Time dilation spacecraft travel problem

[Benzoate]

Problem: How fast must a spacecraft travel relative to the Earth for each day on the Earth to correspond to 2 days on the earth?

My solution:

proper time = 1 day = 86400 seconds
time on space craft= 2 days= 172800 seconds
relavant equation: t=t(0)/(sqrt(1-v^2/c^2)

I would plug in both the proper time and relative time into time dilation equation in order to find the speed of the spacecraft correct?

 

[G01]

The time on the spacecraft would be the proper time. Other than this you are correct.

The proper time is the time between events measure by a clock that is present and at rest at both events. Here, the events are the two points mentioned in the spacecraft 's journey. The only clock present and at rest at both of these events is the one on the ship.