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If the object in motion gains mass, will it affect the change in mass of Earth if it stops revolving around Sun, since mass is responsible for gravity how will be the gravitational force change?

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I've tried to fix the English of this question, but could use some input from the author. – Sklivvz Jan 11 '13 at 16:52
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From the point of view of people standing on the Earth, no effect whatsoever.

That is because the so-called "relativistic mass" is an effect of different frames of reference. (It is also pretty trivial from the POV of someone at rest with respect to the sun, surpressed by factors of order $\frac{30000\text{ m/s}}{300000000\text{ m/s}} = 10^{-4}$.)

For many purposes working scientists have almost entirely stopped using the phrases "relativistic mass" and "rest mass", finding the former concept to be of little practical use.

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So earth doesn't acquire much of gravity from its motion? – Ciasto piekarz Jan 11 '13 at 16:40
From your point of view the Earth acquires no gravity from it's orbit around the sun and a vanishingly small amount from it's rotation (much less than the centrifical pseudoforce of rotation). Again, all relativistic effects depend on the frame of reference. Your frame of reference is essentially at rest with respect to the Earth. – dmckee Jan 11 '13 at 16:42
I actually don't understand what you mean by frame of reference? – Ciasto piekarz Jan 11 '13 at 16:53
@SànLuthra "frame of reference" = "your point of view, in which you are at rest." The apparent increase in the mass of things moving close to the speed of light is dependent on who does the observations. You only see a change if the thing is moving with respect to you. Since the Earth is sitting still as far as you are concerned, you will not see any effect at all. There is no motion in an absolute sense, only relative motion between two different things - this is the underlying principle of special relativity. – Chris White Jan 11 '13 at 18:17

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