# Newton’s law of universal gravitation equation

Gravity sucks, no really. We often think gravity is some concept that is hard to understand. But the crazy thing is, there is a rule that allows us to predict the attraction between two bodies. You know the attraction we mean. The bigger the better so to say. That’s the first part. The greater the mass of a planet, the greater the gravitational pull it will have to another body of mass. The second part is closeness. When two planets are close together, they will have a greater attraction as well. These concepts are nicely summarised in Newton’s law of universal gravitation equation.

Planetary Theft – Universal Gravitation # 1

In comic #1 planetary-theft, we see Bug-man use a missile to move the stolen planet further away from Earth. This is to reduce the force of attraction between earth and the planet. We can understand this idea through the universal gravitation equation.

So what is Newton’s law of universal gravitation equation?

F = the size of the Force between the two bodies (N)

G = the gravitational constant has the value 6.67 × 10-11 (N kg-2 m2 )

m1 = mass of the first object (kg)

m2 = mass of the second object (kg)

r = radius which is the distance between the centre of the two objects (m)

Therefore, by having the force of attraction between the two planets being on the bottom of the fraction, in the universal gravitation equation, we can see this reduces the force.

The other interesting thing to consider is that the further a planet gets from the sun, the slower it can orbit. This is because gravity acts as an invisible string allowing the planets to orbit around it.

The direction of the force of attraction is in a straight line between the two objects. This is the reason we fall directly down. The invisible string between us and the centre of the earth means we will always think gravity is pointing down, towards the ground.

But this string gets weaker the further the distance between the two objects. This is likely how Dr Victor stole the planet in the first case. Going to the outer most planet in another solar system would mean you can more easily knock it off it’s orbit. Thereby, slingshot it through the emptiness of space and potentially catch it ag ain with our sun’s enormous gravitational pull.

From BBC TWO

On Earth, our acceleration due to gravity is 9.8 ms-2, but on our stolen planet, this would be different. No matter what you drop on earth, when no other forces are acting on it, the object will accelerate by 9.8 ms-1, every second.

We find this value using:

F = ma

a = g

F = GMm/r2

mg = GMm/r2

g = GM/r2

Let r be radius of earth (6.37 x 106 m), M be the mass of the earth (5.98 x 1024 kg)

g = (6.67 × 10-11) (5.98 x 1024)/(6.37 x 106 m)2 = 9.8 m/s/s

Attempt and mark these exam-style questions so you can be confident you know and understand the content of this lesson.

## Universal gravitation equation exam-style Questions

Question 1. [1 mark]

Which of the following modifications to the two planets being held together through their gravitational pulls would increase the force of attraction the most.

• a) Doubling the mass of one of the planets
• b) Halving the mass of one of the planets
• c) Doubling the distance between the two planets
• d) Halving the distance between the two planets

Question 2. [2 mark]

The mass of earth is 5.98 x 1024 kg and the mass of the planet that was stolen was 6.38 x 1024 kg. The distance between the two planets centre is 5.57 x 107 m.

Knowing this calculate the force of attraction between the two planets.

Question 3. [3 mark]

On earth, we experience gravity to be 9.8 ms-2. On the stolen planet, gravity would be different, however, our mining machinery is made to work under a range of 6.2 -11.8 ms-2. Explain whether the machinery would be operating on our stolen planet.

Mass of the planet that was stolen was 6.38 x 1024 kg

Radius of the stolen planet was 5.97 x 106 m

Divergent thinking question.

What do you expect to happen if the earth was to collide with a stollen planet of similar size. Make sure you consider the direction of the initial collision.

## Universal gravitation equation Answers with marking rubric

Question 1.

D – Halving the distance between two planets will increase the force of gravity by 4, remember, F=GMm/r2.

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