# PHY C8: Gravitational Fields & Force

Today we’re covering:

• Gravitational Fields
• What is a Gravitational Field?
• What is a Centre of Mass?
• Point Masses
• Inverse Square Law
• Newton’s Law of Gravitation

Let’s dive in!

What is a Gravitational Field?
A region of space where a mass experiences a gravitational force.

It is a type of field of force generated by mass, where lines of force are directed towards the centre of mass.

What is a Centre of Mass?
A point in an object where a force acts on its mass.

To simplify calculations, we assume that objects are point masses:
where they only exist as a single point with a mass.

A bit of notation to know when talking about Point Masses:
A gravitational field is generated when we have at least 1 point mass.
However, to observe any acceleration (& thus force), we need to look at the interaction between 2 point masses.

Both point masses accelerate towards each other.
In general, if both masses have NON-NEGLIGIBLE acceleration:

• m1 = 1st point mass
• m2 = 2nd point mass

In some situations, we talk about a smaller point mass being attracted towards a larger point mass.

Although both point masses accelerate towards each other,
the acceleration of the LARGER mass is negligible (very small).
Thus, we only consider the acceleration of the smaller point mass.

To differentiate the masses during calculations, we write:

• M = larger point mass (the Earth, planets, etc)
• m = smaller point mass

What is the Inverse Square Law?
A general law involving fields that states:
“the strength of a field is inversely proportional to the square of the distance.”

This applies to gravitational fields as well, & is one aspect of Newton’s Law of Gravitation:

What is Newton’s Law of Gravitation?
“The force between 2 point masses is proportional to both masses, & inversely proportional to the distance between the point masses.”

F ∝ m1m2/r2
F = Gm1m2/r2

• r is the distance between the 2 point masses.
This includes both the radius of the bodies + the distance between them.
• G is a proportionality constant:
the Gravitational Constant.
G’s value is 6.67 x 10-11 Nm-2kg-1