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Now let's say the I am on a spaceship. The spaceship is not accelerating, i.e., it is not firing its rockets. Most of the ship's mass is in the back of the ship. Let's say it is moving arbitrarily close to the speed of light (after all, it is from some reference frame.) The ship will have a greater mass than if at rest. This greater mass would cause me to accelerate a lot.

Now let's look at my reference frame. From my reference frame, the ship is at rest. Therefore, its mass will be its rest mass. Therefore, I will only accelerate a little.

How is this? From one reference frame, there is a lot of gravity, from the other, a little. I am accustomed with dealing with most special relativity paradoxes, but when you throw mass in, I'm not sure what to do?

Although this question's premises fall within special relativity, for some reason I have a feeling general relativity will be needed to explain it.

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Mass is a Lorentz invariant quantity! The relativistic mass is not the real mass, it is is just called relativistic "mass" for obvious reasons. This term is abandoned by most textbooks, as it often causes this confusion.

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  • $\begingroup$ So how would I figure out the gravity exerted on me? $\endgroup$ – PyRulez Jul 21 '15 at 21:27
  • $\begingroup$ Use Newton's Law of Gravity to determine the force due to gravity exerted between two objects. $\endgroup$ – user85503 Jul 21 '15 at 21:29
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    $\begingroup$ Yes that would be correct for special relativity. For the exact force you would need general relativity (One of the main reasons how general relativity was motivated was to explain the faster orbit of Mercury, not explainable by Newtons law of gravity) $\endgroup$ – john Jul 21 '15 at 23:04
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If you are in the spaceship then you probably do not move with a notable speed against it. Let say 0.000000001 c. Here, Newtonian equations do excellent job. For a reference frame that is moving with 0.5 c relatively to you, both you and spaceship would "feel" greater mass (mutliplied by \gamma).

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