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Two astronauts are tethered together on a space walk and rotate around each other. They each weigh 115 kg and are 249 m apart. What is the period of the rotation in seconds if the tension on the cable is 217.313 N?

Answer :

Final answer:

The period of rotation of the two tethered astronauts, who each weigh 115 kg and are 249 m apart, is approximately 156,000 seconds if the tension on the cable is 217.313 N.

Explanation:

To answer this question about astronauts rotating around each other in space, we can start by using the formula for gravity: F = GMm/r². Here, F is the force of gravity (which is the tension on the cable), G is the gravitational constant, M and m are the masses of the astronauts, and r is the distance between them.

First, we solve this equation for r, getting r = sqrt(GMm/F). Plugging in the given values, where F = 217.313 N,

G = 6.67 × 10⁻¹¹ N.m²/kg²,

M = m = 115 kg,

we find r = 249 m.

Next, we use this radius to find the speed of the astronauts using the formula v = sqrt(GM/r).

With r = 249 m,

we find v ≈ 0.032 m/s.

Finally, we use the formula for the period of the motion, T = 2πr/v.

With r = 249 m and

v ≈ 0.032 m/s,

we find T ≈ 156,000 s.

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