Question

Sally and Sam are in a spaceship that comes to within 16,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 1020 kg and the mass of Sally is 77 kg. For calculation purposes, assume the two objects to be point masses.

Answer 1

Answer:

  0.017 N

Explanation:

The relevant relation is ...

  F = GMm/r²

where G is the universal gravitational constant, 6.67408 × 10^-11 m^3·kg^-1·s^-2, M and m are the masses of the objects, and r is the distance between them.

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Filling in the given numbers, we find the force to be ...

  F = (6.67408 × 10^-11 m^3·kg^-1·s^-2)(8.7 × 10^20 kg)(77 kg)/(1.6 × 10^7 m)^2

where m in this expression is the unit "meters".

  F = 6.67408 · 8.7 · 77/2.56 × 10^(-11 +20 -2·7) N ≈ 0.017 N

The asteroid exerts a force of about 0.017 N on Sally.

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Additional comment

That's about 0.000023 times the force of Earth's gravity.