8) What is the distance to a particular star system measured by an observer in a...

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Physics

8) What is the distance to a particular star system measured byan observer in a rocket ship traveling to the star system with aspeed of 0.95c? (The distance is 37 trillion km asmeasured by an observer on Earth.)
km
9) A spacecraft has a velocity of 20 m/s and an acceleration of40 m/s² and is descending to land on planet Y and slowsdown by 4 m/s every second. The strength of the planet'sgravitational field is 7 N/kg. If the passengers in the spacecraftaccount for the forces they feel in terms of a single gravitationalfield, how strong would this field have to be?
N/kg

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(8) Solution :-

The distance star from the observer on Earth L = 37 trillion km
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =37Ã— 10 ⁹km

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =37Ã— 10 ¹²m

Speed v = 0.95 c

we know from length contraction L ' = L âˆš[ 1 - ( v² / c ² ) ]

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1.155 Ã—10^13 km

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