A Martian leaves Mars in a spaceship that is heading to Venus. On the way, the spaceship passes earth with a speed v = 0.77c relative to it. Assume that the three planets do not move relative to each other during the trip. The distance between Mars and Venus is 1.20 × 1011 m, as measured by a person on earth. (a) What does the Martian measure for the distance between Mars and Venus? (b) What is the time of the trip (in seconds) as measured by the Martian? Limit your answer to 2 significant digits.
Solution
the three planets can be thought to be stationary.
distance between mass and venus=d1=1.2*10^11 m
part a:
using length contraction, distance measured by the martian=1.2*10^11*sqrt(1-(v/c)^2)
=7.6565*10^10 m
part b:
time of the trip by martian=distance measured by martian/speed
=7.6565*10^10/(0.77*3*10^8)
=331.45 seconds
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A Martian leaves Mars in a spaceship that is heading to Venus- On the.docx
1. A Martian leaves Mars in a spaceship that is heading to Venus. On the way, the spaceship passes
earth with a speed v = 0.77c relative to it. Assume that the three planets do not move relative to
each other during the trip. The distance between Mars and Venus is 1.20 × 1011 m, as
measured by a person on earth. (a) What does the Martian measure for the distance between
Mars and Venus? (b) What is the time of the trip (in seconds) as measured by the Martian? Limit
your answer to 2 significant digits.
Solution
the three planets can be thought to be stationary.
distance between mass and venus=d1=1.2*10^11 m
part a:
using length contraction, distance measured by the martian=1.2*10^11*sqrt(1-(v/c)^2)
=7.6565*10^10 m
part b:
time of the trip by martian=distance measured by martian/speed
=7.6565*10^10/(0.77*3*10^8)
=331.45 seconds
