# Newton's Law of Gravitation

## Key Questions

The Sun's gravitational force pulls on the planets which move perpendicular to this force at all times creating a elliptical (ideally circular) path around the Sun.

#### Explanation:

Let's use the Earth as an example:
As the Sun pulls the Earth towards it, the Earth moves very quickly (velocity around 30km/s) perpendicular to the force of gravity. These two forces create a resultant force pointed between the Sun and the Earth's path (let's just say this 30 degrees). Therefore, at all points around the Sun, the Earth will move at a 30 degree angle, creating a circle with radius r (r=93 million miles).

• In a stronger gravitational field a given mass will have a larger weight.

An object's weight is given by this equation: $w = m g$

Gravitational field strength at a distance, r, from a centre of mass is given by this equation:
$g = \frac{G M}{r} ^ 2$

If an object is nearer a centre of mass then r will be smaller so g will be larger. In that case the weight of the object will be larger. If an object is moved from a distance R away from one centre of mass and placed a distance R away from the centre of a smaller mass then g will be smaller. In that case the weight of the object will be smaller.

A practical example: if an astronaut on earth has a weight of 833 N, on the moon he/she will have a weight of 136 N.

Using $m = \frac{w}{g}$ the mass of the astronaut is $\frac{833}{9.8} = 85 k g$.

So the weight on the moon (${g}_{M} = 1.6 N k {g}^{-} 1$) is: w_M=mg_M=85×1.6=136 N