Question

The space shuttle has a length of 37 m.

(a) In its normal orbital motion around the Earth, the shuttle has a speed of about 8000 m/s and an orbital period of about 90 minutes. Accounting for length contraction, what is the difference of the proper shuttle length and the length of the shuttle as viewed by an observer at rest on the ground?

(b) Suppose the shuttle increases its speed so that it has a length of 34.2 m when viewed by a stationary observer. How long would it take to complete one orbit?

(Please make numbers legible and with units)

Answer 1

Length contraction formula is

.........(1)

L = length observed when moving at speed v

L₀ = Length at rest (proper length)

c = speed of light = 3*10⁸ m/s

Given, L₀ = 37 m

v = 8000 m/s

Putting these values in equation (1),

m

m

The difference of proper length and observed length =

(Answer of part (a))

When observed length of the spce shuttle is 34.2 m, its speed can be calculated from equation (1)

Time period = 90 min = 90*60 s

When speed is 8000 m/s, time period = 90*60 s

When speed is 1 m/s, time period = 90*60*8000 s (when speed is less, time period will be more)

When speed is , time period =

Answer of part (b)