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"Many contemporary authors such as Taylor and Wheeler avoid using the concept of relativistic mass altogether:"The concept of "relativistic mass" is subject to misunderstanding. That's why we don't use it. First, it applies the name mass - belonging to the magnitude of a 4-vector - to a very different concept, the time component of a 4-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of spacetime itself."
The orbital velocity of a body travelling along a parabolic trajectory can be computed as:v = square root 2*standard gravitational parameter/radial distance of orbiting body.At any position the orbiting body has the escape velocity for that position.If the body has the escape velocity with respect to the Earth, this is not enough to escape the Solar System, so near the Earth the orbit resembles a parabola, but further away it bends into an elliptical orbit around the Sun.This velocity (v) is closely related to the orbital velocity of a body in a circular orbit of the radius equal to the radial position of orbiting body on the parabolic trajectory:v = square root 2*v orbital
Then we can also see that a radial parabolic trajectory is a non periodic trajectory on a straight line, where the relative velocity of the two objects is always escape velocity.There are two cases: the bodies move away from each other or towards each other.There is a rather simple expression for the position as a function of time:r = (4.5*standard gravitational parameter*t squared)1/3t = 0 corresponds to the extrapolated time of the fictitious starting or ending at the centre of the central body.At any time the average speed from t = 0 is 1.5 times the current speed, ie: 1.5 times the escape velocity.To have t = 0 at the surface, apply a time shift for the Earth (and any other spherically symmetrical body of similar density) as central body this time shift is 6 minutes and 20 seconds: seven of these periods later the height above the surface is 3 times the radius, etc.