Relativity and suchlike
The attraction between two objects due to gravity is given by:
a = (m1+m2)/d^2
Mass changes with velocity, such that:
as v approaches c, m approaches infinity.
So, with a sufficiently distant object, a gravitational force acting on an object of mass m in a vacuum, the object will increase its velocity v towards the distant object. V will increase unbounded, as there is no counteracting force present. This means that m will increase unbounded as well, due to the relationship posited above.
Under normal reasoning, speeds greater than or equal to c are impossible, due to the impossibility of having an engine capable of moving infinite mass.
However, acceleration due to gravity increases with the mass of the object, so the motive force will be increasing proportionally to the mass. Indeed, the motive force will increase faster than the mass due to the effect of decreasing distance. So, as v increases towards c, and m increases towards infinity, a will also increase towards infinity, as m + m2 will approach infinity and d^2 will be approaching zero.
Is it then possible for gravity to accelerate an object past the speed of light?
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