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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.

Justin Thyme
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    Are you sure you don't want to split this into more questions? It tickles my too broad sense... – L.Dutch Sep 25 '18 at 15:36
  • @L.Dutch Part B is the killer; A, C, and D are all pretty intertwined, IMO – kingledion Sep 25 '18 at 15:37
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    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 Sep 25 '18 at 15:48
  • @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 Sep 25 '18 at 16:05
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    @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 Sep 25 '18 at 16:08
  • @Douwe That possibility is within the scope of question B, Would the change in gravity only occur when the ejected mass gets far enough away as to not be a factor? If this mass ejection occurred over time, instead of in one lump, would that influence the calculations? If the mass were ejected on the axis of the planetary plane, would it not result in Saturn being pulled out of the planetary plane? – Justin Thyme Sep 25 '18 at 16:10
  • @kingledion I agree with the effects of the energy requirements, but you assume half of the Sun's mass would have to be ejected. If only 10% were sufficient, then would question B be cleared? – Justin Thyme Sep 25 '18 at 16:14
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    @Douwe If the mass is ejected in two equal jets moving in opposite directions perpendicular to the ecliptic (planetary plane), then it should have negligible net effect on anything close to the ecliptic, right? – LarsH Sep 26 '18 at 00:00
  • I wondered briefly if the sun could lose enough mass through fusion. The answer to that is no, not by a long shot. – craq Sep 26 '18 at 01:07
  • I agree with @kingledion that part B is a problem. Best delete it. Assume the mass loss happens painlessly, without damaging anything else in the solar system, so Saturn's orbital velocity is now escape velocity. Alien super-beings could mine the Sun with teleportation (for example). No-one needs know that, just that's a mass loss to the Sun. The orbits of the other planets will change too. But I'm sure you know that already. – a4android Sep 26 '18 at 01:56
  • I clarified the question to make B, C, and D ancillary to the main question A. Since some answers address question B (including kingledion) as an ancillary thread, I am afraid that editing it out would make them 'orphan answers'. Since the mass loss has been proven to be 50% of the existing mass, the B thread is very relevant. – Justin Thyme Sep 26 '18 at 02:05
  • @a4android Actually, the theory and calculations supplied in the answers indicate that, when the Sun's mass is reduced to such an extent that Saturn's current velocity becomes escape velocity, then EVERY planet's orbital velocity will become escape velocity. All of the planets will become wanderers at roughly the same time. I did not expect that.. – Justin Thyme Sep 26 '18 at 02:40
  • I didn't expect all the planets to achieve escape velocity either. Rather delightful! At 9.6 km/s it's going to take an extremely long to get anywhere. That's less than one-thirty-thousandth of lightspeed, or one light year per thirty thousand years travel time. Congratulations! Your question inspired some fascinating answers.. – a4android Sep 26 '18 at 12:47
  • @craq I did do the calculations once. The mass-loss rate from nuclear fusion is approximately the mass-loss rate from the stellar wind - in other words, not a lot! – HDE 226868 Sep 26 '18 at 14:11
  • I can't do any of the math, but when you say the Sun loses some of its mass, I'm reminded of space scenes in sci-fi films in which the astronaut propels themselves in a direction by ejecting gas. So the Sun would probably get propelled away from the place of the ejection, and if Saturn is currently moving in the opposite direction, that might contribute. (Hopefully, Earth is moving in just the right direction along its orbit when this happens that its orbit is neither significantly increased nor decreased to cause it to fall into the Sun.) – Real Subtle Sep 26 '18 at 14:11
  • @JustinThyme Assuming the ejected mass is spherical it ceases to be a factor as soon as the ejected shell passes the planet. – Loren Pechtel Jun 06 '20 at 05:44
  • @Loren Pechtel Something I just can not grok about the Shell Theorem. It assumes that the object inside the hollow sphere is non-moving. If the object were moving at orbital speed, when the shell expanded, wouldn't the object continuously move beyond the expanding shell, since gravity would no longer pull it back, causing it to orbit, until it was outside of the sphere? – Justin Thyme the Second Jun 24 '20 at 18:31
  • @JustinThymetheSecond The orbiting object is unaffected until the shell passes and at that point the shell is heading out faster than the object. What happens at that point comes down to how fast the shell is moving, if it's slow enough the planet can overtake. – Loren Pechtel Jun 24 '20 at 21:34

