Question

Ceres, the largest asteroid known, has a mass of roughly 8.7 x1020 kg. If Ceres passes within 12,000km of the spaceship (2.75e4kg) in which you are traveling, what force does it exert on the spaceship?

Answer 1

Answer:

11.1 N

Explanation:

The gravitational force between the asteroid and the ship is given by:

$F=G\frac{mM}{R^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant

$M=8.7\cdot 10^{20} kg$ is the mass of the asteroid

$m=2.75\cdot 10^4 kg$ is the mass of the spaceship

$R=12,000 km=1.2\cdot 10^7 m$ is the distance between the asteroid and the spaceship

Substituting numbers into the equation, we find the force

$F=(6.67\cdot 10^{-11})\frac{(2.75\cdot 10^4 kg)(8.7\cdot 10^{20} kg)}{(1.2\cdot 10^7 m)^2}=11.1 N$