# Gravitational Fields

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Gravitational Fields

Newton’s law of gravitational force F:

‘Any two point masses attract each other with a gravitational force that is directly proportional to the product of their masses and inversely proportional to the square of their separation.’

F=(-)GMm/r^2

Kepler’s 3rd law:

Kepler showed that, for a planet orbiting the Sun, the relationship between the orbital time period T and the orbital radius r is given by:

Orbital time period:

Gravitational field strength g:

The strength of a gravitational field at a point is the force per unit mass (acting on a test mass placed at that point in a field).

( For small heights (h) : acceleration due to free fall and gravitational field strength are the same.)

gravitational field strength in a radial field:

gravitational field lines:

These represent the magnitude and direction of force per unit mass at a point in a field.

Field is always attractive, hence arrows point towards the centre of mass

Equipotential surfaces

Perpendicular to field lines.

V=0 at infinity.

So potential values are always negative.

Gravitational potential V:

The gravitational potential V at a point is the

work done ΔW per unit mass m

(or the change in potential energy ΔE_per unit mass m)

to move a mass m from infinity to that point.

Change in Gravitational potential energy or work done

Total energy