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.