$$ F = Gm_{1}m_{2}/r^2 $$
Where:
- $$F$$ is the force of gravity between the two objects in newtons (N)
- $$G$$ is the gravitational constant, which is approximately 6.674 × 10^-11 N m^2 kg^-2
- $$m_1$$ and $$m_2$$ are the masses of the two objects in kilograms (kg)
- $$r$$ is the distance between the centers of the two objects in meters (m)
In this case, we want to find the force Earth exerts on the Moon. So:
$$M_{earth}=5.972 × 10^24 kg$$
$$M_{moon}= 7.348 × 10^22 kg$$
$$r$$= the average distance between the Earth and the Moon, which is approximately 384,400 km or $$3.844 × 10^8 m$$
Substituting these values into the formula, we get:
$$ F = (6.674 × 10^-11 N m^2 kg^-2)(5.972 × 10^24 kg)(7.348 × 10^22 kg)/(3.844 × 10^8 m)^2 $$
$$ F ≈ 2.0 × 10^20 N $$
Therefore, the force Earth exerts on the Moon is approximately $$2 × 10^20 N$$.
