Question

In 2095 a message arrives at earth from the growing colony at Tau Ceti (11.3 y from earth). The message asks for help in combating a virus that is making people seriously ill (the message includes a complete description of the viral genome). Using advanced technology available on earth, scientists are quickly able to construct a drug that prevents the virus from reproducing. You have to decide how much of the drug can be sent to Tau Ceti. The space probes available on short notice could either boost 200 g of drug (in a standard enclosure) to a speed of 0.95, 1 kg to a speed of 0.90, 5 kg to a speed of 0.80, or 20 kg to a speed of 0.60 relative to the earth. The only problem is that a sample of the drug in a standard enclosure at rest in the laboratory is observed to degrade due to internal chemical processes at a rate that will make it useless after 5.0 y. Is it possible to send the drug to Tau Ceti? If so, how much can you send?

Answer 1

The drug can rest in the rocket for less than 5y. If the rocket would travel the separation from Earth to Tau Ceti at speed of light in Eearth's reference frame is would require 11.3y. Thus accoridng to time dilation in special relativity

$\gamma=\frac{11.3}{5}=2.26$

This corresponds to a velocity wrt to speed of light

$\beta=\sqrt{1-\frac{1}{\gamma^2}}=0.897$

Scientist thus can't send more than 1 kg of drug