Question

Sally and Sam are in a spaceship that comes to within 17,000 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 80 kg. For calculation purposes, assume the two objects to be point masses.

Answer 1

0.01606 or rounded 0.017 N

Step-by-step 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.

Answer 2

0.01606 Newtons

Step-by-step explanation:

r = Distance between the asteroid and Sally = 17000000 m

m₁ = Mass of the asteroid = 8.7× 10²⁰ kg

m₂ = Mass of Sally = 80 kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

From Newton's Universal law of gravity

`F=G(m_1m_2)/(r^2)\\\Rightarrow F=6.67* 10^(-11)* (8.7* 10^(20)* 80)/(17000000^2)\\\Rightarrow F=0.01606\ N`

The force Sally experiences is 0.01606 Newtons