such that the current velocity of Saturn becomes its escape velocity.
The following are ancillary, but not essential, questions that might arise from answering A.
B. Is there any absolute principle of physics that would make this absolutely impossible?
C. Is it feasible that Saturn, along with its moons, could become an intragalaxy or even intergalaxy wanderer using this technique? The ultimate goal is to put a sentient self-sustaining colony on one or more of its moons, and then have it wander the Universe. How to give it the ability to sustain life on a moon for millions of years is another question not within the scope of this question.
D. Does it make more sense from the escape velocity perspective for my ultimate objective to consider another planet, such as Neptune or Jupiter? I need a planet with sufficient composition for it to become a source of power for the moons. Jupiter, for instance, naturally emits a very high level of radiation that could provide a source of energy for its moons as a substitute for the Sun, but again this is beyond the scope of this question.
What happens to the Sun because of the loss of this mass AFTER Saturn becomes a wanderer is not within the scope of this question.
How the Sun actually loses the mass is beyond the scope of this question. That it can somehow lose this mass is to be taken as a given assumption.
science-based gravity orbital-mechanics
asked 6 hours ago
Justin Thyme
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Imagine that, through some cosmic phenomena not yet understood, the Sun 'burps' and ejects a vast amount of its mass into the cosmic void. A huge coronal discharge, perhaps. A pressure bubble inside that bursts. A mega internal explosion. The loss of mass is sudden and dramatic, but in a trajectory that does not traverse the planetary plane, and thus does not destroy any planets. Perhaps it occurs along the axis of the planetary plane. That is, the Sun does not 'burn out', go nova, or any other destructive end-of-life process, it just loses a substantial amount of mass. No other destructive radiation or other event that would immediately destroy the planets.
This loss of mass would result in a dramatic decrease in the gravitational pull of the Sun. This would affect all of the planetary orbits, as their escape velocity from the Solar System would decrease. If they kept their current velocity, I presume they would move further from the Sun.
A. How much mass would the Sun have to lose, in order for Saturn's current velocity to become its escape velocity from the Solar System? This is a tricky calculation and equation, as it has to account for the diminishing gravity of the Sun, not an increased velocity of Saturn. That is, it does not ask for the new velocity of Saturn sufficient to reach the escape velocity of Saturn from the existing Sun, but asks for the the maximum reduced mass of the Sun such that the current velocity of Saturn becomes its escape velocity.
The following are ancillary, but not essential, questions that might arise from answering A.
B. Is there any absolute principle of physics that would make this absolutely impossible?
C. Is it feasible that Saturn, along with its moons, could become an intragalaxy or even intergalaxy wanderer using this technique? The ultimate goal is to put a sentient self-sustaining colony on one or more of its moons, and then have it wander the Universe. How to give it the ability to sustain life on a moon for millions of years is another question not within the scope of this question.
D. Does it make more sense from the escape velocity perspective for my ultimate objective to consider another planet, such as Neptune or Jupiter? I need a planet with sufficient composition for it to become a source of power for the moons. Jupiter, for instance, naturally emits a very high level of radiation that could provide a source of energy for its moons as a substitute for the Sun, but again this is beyond the scope of this question.
What happens to the Sun because of the loss of this mass AFTER Saturn becomes a wanderer is not within the scope of this question.
How the Sun actually loses the mass is beyond the scope of this question. That it can somehow lose this mass is to be taken as a given assumption.
science-based gravity orbital-mechanics
asked 6 hours ago
Justin Thyme
6,6561734
4
Are you sure you don't want to split this into more questions? It tickles my too broad sense...
– L.Dutch♦
6 hours ago
@L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO
– kingledion
6 hours ago
1
Wouldn't the ejected mass have it's own gravitational effects, changing the orbits of the planets as it moves out of the system? 'Current velocity' wouldn't be maintainable then I think.
– Douwe
6 hours ago
@kingledion I agree that question B is somewhat a separate question, but I suspect many answers might bring it up, and so I thought I might make these answers relevant to the question. That is, I can see many posters saying 'It is impossible, period'. But I am willing to edit it out, What say you?
– Justin Thyme
6 hours ago
@JustinThyme The problem is that this is impossible, basically. The energy required to give half a sun escape velocity is so high, that thermodynamic heat dissipation would blow both pieces into cosmic dust. Better just to say, "this happened due to magic, deal with it"
– kingledion
6 hours ago
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up vote
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Imagine that, through some cosmic phenomena not yet understood, the Sun 'burps' and ejects a vast amount of its mass into the cosmic void. A huge coronal discharge, perhaps. A pressure bubble inside that bursts. A mega internal explosion. The loss of mass is sudden and dramatic, but in a trajectory that does not traverse the planetary plane, and thus does not destroy any planets. Perhaps it occurs along the axis of the planetary plane. That is, the Sun does not 'burn out', go nova, or any other destructive end-of-life process, it just loses a substantial amount of mass. No other destructive radiation or other event that would immediately destroy the planets.
This loss of mass would result in a dramatic decrease in the gravitational pull of the Sun. This would affect all of the planetary orbits, as their escape velocity from the Solar System would decrease. If they kept their current velocity, I presume they would move further from the Sun.
A. How much mass would the Sun have to lose, in order for Saturn's current velocity to become its escape velocity from the Solar System? This is a tricky calculation and equation, as it has to account for the diminishing gravity of the Sun, not an increased velocity of Saturn. That is, it does not ask for the new velocity of Saturn sufficient to reach the escape velocity of Saturn from the existing Sun, but asks for the the maximum reduced mass of the Sun such that the current velocity of Saturn becomes its escape velocity.
The following are ancillary, but not essential, questions that might arise from answering A.
B. Is there any absolute principle of physics that would make this absolutely impossible?
C. Is it feasible that Saturn, along with its moons, could become an intragalaxy or even intergalaxy wanderer using this technique? The ultimate goal is to put a sentient self-sustaining colony on one or more of its moons, and then have it wander the Universe. How to give it the ability to sustain life on a moon for millions of years is another question not within the scope of this question.
D. Does it make more sense from the escape velocity perspective for my ultimate objective to consider another planet, such as Neptune or Jupiter? I need a planet with sufficient composition for it to become a source of power for the moons. Jupiter, for instance, naturally emits a very high level of radiation that could provide a source of energy for its moons as a substitute for the Sun, but again this is beyond the scope of this question.
