ADVANCED DYNAMICS — PHY 4241/5227 SOLUTIONS – SET 13

Problem 49: Momentum conservation in the rest frame (m rest mass):

c dm = m g dτ .

Separation of variables gives (with initial mass m_{0}):

∫_{m_{0}}^{m(τ)} = −\frac{g}{c} ∫_{0}^{τ} dτ′ ⇒ m(τ) = m_{0} e^{−gτ/c} .

After τ = 20 years:

m(20 y) = 1.09 × 10^{−9}m_{0} .

End of spacetrip journey.