Earth and Sun are 9.0 light minutes apart, as measured in their rest frame. Part

ID: 1455793 • Letter: E

Question

Earth and Sun are 9.0 light minutes apart, as measured in their rest frame.

Part A

What is the speed of a spacecraft that makes the trip in 4.5 min according to its on-board clocks?

Express your answer using two significant figures.

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Part B

What is the trip time as measured by clocks in the Earth-Sun reference frame?

Express your answer using two significant figures.

Earth and Sun are 9.0 light minutes apart, as measured in their rest frame.

Part A

What is the speed of a spacecraft that makes the trip in 4.5 min according to its on-board clocks?

Express your answer using two significant figures.

v/c =

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Part B

What is the trip time as measured by clocks in the Earth-Sun reference frame?

Express your answer using two significant figures.

t = min

Part A: Lo=60*9*3*10^8 = 1.62*10^11 m

to = 4.7*60 = 282 sec

v=Lo/t = L/to

=t/to

Plug Lo/t into the gamma equation (here =t/to) for v and solve for t.

1/(1-(Lo/(tc))^2)^1/2=t/to

1-(Lo/(tc))^2 = (to/t)^2

t^2 = (Lo/c)^2 + (to)^2

t = ((Lo/c)^2 + (to)^2)^0.5

t = ((1.62*10^11/(3*10^8))^2 +(282)^2)^0.5

t= 609 s

Now plug this value for t into the velocity equation above:

v = Lo/t = 1.62*10^11/(609*3*10^8)

v/c = 0.89

Part B: t= 609 s

t = 609/60 = 10 min = 1.0*10^1 min

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