What happens to the Sun because of the loss of this mass AFTER Saturn becomes a wanderer is not within the scope of this question.
How the Sun actually loses the mass is beyond the scope of this question. That it can somehow lose this mass is to be taken as a given assumption.
science-based gravity orbital-mechanics
asked 6 hours ago
Justin Thyme
6,6561734
Imagine that, through some cosmic phenomena not yet understood, the Sun 'burps' and ejects a vast amount of its mass into the cosmic void. A huge coronal discharge, perhaps. A pressure bubble inside that bursts. A mega internal explosion. The loss of mass is sudden and dramatic, but in a trajectory that does not traverse the planetary plane, and thus does not destroy any planets. Perhaps it occurs along the axis of the planetary plane. That is, the Sun does not 'burn out', go nova, or any other destructive end-of-life process, it just loses a substantial amount of mass. No other destructive radiation or other event that would immediately destroy the planets.
This loss of mass would result in a dramatic decrease in the gravitational pull of the Sun. This would affect all of the planetary orbits, as their escape velocity from the Solar System would decrease. If they kept their current velocity, I presume they would move further from the Sun.
A. How much mass would the Sun have to lose, in order for Saturn's current velocity to become its escape velocity from the Solar System? This is a tricky calculation and equation, as it has to account for the diminishing gravity of the Sun, not an increased velocity of Saturn. That is, it does not ask for the new velocity of Saturn sufficient to reach the escape velocity of Saturn from the existing Sun, but asks for the the maximum reduced mass of the Sun such that the current velocity of Saturn becomes its escape velocity.
The following are ancillary, but not essential, questions that might arise from answering A.
B. Is there any absolute principle of physics that would make this absolutely impossible?
C. Is it feasible that Saturn, along with its moons, could become an intragalaxy or even intergalaxy wanderer using this technique? The ultimate goal is to put a sentient self-sustaining colony on one or more of its moons, and then have it wander the Universe. How to give it the ability to sustain life on a moon for millions of years is another question not within the scope of this question.
D. Does it make more sense from the escape velocity perspective for my ultimate objective to consider another planet, such as Neptune or Jupiter? I need a planet with sufficient composition for it to become a source of power for the moons. Jupiter, for instance, naturally emits a very high level of radiation that could provide a source of energy for its moons as a substitute for the Sun, but again this is beyond the scope of this question.
What happens to the Sun because of the loss of this mass AFTER Saturn becomes a wanderer is not within the scope of this question.
How the Sun actually loses the mass is beyond the scope of this question. That it can somehow lose this mass is to be taken as a given assumption.
science-based gravity orbital-mechanics
science-based gravity orbital-mechanics
asked 6 hours ago
Justin Thyme
6,6561734
asked 6 hours ago
Justin Thyme
6,6561734
edited 1 hour ago
asked 6 hours ago
Justin Thyme
6,6561734
asked 6 hours ago
Justin Thyme
6,6561734
asked 6 hours ago
Justin Thyme
6,6561734
6,6561734
4
Are you sure you don't want to split this into more questions? It tickles my too broad sense...
– L.Dutch♦
6 hours ago
@L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO
– kingledion
6 hours ago
1
Wouldn't the ejected mass have it's own gravitational effects, changing the orbits of the planets as it moves out of the system? 'Current velocity' wouldn't be maintainable then I think.
– Douwe
6 hours ago
@kingledion I agree that question B is somewhat a separate question, but I suspect many answers might bring it up, and so I thought I might make these answers relevant to the question. That is, I can see many posters saying 'It is impossible, period'. But I am willing to edit it out, What say you?
– Justin Thyme
6 hours ago
@JustinThyme The problem is that this is impossible, basically. The energy required to give half a sun escape velocity is so high, that thermodynamic heat dissipation would blow both pieces into cosmic dust. Better just to say, "this happened due to magic, deal with it"
– kingledion
6 hours ago
 |Â
show 2 more comments
4
Are you sure you don't want to split this into more questions? It tickles my too broad sense...
– L.Dutch♦
6 hours ago
@L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO
– kingledion
6 hours ago
1
Wouldn't the ejected mass have it's own gravitational effects, changing the orbits of the planets as it moves out of the system? 'Current velocity' wouldn't be maintainable then I think.
– Douwe
6 hours ago
@kingledion I agree that question B is somewhat a separate question, but I suspect many answers might bring it up, and so I thought I might make these answers relevant to the question. That is, I can see many posters saying 'It is impossible, period'. But I am willing to edit it out, What say you?
– Justin Thyme
6 hours ago
@JustinThyme The problem is that this is impossible, basically. The energy required to give half a sun escape velocity is so high, that thermodynamic heat dissipation would blow both pieces into cosmic dust. Better just to say, "this happened due to magic, deal with it"
– kingledion
6 hours ago
4
4
Are you sure you don't want to split this into more questions? It tickles my too broad sense...
– L.Dutch♦
6 hours ago
Are you sure you don't want to split this into more questions? It tickles my too broad sense...
– L.Dutch♦
6 hours ago
@L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO
– kingledion
6 hours ago
@L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO
– kingledion
6 hours ago
1
1
Wouldn't the ejected mass have it's own gravitational effects, changing the orbits of the planets as it moves out of the system? 'Current velocity' wouldn't be maintainable then I think.
– Douwe
6 hours ago
Wouldn't the ejected mass have it's own gravitational effects, changing the orbits of the planets as it moves out of the system? 'Current velocity' wouldn't be maintainable then I think.
– Douwe
6 hours ago
@kingledion I agree that question B is somewhat a separate question, but I suspect many answers might bring it up, and so I thought I might make these answers relevant to the question. That is, I can see many posters saying 'It is impossible, period'. But I am willing to edit it out, What say you?
– Justin Thyme
6 hours ago
@kingledion I agree that question B is somewhat a separate question, but I suspect many answers might bring it up, and so I thought I might make these answers relevant to the question. That is, I can see many posters saying 'It is impossible, period'. But I am willing to edit it out, What say you?
