Newton’s law of universal gravitation.

Issac Newton was sent home from university because of the out break of the bubonic plague, he used this time very productively.

It is in the Autumn of 1866 that the story told of the apple falling on his head.

He realised that there was a force acting between 2 bodies that had mass, he called this acceleration, gravity.

He determined that gravity would be proportional to the masses of the objects and inversely proportional to the square of the distance between the objects.

where G is a constant = 6.67 x 10-11 Nm2kg-2.

While the idea of masses being attracted to other masses is commonly refered to as gravity if you are answering a question about something that causes motion / acceleration it is only correct to call this 'gravitational force', gravity will not suffice.

Variation of g, and hence W, with distance from centre of Earth (effect of centripetal acceleration not required).

where F = ma implies that we could determine the acceleration due to gravity if we knew details about earth

find the mass of earth 5.97 x 1024 kg

the radius to sea level, (6.378x106m).

the radius to the highest place (8850m)

the radius to the deepest part of the ocean (8581m)

thus find a value of g at each point

where would g be greater at the equator or the north pole ?

what radius would you guess ireland would have?

So by looking at the equation, we can change the force if we change the mass of the planet, or our distance from the centre of gravity of the planet we are on.

Changing mass

Increase in mass → Increase in Force

increasing the radius!

Increase in Distance (from the CoG) → Decrease in Force

Appropriate calculations

Two identical lead spheres of radius R and mass M are touching and attract each other with a gravitational force F. These spheres are replaced with two other spheres made of the same material (lead) but each having a radius 3R.

How does the gravitational force between the new pair compare to the gravitational force between the first pair?

Give an answer such as 2F, except correct!

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Compare gravitational forces

between Earth and Sun and

between Earth and Moon.

examine the force of gravity on a person on earth when a moon is at is closest and furthest from earth,

The data here shows the proof that we get 2 tides per day and explains why, if you can infer it .....

the worlds biggest tides are here, and this is the fun you can have on them

Solar system.

Value of acceleration due to gravity on other bodies in space, on different planets.

Pick or be assigned a planet from the list

e.g. Moon.

earth to moon data here

the dropping ruler reflex experiment, ties into gravity, how fast you react can be measured by where you grip the ruler.

“Weightlessness” and artificial gravity.

w= mg

Circular satellite orbits –

derivation of the relationship

between the period, the mass of the central body and the radius of the orbit.

Appropriate calculations

Satellites and communications.

The formula for the gravitational field strength 𝑔g (in N/kgN/kg) at distance 𝑟r (in metres) from the Earth's centre is:


where 𝑘=4.0×1014Nm2/kg