Chapter 18: Gravitational Force

Gravitational field

It is a region of space where a mass experiences a force.

Newton’s law of gravitation

It states that the two point mases attract each other with a force that is proportional to the product of their mases and inversely proportional to the square of their separation:

F∝m1m2/ r2

F = – Gm1m2/r2   where G is Gravitational Constant; G= 6.67 × 10 -11Nm2kg2.

When one of the masses is of planetary size M,

F = – GMm/r2

The minus sign means that the force is attractive.

Gravitational field Strength, g

A gravitational field is the area around a mass where any other mass will experience a force.

We can think of gravitational field strength as the concentration of field lines at that point. We can see from the figure that the field strength is constant in a uniform field but drops quickly as we move further out in a radial field.

Gravitational field strength is the gravitational force exerted per unit mass on a small object placed at that point.

So, it can be written as.

g=F/M
If we use this equation for gravitational force at a distance r then,
g=- GMm/(r×r×m)
g= – GM/r^2

Gravitational Potential
Gravitational potential at a point in gravitational field is defined as the work done per unit mass in bringing a unit mass from infinity to the point.

Ø = -GM/r

It is negative due to the attractive gravitational force. Therefore, the work done by mass is decreasing its potential difference.

Orbit Period
The orbit period of a satellite is the time taken for one orbit.

The orbit period can be calculated by equating the gravitational force GMm/r2 to centripetal force mv2/r.

Geostationary satellites have an orbital period of 24 hours and are used in telecommunications and television broadcasting.