– Justin Thyme
6 hours ago
@JustinThyme The problem is that this is impossible, basically. The energy required to give half a sun escape velocity is so high, that thermodynamic heat dissipation would blow both pieces into cosmic dust. Better just to say, "this happened due to magic, deal with it"
– kingledion
6 hours ago
@JustinThyme The problem is that this is impossible, basically. The energy required to give half a sun escape velocity is so high, that thermodynamic heat dissipation would blow both pieces into cosmic dust. Better just to say, "this happened due to magic, deal with it"
– kingledion
6 hours ago
 |Â
show 2 more comments
5 Answers
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A naive first calculation
The formulas for orbital velocity and escape velocity are
$$v_o=sqrtfracGMr,quad v_e=sqrtfrac2GMr$$
I get $v_o=9.6text km/s$ for Saturn. For this to equal $v_e$, the Sun's new mass would have to be $0.5M_odot$, if we neglect the mass of the ejected gas.
The event
There are a number of ways a star can lose mass:
- Strong stellar winds can blow away material.
- A binary companion can accrete mass, if the separation is small enough.
- Some sort of dramatic stellar event - an eruption of some sort - can expel mass.
A normal coronal mass ejection may contain $sim10^-18M_odot$, which is also extremely low. Eta Carinae's Great Eruption averaged about $1M_odottext yr^-1$, but this is not an expected event in Sun-like stars. I don't think it's a good choice here, tempting though it may be.
The solar wind blows away mass at a rate of $sim10^-14M_odottext yr^-1$. Even the hottest O stars lose mass at $sim10^5-7M_odottext yr^-1$ at the most. When the Sun becomes an AGB star near the very end of its life, it may lose mass at a rate of $sim10^-4M_odottext yr^-1$, and so an extended AGB phase is a possibility, maybe involving a late thermal pulse leading back to the asymptotic giant branch. That said, Saturn's orbital speed (and orbit in general, including its eccentricity) would likely change slowly over time to stay bound to the Sun. 5,000 years is astronomically short, but not incredibly short.
A more realistic model
I'm imagining that in a dramatic but compressed AGB phase, the Sun's wind is isotropic, sending material streaming away from the star at $sim10^-4M_odottext yr^-1$. We can model the density of the wind by
$$rho_gas(r)=fracdotM4pi r^2v(r)$$
where $dotM$ is the mass loss rate and
$$v(r)=v_inftyleft(1-fracR_*rright)^beta$$
with $R_*$ being the radius of the star. For massive stars, we normally assume that $betaapprox1$. We can then find the gravitational potential by solving Poisson's equation:
$$nabla^2Phi_gas=4pi Grho_gas$$
From this, we can determine the escape velocity:
$$v_e(r)=sqrt2$$
where $Phi(r)=Phi_gas+Phi_odot$, and $Phi_odot$ changes in time as the Sun loses mass. You should be able to work backwards from here to determine the mass-loss rate and wind terminal velocity, given a desired escape velocity (Saturn's current orbital velocity, $9.6text km/s$).
Doing the math
Let's make some (justified) assumptions:
- At Saturn's orbit, $R_*/rll 1$, so we can use the binomial approximation to write
$$rho_gas(r)approxfracdotM4pi v_inftyleft(r^-2+fracR_*r^3right)$$ - The wind is isotropic, so
$$nabla^2Phi_gas=frac1r^2fracddrleft(r^2fracdPhi_gasdrright)=4pi Grho_gas(r)$$
This gives us a potential of the form
$$Phi_gas(r)=Phi_0-fracGdotMv_inftyleft(fracR_*r+fracR_*log (r/r_e)r-log(r/r_e)right)-fracDr$$
for some constants $Phi_0$, $r_e$, and $D$. Therefore,
$$v_e(r,t)=sqrt2left$$
at time $t$. Choosing the correct $dotM$, $v_odot$ and constants will get you the precise situation you want.
answered 6 hours ago
HDE 226868♦
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What will happen
First, the sun will split into two parts, racing away from each other at a relative velocity large enough for them to escape the other's gravitational pull. Newton's third law implies that they both race away from each other, meaning that they are both racing away from Saturn (and the other planets). But lets ignore that in favor of magic. The remnant stays in place relative to Saturn, while the ejected part moves away at high speed.
Initially, the center of gravity of the remnant-ejected system starts moving away from the sun. Saturn can be considered to be orbiting this remnant-ejected system. Assuming the remnant is moving away from Saturn, then the force of its gravity on Saturn will quickly be reduced.
In this case, the Saturn will soon be orbiting just the remnant, which will reform itself as a spherical star-like object. Now we can apply some orbital mechanics equations to see how big the remnant should be.
Escape velocity
Escape velocity is
$$v_e = sqrtfrac2GMr.$$ $G = 6.67times10^-11 text m^3text kg ^-1text s^-2$, $M$ is the mass of the sun, $r = 1.43times10^12text m$.
Saturn's orbital speed varies since its orbit is elliptical, so lets assume its mean orbital velcoity of $9680 text m s^-1$. We set $v_e$ equal to this and solve for the desired mass of the sun:
$$M = fracr v_e^22G = frac1.43times10^12text mcdot 9680^2text m^2text s^-22 cdot 6.67times10^-11text m^3text kg ^-1text s^-2 = 1.00times10^30 text kg$$.
The true mass of the sun is $1.99times10^30text kg$, so if the sun split in half, Saturn would be on the very edge of being attached to each half.
So in that sense, Saturn was the perfect planet to pick. If Saturn was near its perigee when the sun split in half, Saturn would remain gravitationally bound to one or the other fragment. If Saturn was near its apogee, it would be off into interstellar space.
Of course, that assumes the the fragment of the sun went away from saturn. The fragment is obviously moving at or above escape velocity also, so it could potentially get closer to Saturn then recapture it.
answered 6 hours ago
kingledion
66.8k22221381
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
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The math already presented by HDE 226868 and kingledion is bang on so I won't repeat it, but I feel they have neglected one possibility. The mass of a star can theoretically be reduced artificially through the process of star lifting so it may be possible for an arbitrarily advanced civilisation to pull enough material out of the sun, and displace it from the solar system, that Saturn would exceed escape velocity.
answered 6 hours ago
Ash
21.5k256131
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
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Even though @AlexP is right about the mass still existing, it's believable enough that -- unless you're writing Hard SF -- you can just assert that the Sun -- for example -- burped out 20% of it's mass and off zoomed Saturn.
