Question

5. Uranus is 2.871 10m from the sun. A rocket travels along a line from the sun to Uranus at a constant speed of exactly 0.8c relative to the solar system. How long does the journey take as measured by an experimenter on earth? As measured by an astronaut on the rocket! Use the diagram below to help you label your solution. At-1 1,974 s ,at' 7,185 s A-

Answer 1

The observer on Earth is at rest and observer in rocket is moving. Thus, the distance measured by observer on Earth (stationary observer) is proper length and distance measured by observer in rocket (moving observer) is contracted length.

Proper length ($L_0$) =

2.871 1012 m

Contracted length (L) =

V I

where v is speed of rocket

し 2.871 * 1012V/1-(0.8c)2/C2 = 2.871 * 1012 * 0.6 1,723 * 1012 m

Time measured by observer on Earth = distance/speed of rocket

Lo 2.871 1012 0.8c 2.871 1012 0.8 (3 108) 11963s taking c 3108 m/s)

For experimenter on Earth, journey takes

At-11963 s

Time measured by observer in rocket = distance/speed of rocket

1.723 1012 0.8c 1.723 1012 0.8 (3 108) 7179 s taking c310s m/s)

For astronaut on rocket, journey takes

$\Delta t'= 7179\ s$