If a spaceship travels to a planet one light-year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more
than one year as measured by a clock on Earth). The value obtained by dividing the distance traveled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or a proper velocity. There is no
limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. A light signal that left the Earth at the same time as the traveller would always get to the destination before the traveller. The
traveler will not measure her or his speed as being higher than the speed of light, but will see a length contraction of the universe in her or his direction of travel
vp can “exceed” c, r / t/
vp = r/{t(1 – [v/c]2) ½ }
vp = v/(1 – [v/c]2) ½

Lazarus Cain is an ex-NASA intern who has strong interest in this field

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