Question

A deep-space vehicle moves away from the Earth with a speed of 0.870c. An astronaut on the vehicle measures a time interval of 3.10 s to rotate her body through 1.00 rev as she floats in the vehicle. What time interval is required for this rotation according to an observer on the Earth

Answer 1

t₀ = 1.55 s

Step-by-step explanation:

According to Einstein's Theory of Relativity, when an object moves with a speed comparable to speed of light, the time interval measured for the event, by an observer in motion relative to the event is not the same as measured by an observer at rest.

It is given as:

t = t₀/[√(1 - v²/c²)]

where,

t = time measured by astronaut in motion = 3.1 s

t₀ = time required according to observer on earth = ?

v = relative velocity = 0.87 c

c = speed of light

3.1 s = t₀/[√(1 - 0.87²c²/c²)]

(3.1 s)(0.5) = t₀

t₀ = 1.55 s

Answer 2

• The time interval required for this rotation according to an observer on the Earth =
  `6.29sec`

Step-by-step explanation:

Time interval required for this rotation according to an observer on the Earth is given as
`\delta t`

where,

`t_o = 3.1\\\\v = 0.87`

`\delta t = \frac{t_o}{\sqrt{1-(v^2)/(c^2)}}\\\\\delta t = \frac{3.1}{\sqrt{1-((0.87c)/(c))^2}}\\\\\delta t = 6.29sec`

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