Hello!
This question is about the special relativity theory. It states (and there are many experiments confirming it) that the speed of light in a vacuum is a constant, denoted `c,` regardless of the frame of reference. This gives some paradoxical results.
Denote the given speed of a rocket as `v.` Then the Lorentz factor `gamma = sqrt(1-(v^2)/(c^2))` describes the changes in observed length, time and mass of a moving object. Namely, length is contracted,...
Hello!
This question is about the special relativity theory. It states (and there are many experiments confirming it) that the speed of light in a vacuum is a constant, denoted `c,` regardless of the frame of reference. This gives some paradoxical results.
Denote the given speed of a rocket as `v.` Then the Lorentz factor `gamma = sqrt(1-(v^2)/(c^2))` describes the changes in observed length, time and mass of a moving object. Namely, length is contracted, time is dilated and mass is increased with this factor. In numbers it is `sqrt(1-(0.68)^2) approx0.73` (dimensionless).
Therefore
a) the length will be `96*gamma approx 70.4 (m),`
b) the apparent mass will be `(4.5*10^3)/gamma approx6139 (kg),`
c) the dilated time is given to be `15` years, so the time for astronauts will be less by `gamma,` i.e. `15*gamma approx 11 (years).` Note that it is a simplification, because to return a rocket must change its velocity.
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