D1a - Newton's Law of Gravity

• Physics
• Secondary Education

D1a - Newton's Law of Gravity

Learning Objectives:

• What is gravity?
• Newton's equation
• Assumptions in Newton's equation
•  gravitational field strength
• Representing gravity.

What do you know about gravity?

What is gravity?

If you were to strip the universe back to the most basic components you would find that it contains stuff (matter etc) and forces.

As far as we know there are four fundamental forces of nature. They are the strong nuclear force, the weak nuclear force, the electromagnetic force and gravity.

Gravity is the force that we are probably most familiar with as it governs the stars and planets.

The truth about gravity

Gravity was later discovered by Einstein to not really be a force but instead a curvature of spacetime.

Newton

In 1687 Newton published his law of gravitation which was said to be inspired by an apple falling.

What is the formula for the law of gravitation?

1. F=​m​1​​m​2​​r​2​​​​G​​
2. F=​r​2​​​​Gm​1​​m​2​​​​
3. F=​r​​G(m​1​​+m​2​​)​​
4. F=G​r​2​​​​M​​

What does 'G' represent in the law of gravitation formula?

1. Acceleration due to gravity
2. Mass of the object
3. Gravitational constant
4. Distance between the objects

What happens to the gravitational force if the distance between two objects doubles?

1. It becomes one-fourth of the original force
2. It becomes half of the original force
3. It remains the same
4. It doubles

The gravitational force between a star of mass M and a planet of mass m is F. What would the force (F_2) be between the star and a planet of mass 3m and 4 times the distance?

Newton's law of gravitation assumes all bodies to be point masses i.e. they have no size. What are the correct conditions under which an extended body can be assumed to be a point mass?

1. The distance separating the masses is significantly large.
2. The masses have a similar magnitude.
3. The density of each mass is the same
4. The masses are spherically symmetric.

Point Masses

In physics we ALWAYS start with the simplest case. To do this we need to make some assumptions. In the case of Newton's law of gravity we simplify any extended body into a point mass. This works very well as long as:

1. The distance between the two masses is very large
2. the masses are spherically symmetric.

Gravitational Field

What are fields?

on the left we have a field of wheat.

This is a region where wheat is grown

What are fields?

On the right we have a soccer field.

This is a region where people play soccer.

Gravitational field

Following this logic a gravitational field is simply a region where gravity exerts an influence (force) on other masses

more information

We will encounter other fields in physics (e.g. electric and magnetic fields) that are defined in similar ways. Fields are a better way of describing non-contact forces as they remove the necessity of considering 'action at a distance' forces which violate Einstein's principles in relativity .

Field lines

The black arrows here represent field lines. A field line is an imaginary line which points in the direction a 'test mass' would experience a force. Gravity is ALWAYS attractive and so the field lines always point towards the mass we are interested in.

equipotential lines

The red circles here represent equipotential lines. These are lines that are perpendicular to the field lines at each point and trace out a line where the potential energy is the same. If you travel along one of these lines gravity will do no work as you would not be losing or gaining energy.

Field strength

Notice that as you get closer to the mass the field line density increases (the field lines are closer together along single equipotential). This signifies that the gravitational field is stronger where the field density increases.

zooming in

Note that close to the surface of the earth the field lines can be assumed to be parallel (uniform) as the curvature of the earth is not evident locally.

What do gravitational field lines around a spherical mass represent?

1. lines where gravitational potential energy is the same
2. The force of gravity
3. The distance between different points in space
4. The direction of the force experienced by a mass

What do equipotential surfaces for gravity indicate?

1. Areas of maximum gravity
2. Points with different gravitational forces
3. Points with the same gravitational potential
4. Locations of zero gravity

How is gravitational field strength related to distance from a spherical mass?

1. It increases with increasing distance from the mass
2. It is unrelated to distance from the mass
3. It remains constant at all distances
4. It decreases with increasing distance from the mass

Given that the radius of the earth is
m, and g=9.81 N/kg . What is the mass of the Earth?

6.4⋅10​6​​

point mass

Remember that Newton's law of gravity works for point masses. So technically we imagine that all of the mass is located at the origin (r=0). When working out the field strength at the surface of a planet we can still use the equation and the answer is accurate.

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