A group of astronauts have landed on a new planet to terraform. This planet orbits a small star in a circular orbit. The planet orbits at a speed of 1000 m/s in a counterclockwise direction. The planet is a distance 400 x106 m from the center of the star. The radius of the planet is 1.5 x 106 m. The astronauts on the surface of the planet measure the speed of the surface to be about 5 m/s and also rotating in a counterclockwise direction. The end goal is to accelerate the rotational speed of the planet to make it the same length of day as earth.
Determine
a) The current length of a day (time between sunrises) for the astronauts.
b) the maximum possible acceleration experienced if it takes 10 days to accelerate the planet under constant acceleration to reach a 24-hour day.

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topeadeniran2 topeadeniran2 · Answer 1 · 2022-05-30T14:50:41+02:00

The current length of a day or time between sunrises for the astronauts will be 523.6 hours.

The current length of day for the astronauts will be:

T = 2πR/V

T = (2π × 1.5 × 10^6)/5

T = 523.6 hours.

The maximum possible acceleration experienced if it takes 10 days to accelerate will be:

= 1/(240 × 3600s)(2π × 1.5 × 10^6/24 × 3600)

= 1.20 × 10^-4 m/s².

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