Force of attraction and calculating magnitude

Question

The mass of Bennu asteroid is 78 Billion Kilograms. Its average radius is 250 meters.

Mass of Osiris-REx spaceship is 880 Kg, orbiting the asteroid at an average distance of 1800 meters from the surface.

The Universal Gravitational Constant G = 6.67 ∗ 10−11 N 2/k 2

A – Calculate the force of attraction between the asteroid and the orbiting

spaceship.

B – Drive an equation to find "g," acceleration due to the force of gravity, at the surface of Bennu asteroid. Then calculate its magnitude.

Answer 1

A) First, find the distance (r) from the center of Bennu to the spacecraft: r = 250 m + 1800 m = 2050 m. Then use F = Gm₁m₂ / r² to find the force F = (6.67 x 10^-11)(78 x 10⁹)(880) / 2050² = 1.09 x 10^-3 N.

B) Derive the equation from F = Gm₁m₂ / r² understanding that F is the weight of the 880 kg spacecraft which is m₂"g" in this case.

So m₂"g" = Gm₁m₂ / r² and "g" = Gm₁ / r². The surface of Bennu is 250 m from the center so that is r now so we can calculate "g" = (6.67 x 10^-11)(78 x 10⁹) / 250² = 8.3 x 10^-5 m/s/s.