For more realism, have the mass get burped in the opposite direction of where Saturn is. Saturn (and all the other planets...) gets pulled towards the new epicenter and then flies out into interstellar space.
answered 6 hours ago
RonJohn
12.5k12661
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
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Interesting. Not that I want to answer my own question, but I would like to sum up the math from both HDE 226868 and kingledion (to whom I acknowledge and thank very much for their input).
As a general rule of thumb, it looks like the mass of an orbited body has to be reduced by about 50%, or half, in order for an existing orbital velocity of a satellite to become the escape velocity of the satellite to the reduced orbited mass.
This could be a useful rule of thumb in so many different situations.
How it gets reduced by 50%, of course, is another question.
answered 2 mins ago
Justin Thyme
6,6561734
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5 Answers
5
active
oldest
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5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
A naive first calculation
The formulas for orbital velocity and escape velocity are
$$v_o=sqrtfracGMr,quad v_e=sqrtfrac2GMr$$
I get $v_o=9.6text km/s$ for Saturn. For this to equal $v_e$, the Sun's new mass would have to be $0.5M_odot$, if we neglect the mass of the ejected gas.
The event
There are a number of ways a star can lose mass:
- Strong stellar winds can blow away material.
- A binary companion can accrete mass, if the separation is small enough.
- Some sort of dramatic stellar event - an eruption of some sort - can expel mass.
A normal coronal mass ejection may contain $sim10^-18M_odot$, which is also extremely low. Eta Carinae's Great Eruption averaged about $1M_odottext yr^-1$, but this is not an expected event in Sun-like stars. I don't think it's a good choice here, tempting though it may be.
The solar wind blows away mass at a rate of $sim10^-14M_odottext yr^-1$. Even the hottest O stars lose mass at $sim10^5-7M_odottext yr^-1$ at the most. When the Sun becomes an AGB star near the very end of its life, it may lose mass at a rate of $sim10^-4M_odottext yr^-1$, and so an extended AGB phase is a possibility, maybe involving a late thermal pulse leading back to the asymptotic giant branch. That said, Saturn's orbital speed (and orbit in general, including its eccentricity) would likely change slowly over time to stay bound to the Sun. 5,000 years is astronomically short, but not incredibly short.
A more realistic model
I'm imagining that in a dramatic but compressed AGB phase, the Sun's wind is isotropic, sending material streaming away from the star at $sim10^-4M_odottext yr^-1$. We can model the density of the wind by
$$rho_gas(r)=fracdotM4pi r^2v(r)$$
where $dotM$ is the mass loss rate and
$$v(r)=v_inftyleft(1-fracR_*rright)^beta$$
with $R_*$ being the radius of the star. For massive stars, we normally assume that $betaapprox1$. We can then find the gravitational potential by solving Poisson's equation:
$$nabla^2Phi_gas=4pi Grho_gas$$
From this, we can determine the escape velocity:
$$v_e(r)=sqrt2$$
where $Phi(r)=Phi_gas+Phi_odot$, and $Phi_odot$ changes in time as the Sun loses mass. You should be able to work backwards from here to determine the mass-loss rate and wind terminal velocity, given a desired escape velocity (Saturn's current orbital velocity, $9.6text km/s$).
Doing the math
Let's make some (justified) assumptions:
- At Saturn's orbit, $R_*/rll 1$, so we can use the binomial approximation to write
$$rho_gas(r)approxfracdotM4pi v_inftyleft(r^-2+fracR_*r^3right)$$ - The wind is isotropic, so
$$nabla^2Phi_gas=frac1r^2fracddrleft(r^2fracdPhi_gasdrright)=4pi Grho_gas(r)$$
This gives us a potential of the form
$$Phi_gas(r)=Phi_0-fracGdotMv_inftyleft(fracR_*r+fracR_*log (r/r_e)r-log(r/r_e)right)-fracDr$$
for some constants $Phi_0$, $r_e$, and $D$. Therefore,
$$v_e(r,t)=sqrt2left$$
at time $t$. Choosing the correct $dotM$, $v_odot$ and constants will get you the precise situation you want.
answered 6 hours ago
HDE 226868♦
61k12214393
add a comment |Â
up vote
5
down vote
A naive first calculation
The formulas for orbital velocity and escape velocity are
$$v_o=sqrtfracGMr,quad v_e=sqrtfrac2GMr$$
I get $v_o=9.6text km/s$ for Saturn. For this to equal $v_e$, the Sun's new mass would have to be $0.5M_odot$, if we neglect the mass of the ejected gas.
The event
There are a number of ways a star can lose mass:
- Strong stellar winds can blow away material.
- A binary companion can accrete mass, if the separation is small enough.
- Some sort of dramatic stellar event - an eruption of some sort - can expel mass.
A normal coronal mass ejection may contain $sim10^-18M_odot$, which is also extremely low. Eta Carinae's Great Eruption averaged about $1M_odottext yr^-1$, but this is not an expected event in Sun-like stars. I don't think it's a good choice here, tempting though it may be.
The solar wind blows away mass at a rate of $sim10^-14M_odottext yr^-1$. Even the hottest O stars lose mass at $sim10^5-7M_odottext yr^-1$ at the most. When the Sun becomes an AGB star near the very end of its life, it may lose mass at a rate of $sim10^-4M_odottext yr^-1$, and so an extended AGB phase is a possibility, maybe involving a late thermal pulse leading back to the asymptotic giant branch. That said, Saturn's orbital speed (and orbit in general, including its eccentricity) would likely change slowly over time to stay bound to the Sun. 5,000 years is astronomically short, but not incredibly short.
A more realistic model
I'm imagining that in a dramatic but compressed AGB phase, the Sun's wind is isotropic, sending material streaming away from the star at $sim10^-4M_odottext yr^-1$. We can model the density of the wind by
$$rho_gas(r)=fracdotM4pi r^2v(r)$$
where $dotM$ is the mass loss rate and
$$v(r)=v_inftyleft(1-fracR_*rright)^beta$$
with $R_*$ being the radius of the star. For massive stars, we normally assume that $betaapprox1$. We can then find the gravitational potential by solving Poisson's equation:
$$nabla^2Phi_gas=4pi Grho_gas$$
From this, we can determine the escape velocity:
$$v_e(r)=sqrt2$$
where $Phi(r)=Phi_gas+Phi_odot$, and $Phi_odot$ changes in time as the Sun loses mass. You should be able to work backwards from here to determine the mass-loss rate and wind terminal velocity, given a desired escape velocity (Saturn's current orbital velocity, $9.6text km/s$).
