# Gravitational Fields

- Created by: Megan mcHarron
- Created on: 19-10-18 09:23

**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.

**Potential Gradient **

**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**…

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