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First of all let me clarify, I understand that nothing with mass can move at the speed of light or higher.

I have come across a question I was asked which I was unable to answer fully and would like to understand myself.

The usual questions like "If you imagine a rocket with an engine that produces thrust for eternity, wouldn't it eventually reach the speed of light?" are quite common, and it's not hard to explain why this is not true (since the mass increases with speed).

However, what if one would take a large mass out in deep space, and then release an object a large distance from this mass (not affected by other masses). The object will start to accelerate towards the mass, and this acceleration is not dependent on the mass of the object. So it will continue to accelerate and, if the initial seperation was enough, eventually reach an extremely high speed.

Why can't it reach the speed of light?

Note that I'm not trying to say "See, it can reach the speed of light!!!??!!", I understand there issomethingthat makes this thought experiment fail miserably, I just can't figure out what it is.

Is there perhaps some way to show that the object will always reach the large mass before it reaches the speed of light? (After which it will pass (or crush onto) the object and thus slow down again).

I hope my 'assumption' that the acceleration is independend on the mass of the object remains correct here (Since [itex]m_1a = G\frac{m_1m_2}{r^2}[/itex], the m_1 cancels).

Finally I realise that the force of gravity will be MUCH smaller at the initial 'starting point' than for example 1 meter from the large mass. (According to my calculation, at 1m from a mass similar to Earth, the force is approximately 10^14 times the massof the object, at the intial distance required to reach the light speed (about 1.53*10^7m (which seems small??)) the force is about 1.7 times the mass of the object...)

Does this have anything to do with it?

Thanks...

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# On the speed of light, accelerate toward mass

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