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If it were possible to launch a projectile at the speed of light from a body with the mass equal to that of our sun but a density such that its escape velocity was the speed of light how far would it go into empty space before its velocity dropped to one metre per second and how long would it take?

The question was only partly related to light escaping from dense bodies but before seeking the answer to light i will re-frame the question as follows;

If a projectile were launched from a body with the mass equal to that of our sun but a density such that its escape velocity was only 1/100th of the speed of light how far would it go into empty space before its velocity dropped to one metre per second and how long would it take? This move the question away from relativity issues. I think the distance is actually 2*G*M but how long does it take?

Alan Smith
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  • The question I've suggested as a link discusses this, and for a more mathematical treatment you might want to look at Why is a black hole black?. The object you describe wouldn't move outwards at all. Even light itself can't move outwards at or inside the event horizon. – John Rennie Jun 03 '14 at 07:24
  • @JohnRennie : he does say that whatever object he is thinking of has escape velocity equal to the speed of light and not more than that, certainly light would escape such a body! It is rather interesting to think what would happen afterwards. – – Rijul Gupta Jun 03 '14 at 07:55
  • @rijulgupta: The point at which the Newtonian escape velocity equals the speed of light is the event horizon. – John Rennie Jun 03 '14 at 08:00
  • @JohnRennie: But we are not shooting anything from behind the event horizon now, atleast does not look like that from the question. Just as if "from" the event horizon. Like when we talk of escape velocity from earth, we do not talk from inside the earth, just from the surface of it. – Rijul Gupta Jun 03 '14 at 08:03
  • @rijulgupta: the two links I suggested both explain that there is no escape from the event horizon. You don't need to be behind the event horizon to be trapped. At the event horizon you're also trapped. – John Rennie Jun 03 '14 at 08:04

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