A gravitational field is an area of space subject to the force of gravity. Due to the inverse square law relationship, the strength of the field fades quickly with distance.
The field strength is defined as
The force per unit mass OR
g = F/m in Nkg-1
Planets and other spherical objects exhibit radial fields, that is the field fades along the radius extending into space from the centre of the planet according to the equation
g = -GM/r2
Where M is
the mass of the planet
Potential is a measure of the energy in the field at a point compared to an infinite distance away.
The zero of potential is defined at
Potential at a point is
the work done to move unit mass from infinity to that point. It has a negative value.
The equation for potential in a radial field is
V = -GM/r
In stronger gravitational fields, the potential graph is steeper. The potential gradient is
And the field strength g is
equal to the magnitude of the Potential gradient
g = -ΔV/Δr
Graph of Field strength against distance
Outside the planet field strength
follows an inverse square law
Inside the planet field strength
fades linearly to zero at the centre of gravity
Field strength is always
Graph of Potential against distance
Potential is always
Potential has zero value at
Compared to Field strength graph,
Potential graph is less steep
Circular orbits follow the simple rules of gravitation and circular motion. We can put the force equations equal to each other.
F = mv2/r = -Gm1m2/r2
So we can calculate v
v2 = -Gm1/r
Period T is the time for a complete orbit, a year. It is given by the formula.