4 Answers4

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A naive first calculation

The formulas for orbital velocity and escape velocity are $$v_o=\sqrt{\frac{GM}{r}},\quad v_e=\sqrt{\frac{2GM}{r}}$$ I get $v_o=9.6\text{ km/s}$ 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. By doing the algebra, you can see that this number is the same for any mass and any orbital radius. In short, if Saturn achieves escape velocity because of solar mass loss, so should the other planets (assuming circular orbits).

A more realistic model

Here's why it's actually important that we establish how the Sun loses mass. As others have said, the ejected matter will then influence the gravitational potential, and by extension the escape velocity at Saturn's orbit.

To start, we need to model the solar mass loss. I'm imagining that in a dramatic but compressed asymptotic giant branch phase, the Sun is losing mass at a rate of $\sim10^{-4}M_{\odot}\text{ yr}^{-1}$; its wind is isotropic, sending material streaming away from the star in all directions. I'll ignore the fact that strong winds from evolved Sun-like stars can ablate planets. We can model the density of the wind by $$\rho(r)=\frac{\dot{M}}{4\pi r^2v(r)}$$ where $\dot{M}$ is the mass loss rate and $$v(r)=v_{\infty}\left(1-\frac{R_*}{r}\right)^\beta$$ with $R_*$ being the radius of the star. For massive stars, we normally assume that $\beta\approx1$. We can then find the gravitational potential by solving Poisson's equation. From this, we can determine the escape velocity: $$v_e(r)=\sqrt{2|\Phi(r)|}$$ where $\Phi(r)$ is the gravitational potential of both the Sun and the gas. 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, $9.6\text{ km/s}$).

Calculating the potential for other mass-loss scenarios is beyond me, because I don't know the proper density distribution; I can only talk about modeling stellar winds. I suspect that bipolar jets would contribute very little, as they are away from the orbital plane and would presumably be moving very quickly (even compared to $v_{\infty}$, which can be $\sim2000\text{ km/s}$ for massive stars, though perhaps a mere $\sim300\text{ km/s}$ for a Sun-like star). Similarly, a massive coronal mass ejection or super-super-superflare wold be hard to model.

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HDE 226868
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    This sounds utterly crazy but I have to agree--orbital energy is half of escape energy, thus half the central mass and everything flies off. – Loren Pechtel Jun 06 '20 at 05:42
  • I was wondering about the sun's red giant phase--nope, it's only going to lose about 1/3 of it's mass, the planets stay attached. Can any star lose half it's mass in it's red giant phase? – Loren Pechtel Jun 06 '20 at 05:45
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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.

EDIT

That is, when the Sun's mass decreases by 50%, EVERY planet's orbital velocity will become its escape velocity, at pretty much the same time. Strange, but apparently true.

End Edit

This could be a useful rule of thumb in so many different situations.

How it gets reduced by 50%, of course, is another question.

Justin Thyme
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  • Just as a note on proving that relation: You can show, from Kepler's third law, that a planet's orbital speed is $v_{\text{orb}}=\sqrt{\frac{GM_{\odot}}{a}}$, with $a$ the semi-major axis. That's equal to the escape velocity from that point when we reduce the Sun's mass by a factor of 2 (just take the formula for escape velocity and set $M=M_{\odot}/2$). – HDE 226868 Jun 05 '20 at 15:35
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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.

RonJohn
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    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 Sep 25 '18 at 20:06
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    The sun doesn't have to split into two parts, why not three: Two quarters, each of which fly off in opposite directions (say, poleward), and the third part, the remaining half, can remain right where the sun always was, since the equal-and-opposite reactions from the two ejected parts cancel each other out? – Beanluc Sep 26 '18 at 00:48
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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.

Ash
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  • 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 Sep 25 '18 at 16:21
  • @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 Sep 25 '18 at 18:25