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A clock on a moving spacecraft runs 1s slower per day relative to an identical clock on earth. What is the relative speed of the spacecraft?

Sagot :

The craft is moving at a speed of v = 0.024c or around 7 million metres per second or 16 million miles per hour.

The time dilation factor is equal to 3600/3599 if we only want 3599 seconds of the craft's time to pass for every hour (3600 seconds) of Earth time. However, there is a connection as well.

γ = [tex]\frac{3600}{3599}[/tex] = Dilation factor

Also, γ = 1/ √[tex]1-v^{2}[/tex]/[tex]c^{2}[/tex]

which we can solve algebrically to yield,

[tex]\frac{v}{c}[/tex] = √1-1/γ[tex]^{2}[/tex]

we get,

[tex]\frac{v}{c}[/tex] = 0.024

v= 0.024c

Accordingly, the craft is moving at a speed of v = 0.024c, or around 7 million metres per second or 16 million miles per hour.

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