Because the earth is freely falling around the sun, its center defines a pretty

Question

Because the earth is freely falling around the sun, its center defines a pretty good inertial reference frame. With this in mind, consider the fates of two identical twins, one living since infancy at the north pole and the other living since infancy on the equator. Imagine that both twins die after exactly the same biological time has passed (as determined by their own bodies). If this is so, about how much longer will the equatorial twin live than the northern twin, if both live for approximately normal time spans? Describe any approximations or assumptions that you have to make.

Explanation / Answer

The points on the equator are moving with a velocity of 460 m/s.
The twin at the north pole will be stationary with respect to a stationary observer and the twin at the equator will be moving with a velocity v = 460 m/s.

Time dilation, t = to/sqrt[1 - v2/c2]
= to/sqrt[1 - (460)2/(3 x 108)2]
to - t = 2.35 x 10-12 t

Suppose an average man lives for 75 years
75 years = 75 x 365 x 24 x 60 x 60 s
The extra time lived according to a stationary observer
= (2.35 x 10-12) x 75 x 365 x 24 x 60 x 60
= 5.6 ms

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.