Doing the math
Let's make some (justified) assumptions:
- At Saturn's orbit, $R_*/rll 1$, so we can use the binomial approximation to write
$$rho_gas(r)approxfracdotM4pi v_inftyleft(r^-2+fracR_*r^3right)$$ - The wind is isotropic, so
$$nabla^2Phi_gas=frac1r^2fracddrleft(r^2fracdPhi_gasdrright)=4pi Grho_gas(r)$$
This gives us a potential of the form
$$Phi_gas(r)=Phi_0-fracGdotMv_inftyleft(fracR_*r+fracR_*log (r/r_e)r-log(r/r_e)right)-fracDr$$
for some constants $Phi_0$, $r_e$, and $D$. Therefore,
$$v_e(r,t)=sqrt2left$$
at time $t$. Choosing the correct $dotM$, $v_odot$ and constants will get you the precise situation you want.
answered 6 hours ago
HDE 226868♦
61k12214393
add a comment |Â
up vote
5
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up vote
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A naive first calculation
The formulas for orbital velocity and escape velocity are
$$v_o=sqrtfracGMr,quad v_e=sqrtfrac2GMr$$
I get $v_o=9.6text km/s$ for Saturn. For this to equal $v_e$, the Sun's new mass would have to be $0.5M_odot$, if we neglect the mass of the ejected gas.
The event
There are a number of ways a star can lose mass:
- Strong stellar winds can blow away material.
- A binary companion can accrete mass, if the separation is small enough.
- Some sort of dramatic stellar event - an eruption of some sort - can expel mass.
A normal coronal mass ejection may contain $sim10^-18M_odot$, which is also extremely low. Eta Carinae's Great Eruption averaged about $1M_odottext yr^-1$, but this is not an expected event in Sun-like stars. I don't think it's a good choice here, tempting though it may be.
The solar wind blows away mass at a rate of $sim10^-14M_odottext yr^-1$. Even the hottest O stars lose mass at $sim10^5-7M_odottext yr^-1$ at the most. When the Sun becomes an AGB star near the very end of its life, it may lose mass at a rate of $sim10^-4M_odottext yr^-1$, and so an extended AGB phase is a possibility, maybe involving a late thermal pulse leading back to the asymptotic giant branch. That said, Saturn's orbital speed (and orbit in general, including its eccentricity) would likely change slowly over time to stay bound to the Sun. 5,000 years is astronomically short, but not incredibly short.
A more realistic model
I'm imagining that in a dramatic but compressed AGB phase, the Sun's wind is isotropic, sending material streaming away from the star at $sim10^-4M_odottext yr^-1$. We can model the density of the wind by
$$rho_gas(r)=fracdotM4pi r^2v(r)$$
where $dotM$ is the mass loss rate and
$$v(r)=v_inftyleft(1-fracR_*rright)^beta$$
with $R_*$ being the radius of the star. For massive stars, we normally assume that $betaapprox1$. We can then find the gravitational potential by solving Poisson's equation:
$$nabla^2Phi_gas=4pi Grho_gas$$
From this, we can determine the escape velocity:
$$v_e(r)=sqrt2$$
where $Phi(r)=Phi_gas+Phi_odot$, and $Phi_odot$ changes in time as the Sun loses mass. You should be able to work backwards from here to determine the mass-loss rate and wind terminal velocity, given a desired escape velocity (Saturn's current orbital velocity, $9.6text km/s$).
Doing the math
Let's make some (justified) assumptions:
- At Saturn's orbit, $R_*/rll 1$, so we can use the binomial approximation to write
$$rho_gas(r)approxfracdotM4pi v_inftyleft(r^-2+fracR_*r^3right)$$ - The wind is isotropic, so
$$nabla^2Phi_gas=frac1r^2fracddrleft(r^2fracdPhi_gasdrright)=4pi Grho_gas(r)$$
This gives us a potential of the form
$$Phi_gas(r)=Phi_0-fracGdotMv_inftyleft(fracR_*r+fracR_*log (r/r_e)r-log(r/r_e)right)-fracDr$$
for some constants $Phi_0$, $r_e$, and $D$. Therefore,
$$v_e(r,t)=sqrt2left$$
at time $t$. Choosing the correct $dotM$, $v_odot$ and constants will get you the precise situation you want.
answered 6 hours ago
HDE 226868♦
61k12214393
A naive first calculation
The formulas for orbital velocity and escape velocity are
$$v_o=sqrtfracGMr,quad v_e=sqrtfrac2GMr$$
I get $v_o=9.6text km/s$ for Saturn. For this to equal $v_e$, the Sun's new mass would have to be $0.5M_odot$, if we neglect the mass of the ejected gas.
The event
There are a number of ways a star can lose mass:
- Strong stellar winds can blow away material.
- A binary companion can accrete mass, if the separation is small enough.
- Some sort of dramatic stellar event - an eruption of some sort - can expel mass.
A normal coronal mass ejection may contain $sim10^-18M_odot$, which is also extremely low. Eta Carinae's Great Eruption averaged about $1M_odottext yr^-1$, but this is not an expected event in Sun-like stars. I don't think it's a good choice here, tempting though it may be.
The solar wind blows away mass at a rate of $sim10^-14M_odottext yr^-1$. Even the hottest O stars lose mass at $sim10^5-7M_odottext yr^-1$ at the most. When the Sun becomes an AGB star near the very end of its life, it may lose mass at a rate of $sim10^-4M_odottext yr^-1$, and so an extended AGB phase is a possibility, maybe involving a late thermal pulse leading back to the asymptotic giant branch. That said, Saturn's orbital speed (and orbit in general, including its eccentricity) would likely change slowly over time to stay bound to the Sun. 5,000 years is astronomically short, but not incredibly short.
