The Moon reportedly doesn't "need" the Earth to revolve around the Sun. If the Earth wasn't there, the Moon would continue its current path from a heliocentric reference frame around the Sun. My question is whether that would happen to some of the moons of Jupiter and Saturn too. If Jupiter or Saturn weren't there, would Ganymede or Titan continue to freely revolve around the Sun, or what would happen to their orbits?

Thank you.

  • $\begingroup$ The escape velocity of the Sun at the distance of Earth's orbit is 42.1 kilometers per second. Earth's average orbital velocity is 29.78 kilometers per second. Thus an object at Earth's orbit would need to gain about 12.32 kilometers per second to escape from the Sun. The Moon's orbital velocity around the Earth is 1.022 kilometers per second. Thus it could not escape from the Sun if the Earth disappeared. And that description of why the Moon could not escape from the Sun if the Earth disappeared is far more correct than your version, which mentions mostly irrelevant details. $\endgroup$ – M. A. Golding May 17 '20 at 19:15
  • $\begingroup$ I don't have a "version". I stated the fact that the Moon would continue its current path even if the Earth disappeared suddenly. I'm talking about its current orbit rather than whether it would escape the Sun's gravity or not or fall into the Sun. And your answer is a comment rather than an answer to my question, it doesn't deal with the Galilean moons and Titan. $\endgroup$ – The Architect May 18 '20 at 4:50
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    $\begingroup$ BTW, you may have received downvotes because we don't normally permit questions about hypothetical scenarios that break the laws of physics. If you throw the rulebook out the window, how do you judge the correctness of an answer? $\endgroup$ – PM 2Ring May 18 '20 at 5:39
  • $\begingroup$ However, I think your question is ok because it's attempting to understand Newtonian gravity, and making a planet magically disappear doesn't interfere with the orbit calculations. OTOH, in general relativity you can't do the mathematics if mass-energy can pop in or out of existence, or get teleported around (although I suppose you can invoke a traversable wormhole to do that sort of thing). $\endgroup$ – PM 2Ring May 18 '20 at 5:39
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    $\begingroup$ Universe Sandbox is a great piece of software for trying out hypotheticals like this. I suggest you check it out. $\endgroup$ – Jim421616 May 21 '20 at 6:20

They might escape from the solar system, if the angles are right. If not, they'll probably wind up in elliptical orbits around the Sun. We'll use a simplifying assumption that the orbits are circular to make the calculations easier; All objects mentioned have orbital eccentricity of less than 0.05.

The mean orbital velocity of Jupiter is 13.1 km/s, which makes Solar escape velocity at Jupiter's mean distance from the sun 18.5 km/s, a difference of 5.4 km/s.

The mean orbital velocities of the Galilean Moons of Jupiter are:

  • Io: 17.3 km/s
  • Europa: 14.3 km/s
  • Ganymede: 10.9km/s
  • Callisto: 8.2 km/s.

Which means, if the geometry is right, with the direction of travel of the moon in the same direction of the direction of travel of Jupiter at the time of the disappearance, the resulting vectors could add up to any of the Galilean moons exceeding solar escape velocity if Jupiter suddenly vanishes, and exiting the solar system.

Doing some trigonometry to find the limiting angle:

  • Io: Reaches Solar escape velocity if the moon was traveling within 106° of Jupiter's direction.
  • Europa: Escapes if traveling within 95°
  • Ganymede: Escapes if direction within 79°
  • Callisto: Escapes if direction within 62°

There's also a tiny, tiny chance of Europa or Io being in the right positions and having the right direction to hit the Sun if their directions at the time of disappearance were exactly right, but the chance of that is extremely unlikely.

For comparison, Saturn has a mean velocity of 9.5 km/s, (Solar Escape Velocity at that distance is about 13.4 km/s) and Titan has a mean velocity relative to Saturn of about 5.5 km/s.

Titan could escape under the right conditions (Within 56° of Saturn's direction of travel), but doesn't have enough Saturn-relative velocity to have a chance of crashing into the Sun without help.

  • $\begingroup$ So the moons' orbital velocities need to be added to the velocity of the planet? $\endgroup$ – The Architect May 17 '20 at 14:51
  • $\begingroup$ Basically, that's the limiting case. If the you can't exceed escape velocity by adding the velocity of the planet to the velocity of the moon, then the moon cannot reach solar escape without assistance. I can do a bit of trigonometry to work out the limiting angles. $\endgroup$ – notovny May 17 '20 at 14:53
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    $\begingroup$ @The Architect The moon's orbital velocities are added to the velocity of the planet if whey happen to be travelling in exactly the same direction as the planet, or subtracted if they happen to be travelling in exactly the opposite direction to the planet. And in the vast majority of cases the directions of the moons will be intermediate and less than their full orbital velocity will be added or subtracted to that of Jupiter. $\endgroup$ – M. A. Golding May 17 '20 at 19:08

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