[thedoc (OP)]

Munyaradzi Tobaiwa‎  asked the Naked Scientists:
   If the sun disappeared, what would happen to the planets?
What do you think?

[alancalverd]

They would fly away at a tangent to their orbits.

[JoeBrown]

Until they encountered a deeper well of gravity, then they would either orbit or collide or perhaps both.

Would the Earth and the Moon remain paired up???  It would make a bit of difference where the moon was in orbital relation to the Earth when the gravity wave passes.

[jeffreyH]

To expand on Alan's point, it would depend upon where the planets were in their orbits in relation to one another. There could be cases in which two tangents intercept in which case the planets would collide. In other cases two or more planets may end up moving away in unison having entered into a system of complex orbits.

[jeffreyH]

Something occurred to me after posting the above. If we have a function c(x) that describes a circular orbit and a function p(x) that describes the orbital path around a galaxy the function p(c(x)) will describe increasing orbital speed with increasing distance from the galactic centre. Therefore time dilation will increase with radial distance. I haven't considered the implications yet.

[evan_au]

Until they encountered a deeper well of gravity, then they would either orbit or collide or perhaps both.

A planet approaching another star from interstellar space will be traveling with greater velocity than the escape velocity of that star.

So if there are no other planets around the other star, it will follow a hyperbolic or parabolic orbit, and just pass once; you wouldn't call this an orbit.

However, if the other star has planets, it could:

• Collide, as you say: This is unlikely in a single pass
  
• Interact gravitationally: Transferring some of its momentum to another planet could slow down the newcomer enough to enter orbit around the star. After which it it will continue to disturb the orbits of the existing planets, possibly triggering the planetary orbits to become chaotic. It could well collide itself, or cause other planets to collide.

the function p(c(x)) will describe increasing orbital speed with increasing distance from the galactic centre. Therefore time dilation will increase with radial distance.

The way astronomers applied Kepler, Newton and Einstein, the orbital speed should decrease the farther you are from the center of a galaxy.

This means that velocity-related time dilation should be lower for stars farther from the galactic center; it also means that time dilation related to gravitational wells should be lower for these more distant stars.

However, studying the red-shift profiles of galaxies shows that in fact the rotational velocity is fairly constant (and perhaps increasing slightly) with distance from the galactic center. This was one basis for the Dark Matter hypothesis.
https://en.wikipedia.org/wiki/Galaxy_rotation_curve

Taking into account the observed galaxy rotation curve, time dilation related to gravitational wells should be lower for these more distant stars, which is counteracted by velocity-related time dilation which should be roughly constant (or increasing slightly) for stars farther from the galactic center. The overall effect on time dilation would need to be worked out on a case-by-case basis.

[jeffreyH]

Interestingly, the central stars of planetary systems should also experience lower time dilation than the orbiting planets.

[evan_au]

the central stars of planetary systems should also experience lower time dilation than the orbiting planets.

This is the opposite of the way I understood it?

My understanding was that the location closest to the bottom of the gravitational well (like the Sun's surface or Mercury) would experience the most gravitational time dilation, while locations farthest from the gravitational well (Pluto, the edge of our galaxy, or the Small Magellenic Cloud) would experience the least time dilation. Earth is somewhere in the middle of this range.

This is confirmed by the fact that the gravitational time dilation is measurable in the precession of the perihelion of Mercury's orbit, but is negligible in the orbits of more distant planets.

Or by "lower time dilation", do you mean "time moves more slowly" (as seen by a distant observer)?

[jeffreyH]

the central stars of planetary systems should also experience lower time dilation than the orbiting planets.

This is the opposite of the way I understood it?

My understanding was that the location closest to the bottom of the gravitational well (like the Sun's surface or Mercury) would experience the most gravitational time dilation, while locations farthest from the gravitational well (Pluto, the edge of our galaxy, or the Small Magellenic Cloud) would experience the least time dilation. Earth is somewhere in the middle of this range.

This is confirmed by the fact that the gravitational time dilation is measurable in the precession of the perihelion of Mercury's orbit, but is negligible in the orbits of more distant planets.

Or by "lower time dilation", do you mean "time moves more slowly" (as seen by a distant observer)?

No I stated a thought process badly. I did not engage brain before typing. I was comparing the path length of a star around the galaxy with those of orbiting planets. If the star described a hypothetical perfectly circular galactic orbit then the path lengths of the planets would be stretched and meandering in comparison.