A more realistic model
I'm imagining that in a dramatic but compressed AGB phase, the Sun's wind is isotropic, sending material streaming away from the star at $sim10^-4M_odottext yr^-1$. We can model the density of the wind by
$$rho_gas(r)=fracdotM4pi r^2v(r)$$
where $dotM$ is the mass loss rate and
$$v(r)=v_inftyleft(1-fracR_*rright)^beta$$
with $R_*$ being the radius of the star. For massive stars, we normally assume that $betaapprox1$. We can then find the gravitational potential by solving Poisson's equation:
$$nabla^2Phi_gas=4pi Grho_gas$$
From this, we can determine the escape velocity:
$$v_e(r)=sqrt2$$
where $Phi(r)=Phi_gas+Phi_odot$, and $Phi_odot$ changes in time as the Sun loses mass. You should be able to work backwards from here to determine the mass-loss rate and wind terminal velocity, given a desired escape velocity (Saturn's current orbital velocity, $9.6text km/s$).
Doing the math
Let's make some (justified) assumptions:
- At Saturn's orbit, $R_*/rll 1$, so we can use the binomial approximation to write
$$rho_gas(r)approxfracdotM4pi v_inftyleft(r^-2+fracR_*r^3right)$$ - The wind is isotropic, so
$$nabla^2Phi_gas=frac1r^2fracddrleft(r^2fracdPhi_gasdrright)=4pi Grho_gas(r)$$
This gives us a potential of the form
$$Phi_gas(r)=Phi_0-fracGdotMv_inftyleft(fracR_*r+fracR_*log (r/r_e)r-log(r/r_e)right)-fracDr$$
for some constants $Phi_0$, $r_e$, and $D$. Therefore,
$$v_e(r,t)=sqrt2left$$
at time $t$. Choosing the correct $dotM$, $v_odot$ and constants will get you the precise situation you want.
answered 6 hours ago
HDE 226868♦
61k12214393
edited 5 hours ago
answered 6 hours ago
HDE 226868♦
61k12214393
answered 6 hours ago
HDE 226868♦
61k12214393
answered 6 hours ago
HDE 226868♦
61k12214393
61k12214393
add a comment |Â
add a comment |Â
up vote
2
down vote
What will happen
First, the sun will split into two parts, racing away from each other at a relative velocity large enough for them to escape the other's gravitational pull. Newton's third law implies that they both race away from each other, meaning that they are both racing away from Saturn (and the other planets). But lets ignore that in favor of magic. The remnant stays in place relative to Saturn, while the ejected part moves away at high speed.
Initially, the center of gravity of the remnant-ejected system starts moving away from the sun. Saturn can be considered to be orbiting this remnant-ejected system. Assuming the remnant is moving away from Saturn, then the force of its gravity on Saturn will quickly be reduced.
In this case, the Saturn will soon be orbiting just the remnant, which will reform itself as a spherical star-like object. Now we can apply some orbital mechanics equations to see how big the remnant should be.
Escape velocity
Escape velocity is
$$v_e = sqrtfrac2GMr.$$ $G = 6.67times10^-11 text m^3text kg ^-1text s^-2$, $M$ is the mass of the sun, $r = 1.43times10^12text m$.
Saturn's orbital speed varies since its orbit is elliptical, so lets assume its mean orbital velcoity of $9680 text m s^-1$. We set $v_e$ equal to this and solve for the desired mass of the sun:
$$M = fracr v_e^22G = frac1.43times10^12text mcdot 9680^2text m^2text s^-22 cdot 6.67times10^-11text m^3text kg ^-1text s^-2 = 1.00times10^30 text kg$$.
The true mass of the sun is $1.99times10^30text kg$, so if the sun split in half, Saturn would be on the very edge of being attached to each half.
So in that sense, Saturn was the perfect planet to pick. If Saturn was near its perigee when the sun split in half, Saturn would remain gravitationally bound to one or the other fragment. If Saturn was near its apogee, it would be off into interstellar space.
Of course, that assumes the the fragment of the sun went away from saturn. The fragment is obviously moving at or above escape velocity also, so it could potentially get closer to Saturn then recapture it.
answered 6 hours ago
kingledion
66.8k22221381
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
 |Â
show 5 more comments
up vote
2
down vote
What will happen
First, the sun will split into two parts, racing away from each other at a relative velocity large enough for them to escape the other's gravitational pull. Newton's third law implies that they both race away from each other, meaning that they are both racing away from Saturn (and the other planets). But lets ignore that in favor of magic. The remnant stays in place relative to Saturn, while the ejected part moves away at high speed.
Initially, the center of gravity of the remnant-ejected system starts moving away from the sun. Saturn can be considered to be orbiting this remnant-ejected system. Assuming the remnant is moving away from Saturn, then the force of its gravity on Saturn will quickly be reduced.
In this case, the Saturn will soon be orbiting just the remnant, which will reform itself as a spherical star-like object. Now we can apply some orbital mechanics equations to see how big the remnant should be.
Escape velocity
Escape velocity is
$$v_e = sqrtfrac2GMr.$$ $G = 6.67times10^-11 text m^3text kg ^-1text s^-2$, $M$ is the mass of the sun, $r = 1.43times10^12text m$.
Saturn's orbital speed varies since its orbit is elliptical, so lets assume its mean orbital velcoity of $9680 text m s^-1$. We set $v_e$ equal to this and solve for the desired mass of the sun:
$$M = fracr v_e^22G = frac1.43times10^12text mcdot 9680^2text m^2text s^-22 cdot 6.67times10^-11text m^3text kg ^-1text s^-2 = 1.00times10^30 text kg$$.
The true mass of the sun is $1.99times10^30text kg$, so if the sun split in half, Saturn would be on the very edge of being attached to each half.
So in that sense, Saturn was the perfect planet to pick. If Saturn was near its perigee when the sun split in half, Saturn would remain gravitationally bound to one or the other fragment. If Saturn was near its apogee, it would be off into interstellar space.
Of course, that assumes the the fragment of the sun went away from saturn. The fragment is obviously moving at or above escape velocity also, so it could potentially get closer to Saturn then recapture it.
answered 6 hours ago
kingledion
66.8k22221381
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
 |Â
show 5 more comments
up vote
2
down vote
up vote
2
down vote
What will happen
First, the sun will split into two parts, racing away from each other at a relative velocity large enough for them to escape the other's gravitational pull. Newton's third law implies that they both race away from each other, meaning that they are both racing away from Saturn (and the other planets). But lets ignore that in favor of magic. The remnant stays in place relative to Saturn, while the ejected part moves away at high speed.
