How Is Age Calculated in the Twin Paradox?

[MathematicalPhysicist]

what is the maths of this paradox?
or more precisely how do you compute the age of the man who stays in Earth while the other one in the spacecraft has spent a year in the vehicle?

thanks in advance.

 

[Janus]

Originally posted by loop quantum gravity
what is the maths of this paradox?
or more precisely how do you compute the age of the man who stays in Earth while the other one in the spacecraft has spent a year in the vehicle?

thanks in advance.

For the unaccelerated parts of the trip, you use

T₀ = t₁/[squ](1-v²/c²)

For those parts where the spacecraft is undergoing acceleration, you use

T₀ = c/a * sinh(at₁/c)

To find v after time t₁ at acceleration a:

v = c * tanh(at/c)

 

[MathematicalPhysicist]

Originally posted by Janus
For the unaccelerated parts of the trip, you use

T₀ = t₁/[squ](1-v²/c²)

For those parts where the spacecraft is undergoing acceleration, you use

T₀ = c/a * sinh(at₁/c)

To find v after time t₁ at acceleration a:

v = c * tanh(at/c)

does t0 for the person in earth?

 

[Janus]

Originally posted by loop quantum gravity
does t0 for the person in earth?

Yes.