A spaceship moves radially away from Earth with acceleration 38 m/s2. How long does it take for the sodium streetlamps (λ ≌ 589 nm) on Earth to be invisible (with a powerful telescope) to the human eye of the astronauts? The range of visible wavelengths is about 400-700 nm.

t= 1.34x10power 6 sec

Explanation:

l = lo ( 1+b / 1+b /)1/2 where L = wave length

(700mn/589mm)2 = 1.41 = 1+b/1-b

1.41-1.41b = 1+b

0.41= 2.41b

b = 0.17

v=5.1 x 10 7 m/s

v = at

t = a/v = 5.1 x 10power 7 m/s / 38m/s2= 1.34*10 power 6

t= 1.34x10power 6 sec

the results is a decrease in air temperature with an increase of altitude.

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