Initially, the center of gravity of the remnant-ejected system starts moving away from the sun. Saturn can be considered to be orbiting this remnant-ejected system. Assuming the remnant is moving away from Saturn, then the force of its gravity on Saturn will quickly be reduced.
In this case, the Saturn will soon be orbiting just the remnant, which will reform itself as a spherical star-like object. Now we can apply some orbital mechanics equations to see how big the remnant should be.
Escape velocity
Escape velocity is
$$v_e = sqrtfrac2GMr.$$ $G = 6.67times10^-11 text m^3text kg ^-1text s^-2$, $M$ is the mass of the sun, $r = 1.43times10^12text m$.
Saturn's orbital speed varies since its orbit is elliptical, so lets assume its mean orbital velcoity of $9680 text m s^-1$. We set $v_e$ equal to this and solve for the desired mass of the sun:
$$M = fracr v_e^22G = frac1.43times10^12text mcdot 9680^2text m^2text s^-22 cdot 6.67times10^-11text m^3text kg ^-1text s^-2 = 1.00times10^30 text kg$$.
The true mass of the sun is $1.99times10^30text kg$, so if the sun split in half, Saturn would be on the very edge of being attached to each half.
So in that sense, Saturn was the perfect planet to pick. If Saturn was near its perigee when the sun split in half, Saturn would remain gravitationally bound to one or the other fragment. If Saturn was near its apogee, it would be off into interstellar space.
Of course, that assumes the the fragment of the sun went away from saturn. The fragment is obviously moving at or above escape velocity also, so it could potentially get closer to Saturn then recapture it.
answered 6 hours ago
kingledion
66.8k22221381
What will happen
First, the sun will split into two parts, racing away from each other at a relative velocity large enough for them to escape the other's gravitational pull. Newton's third law implies that they both race away from each other, meaning that they are both racing away from Saturn (and the other planets). But lets ignore that in favor of magic. The remnant stays in place relative to Saturn, while the ejected part moves away at high speed.
Initially, the center of gravity of the remnant-ejected system starts moving away from the sun. Saturn can be considered to be orbiting this remnant-ejected system. Assuming the remnant is moving away from Saturn, then the force of its gravity on Saturn will quickly be reduced.
In this case, the Saturn will soon be orbiting just the remnant, which will reform itself as a spherical star-like object. Now we can apply some orbital mechanics equations to see how big the remnant should be.
Escape velocity
Escape velocity is
$$v_e = sqrtfrac2GMr.$$ $G = 6.67times10^-11 text m^3text kg ^-1text s^-2$, $M$ is the mass of the sun, $r = 1.43times10^12text m$.
Saturn's orbital speed varies since its orbit is elliptical, so lets assume its mean orbital velcoity of $9680 text m s^-1$. We set $v_e$ equal to this and solve for the desired mass of the sun:
$$M = fracr v_e^22G = frac1.43times10^12text mcdot 9680^2text m^2text s^-22 cdot 6.67times10^-11text m^3text kg ^-1text s^-2 = 1.00times10^30 text kg$$.
The true mass of the sun is $1.99times10^30text kg$, so if the sun split in half, Saturn would be on the very edge of being attached to each half.
So in that sense, Saturn was the perfect planet to pick. If Saturn was near its perigee when the sun split in half, Saturn would remain gravitationally bound to one or the other fragment. If Saturn was near its apogee, it would be off into interstellar space.
Of course, that assumes the the fragment of the sun went away from saturn. The fragment is obviously moving at or above escape velocity also, so it could potentially get closer to Saturn then recapture it.
answered 6 hours ago
kingledion
66.8k22221381
edited 2 hours ago
answered 6 hours ago
kingledion
66.8k22221381
answered 6 hours ago
kingledion
66.8k22221381
answered 6 hours ago
kingledion
66.8k22221381
66.8k22221381
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
 |Â
show 5 more comments
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
The wikipedia page on escape velocity states that the formula you used is valid for a spherically symmetric, massive body. I am not sure a burping Sun would qualify for this.
– L.Dutch♦
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
Does this still apply if the mass ejection occurs on the planetary axis, such that neither of the two parts changes anything about the center of the planetary rotation?
– Justin Thyme
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
@JustinThyme No; I'm working on a more complex gravitational potential field equation based on ejection, so as to out-math HDE
– kingledion
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
Second, the question does not assume the ejected mass reaches escape velocity, never to return back to the sun, but only that it escapes the sun long enough to change the gravitational pull of the sun itself.
– Justin Thyme
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
@JustinThyme Oh, well that second idea will almost definitely not work, given the mass change requirement of the sun.
– kingledion
6 hours ago
 |Â
show 5 more comments
up vote
1
down vote
The math already presented by HDE 226868 and kingledion is bang on so I won't repeat it, but I feel they have neglected one possibility. The mass of a star can theoretically be reduced artificially through the process of star lifting so it may be possible for an arbitrarily advanced civilisation to pull enough material out of the sun, and displace it from the solar system, that Saturn would exceed escape velocity.
answered 6 hours ago
Ash
21.5k256131
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
add a comment |Â
up vote
1
down vote
The math already presented by HDE 226868 and kingledion is bang on so I won't repeat it, but I feel they have neglected one possibility. The mass of a star can theoretically be reduced artificially through the process of star lifting so it may be possible for an arbitrarily advanced civilisation to pull enough material out of the sun, and displace it from the solar system, that Saturn would exceed escape velocity.
answered 6 hours ago
Ash
21.5k256131
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
add a comment |Â
up vote
1
down vote
up vote
1
down vote
The math already presented by HDE 226868 and kingledion is bang on so I won't repeat it, but I feel they have neglected one possibility. The mass of a star can theoretically be reduced artificially through the process of star lifting so it may be possible for an arbitrarily advanced civilisation to pull enough material out of the sun, and displace it from the solar system, that Saturn would exceed escape velocity.
answered 6 hours ago
Ash
21.5k256131
The math already presented by HDE 226868 and kingledion is bang on so I won't repeat it, but I feel they have neglected one possibility. The mass of a star can theoretically be reduced artificially through the process of star lifting so it may be possible for an arbitrarily advanced civilisation to pull enough material out of the sun, and displace it from the solar system, that Saturn would exceed escape velocity.
answered 6 hours ago
Ash
21.5k256131
answered 6 hours ago
Ash
21.5k256131
answered 6 hours ago
Ash
21.5k256131
answered 6 hours ago
Ash
21.5k256131
21.5k256131
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
add a comment |Â
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
Interesting. perhaps quantum mechanics, and the indeterminacy principle. The mass is here, then it is over there, but is never in the middle. Again, HOW it happens is beyond the scope of the question.
