# 15.1.2 Gravitational Force Between Point Masses

### Newton's Law of Gravitation

• The gravitational force between two bodies outside a uniform field e.g. between the Earth and the Sun, is defined by Newton’s Law of Gravitation
• Recall that the mass of a uniform sphere can be considered to be a point mass at its centre
• Newton’s Law of Gravitation states that:

The gravitational force between two point masses is proportional to the product of the masses and inversely proportional to the square their separation

• Where:
• FG = gravitational force between two masses (N)
• G = Newton’s gravitational constant
• m1 and m2 = two points masses (kg)
• r = distance between the centre of the two masses (m)

• Although planets are not point masses, their separation is much larger than their radius
• Therefore, Newton’s law of gravitation applies to planets orbiting the Sun
• The 1/r2 relation is called the ‘inverse square law’
• This means that when a mass is twice as far away from another, its force due to gravity reduces by (½)2 = ¼

#### Exam Tip

A common mistake in exams is to forget to add together the distance from the surface of the planet and its radius to obtain the value of r. The distance r is measured from the centre of the mass, which is from the centre of the planet. ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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