# 5.7.4 Newton's Law of Gravitation

## Newton's Law of Gravitation

• The gravitational force between two masses, e.g., between the Earth and the Sun, is defined by Newton’s Law of Gravitation

• Newton’s Law of Gravitation states:

The gravitational force F between two masses m1 and m2 is proportional to the product of their masses and inversely proportional to the square of their separation, r

• In equation form, this is written as: • Where:
• F = gravitational force between two point masses m1 and m2 (N)
• G = Newton’s gravitational constant
• m1 and m2 = mass of body 1 and mass of body 2 (kg)
• r = distance between the centre of the two masses (m)

• The 1/r2 relation is called the ‘inverse square law’
• This means that if the distance between two masses doubles, r becomes 2r
• Therefore, 1/r2 becomes 1/(2r)2, which is equal to 1/4r2
• Hence, the gravitational force between the two masses reduces by a factor of four

• The negative sign indicates that the gravitational force F between the two point masses m1 and m2 is attractive The gravitational force between two masses is defined by Newton’s Law of Gravitation

#### Worked example

A satellite with mass 6500 kg is orbiting the Earth at 2000 km above the Earth's surface. The magnitude of the gravitational force between them is 37 kN.

Calculate the mass of the Earth.

(Radius of the Earth = 6400 km) #### Exam Tip

A few common mistakes to be aware of are:

• forgetting 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 between the centre of each mass, which is from the centre of the planet to the centre of the satellite!
• forgetting that the distance between point masses m1 and m2 is squared. Remember this whenever you use Newton's Law of Gravitation!
• Note in this worked example, we calculated the magnitude of the gravitational force F. Therefore, we could ignore the negative sign. Make sure you are aware of this! ### Get unlimited access

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