– Justin Thyme
6 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
@JustinThyme Only kind of, the question asks if there are factors that make the situation impossible, one of the biggest barriers is actually moving enough mass far enough to make it happen. Any known natural mass removal process would be extremely violent, too violent to leave the rest of the solar system, or even possibly Saturn itself in one piece.
– Ash
3 hours ago
add a comment |Â
up vote
0
down vote
Even though @AlexP is right about the mass still existing, it's believable enough that -- unless you're writing Hard SF -- you can just assert that the Sun -- for example -- burped out 20% of it's mass and off zoomed Saturn.
For more realism, have the mass get burped in the opposite direction of where Saturn is. Saturn (and all the other planets...) gets pulled towards the new epicenter and then flies out into interstellar space.
answered 6 hours ago
RonJohn
12.5k12661
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
add a comment |Â
up vote
0
down vote
Even though @AlexP is right about the mass still existing, it's believable enough that -- unless you're writing Hard SF -- you can just assert that the Sun -- for example -- burped out 20% of it's mass and off zoomed Saturn.
For more realism, have the mass get burped in the opposite direction of where Saturn is. Saturn (and all the other planets...) gets pulled towards the new epicenter and then flies out into interstellar space.
answered 6 hours ago
RonJohn
12.5k12661
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
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Even though @AlexP is right about the mass still existing, it's believable enough that -- unless you're writing Hard SF -- you can just assert that the Sun -- for example -- burped out 20% of it's mass and off zoomed Saturn.
For more realism, have the mass get burped in the opposite direction of where Saturn is. Saturn (and all the other planets...) gets pulled towards the new epicenter and then flies out into interstellar space.
answered 6 hours ago
RonJohn
12.5k12661
Even though @AlexP is right about the mass still existing, it's believable enough that -- unless you're writing Hard SF -- you can just assert that the Sun -- for example -- burped out 20% of it's mass and off zoomed Saturn.
For more realism, have the mass get burped in the opposite direction of where Saturn is. Saturn (and all the other planets...) gets pulled towards the new epicenter and then flies out into interstellar space.
answered 6 hours ago
RonJohn
12.5k12661
answered 6 hours ago
RonJohn
12.5k12661
answered 6 hours ago
RonJohn
12.5k12661
answered 6 hours ago
RonJohn
12.5k12661
12.5k12661
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
add a comment |Â
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
I am thinking that I will probably have to do some hand waving. If it takes half the mass to be removed, I have to contend with Newton's Law. The Sun would accelerate away from its position at exactly the same rate the other half would be 'ejected'. There would be two equal Suns moving in opposite directions. I did not expect the required mass to be quite so high.
– Justin Thyme
2 hours ago
add a comment |Â
up vote
0
down vote
Interesting. Not that I want to answer my own question, but I would like to sum up the math from both HDE 226868 and kingledion (to whom I acknowledge and thank very much for their input).
As a general rule of thumb, it looks like the mass of an orbited body has to be reduced by about 50%, or half, in order for an existing orbital velocity of a satellite to become the escape velocity of the satellite to the reduced orbited mass.
This could be a useful rule of thumb in so many different situations.
How it gets reduced by 50%, of course, is another question.
answered 2 mins ago
Justin Thyme
6,6561734
add a comment |Â
up vote
0
down vote
Interesting. Not that I want to answer my own question, but I would like to sum up the math from both HDE 226868 and kingledion (to whom I acknowledge and thank very much for their input).
As a general rule of thumb, it looks like the mass of an orbited body has to be reduced by about 50%, or half, in order for an existing orbital velocity of a satellite to become the escape velocity of the satellite to the reduced orbited mass.
This could be a useful rule of thumb in so many different situations.
How it gets reduced by 50%, of course, is another question.
answered 2 mins ago
Justin Thyme
6,6561734
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Interesting. Not that I want to answer my own question, but I would like to sum up the math from both HDE 226868 and kingledion (to whom I acknowledge and thank very much for their input).
As a general rule of thumb, it looks like the mass of an orbited body has to be reduced by about 50%, or half, in order for an existing orbital velocity of a satellite to become the escape velocity of the satellite to the reduced orbited mass.
This could be a useful rule of thumb in so many different situations.
How it gets reduced by 50%, of course, is another question.
answered 2 mins ago
Justin Thyme
6,6561734
Interesting. Not that I want to answer my own question, but I would like to sum up the math from both HDE 226868 and kingledion (to whom I acknowledge and thank very much for their input).
As a general rule of thumb, it looks like the mass of an orbited body has to be reduced by about 50%, or half, in order for an existing orbital velocity of a satellite to become the escape velocity of the satellite to the reduced orbited mass.
This could be a useful rule of thumb in so many different situations.
How it gets reduced by 50%, of course, is another question.
answered 2 mins ago
Justin Thyme
6,6561734
answered 2 mins ago
Justin Thyme
6,6561734
answered 2 mins ago
Justin Thyme
6,6561734
answered 2 mins ago
Justin Thyme
6,6561734
6,6561734
add a comment |Â
add a comment |Â
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4
Are you sure you don't want to split this into more questions? It tickles my too broad sense...
– L.Dutch♦
6 hours ago
@L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO
– kingledion
6 hours ago
1
Wouldn't the ejected mass have it's own gravitational effects, changing the orbits of the planets as it moves out of the system? 'Current velocity' wouldn't be maintainable then I think.
– Douwe
6 hours ago
@kingledion I agree that question B is somewhat a separate question, but I suspect many answers might bring it up, and so I thought I might make these answers relevant to the question. That is, I can see many posters saying 'It is impossible, period'. But I am willing to edit it out, What say you?
– Justin Thyme
6 hours ago
@JustinThyme The problem is that this is impossible, basically. The energy required to give half a sun escape velocity is so high, that thermodynamic heat dissipation would blow both pieces into cosmic dust. Better just to say, "this happened due to magic, deal with it"
– kingledion
6 hours ago