An astronaut travels to a distant star with a speed of 0.55c relative to Earth.

Question

An astronaut travels to a distant star with a speed of 0.55c relative to Earth. The star is stationary relative to the Earth. From the astronaut's point of view, the star is 7.5 light-years from Earth.

(10 points) What is the distance between the Earth and the star, as measured by an observer on the Earth? Give your answer in light-years.  

(5 points) How long (in years) does it take to travel from earth to the star in the time frame of the astronaut?

(5 points) How long (in years) does it take for the space ship to travel from earth to the star in the time frame of earth observers?

Explanation / Answer

a)

The astronaut thinks the distance is d=vt= 7.5 ly

so we know L=L0/

7.5 ly= L0 *sqrt(1-0.55^2)

so L0 = 8.98 light years=9.0 ly

b)

in the frame of astronaut, the time taken is:

t=L/v=7.5/0.55c=13.6 years

c)

In the frame of astronaut, the time taken is:

t=L0/v=9.0 ly/0.55c=16.3 years

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.