### Gravitational Acceleration

Since there is a gravitational force of attraction between two objects, as a result of these forces, these objects can accelerate. This acceleration is then obviously called
gravitational acceleration.

The symbol for gravitational acceleration is:

### g

with usual acceleration units of m.s^{-2}.

### Equation

- g is not a constant
- g changes from place to place
- g is a vector quantity so a magnitude and a direction must be provided

So how is gravitational acceleration calculated?

You use the same data sheet.

Study this example.

### Example 1

**An asteroid of mass 2 x 10**^{5} kg is a distance of 4 x 10^{8} m away from the Earth's SURFACE.

(ignore radius of asteroid, too small.)

**1. Calculate the acceleration of the ASTEROID.**

**Urgent:**

In the acceleration equation there is ONE mass. Although you want to calculate the acceleration of the asteroid, USE THE MASS OF THE EARTH!

This is because the asteroid is not accelerating itself. The Earth is actually responsible for pulling the asteroid in!

The value of **r** for the equation is from center to center. Hence:

Substitute into acceleration equation:

**2. What happens to the acceleration of the asteroid as it approaches the Earth?**

The acceleration increases.

From the equation :

G and M are constant.

So as **r** decreases, **g** increases.

### If you wanted to calculate the acceleration of the Earth as a result of the asteroids pull, then
use the asteroids mass in the equation.