Answer to Question #169112 in Mechanics | Relativity for Sonny Coufax

Question

You are standing still on a spacecraft that is ravelling toward the Sun and 0.25c. a) How fast are you moving relative to a person that is on Earth observing your spacecraft's motion? b) You get out your radar gun and point it at the Sun. What speed do you measure for sunlight, given that your spacecraft is travelling toward the Sun at 0.25 c? c) At what speed, relative to c, do relativistic effects become significant? 

Answer 1

traveling toward the Sun AT 0.25c? relative to what? velocities with no reference don't mean much. Relative to earth? then answer to #1 is 0.25c.

"What speed do you measure for sunlight" light always travels at C, 299,792,458 m/s, to any observer. But you cannot use a radar gun to measure the speed of light.

depends on what you call "significant"

for 1%:

$γ = \large\frac{1}{\sqrt{1-(\frac{v}{c})^2}}$ $= 1.01$

$1-\large(\frac{v}{c})^2$ $= 0.98$

$v= 0.140c$

for 10%

$γ = \large\frac{1}{\sqrt{1-(\frac{v}{c})^2}}$ $= 1.1$   $1-\large(\frac{v}{c})^2$ $= 0.826$    $v = 0.417c$