# The maths of the twin paradox

Gold Member
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?

Janus
Staff Emeritus
Gold Member
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?

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)

Gold Member

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
Staff Emeritus