Background

A distant asteroid is on a path to collide with the Earth and moon. The Earth, moon, asteroid and sun move together under mutual gravitational attraction. You may recall that the force due to gravity, $\v F$, between any two objects is governed by

$$\v F = -\frac{G m_1 m_2 \v r}{\vert\v r\vert^3}$$

where G is the universal gravitational constant, m₁ and m₂ are the respective masses of the two objects, and $\v r$ is the displacement vector between the two objects.

The following data may be helpful to you:

Constant	Value
G ( $\frac{\rm km^3}{\rm kg \ s^2}$)	$6.67260 \times 10^{-20}$
Mass of Sun (kg)	$1.98900 \times 10^{30}$
Mass of Earth (kg)	$5.97400 \times 10^{24}$
Mass of Earth's moon (kg)	$7.35000 \times 10^{22}$
Mass of asteroid (kg)	$5.00000 \times 10^{22}$