GRAVITATIONAL FIELDS

Mass

Measure of inertia or resistance to change of motion of an object.

Weight

The force of gravity acting on an object.

GFS, g

The force per unit mass on a small test mass placed in the field.

Equation for GFS

g=\frac{F}{m}

Radial field

A field in which the field lines are straight and converge (or diverge) as if a single point.

Uniform field

A region where the field strength is the same in magnitude and direction at every point in the field.

Newton’s law of gravitational attraction assumes that the gravitational force between any two point objects with mass is:

ALWAYS an attractive force.

PROPORTIONAL to the PRODUCT of the MASSES of the objects.

INVERSELY PROPORTIONAL to the SQUARE of their SEPARATIONS, r.

When \Sigma F=0

\frac{m1}{r1^2}=\frac{m2}{r2²}

Inverse Square law equation

F=\frac{k}{r²}

Gravitational Potential ENERGY

At a point in the field, its the work done to move a small test mass from infinity to that point.

Gravitational Potential

At a point in a gravitational field, it is the work done per unit mass to move a small test mass from infinity to that point.

Equipotentials

A line or surface in a field along which the electric or gravitational potential is constant.

The Potential Gradient

At a point in a field, its is the change of potential per unit change of distance along the field line at that point.

The Potential Gradient equation

gdt=\frac{\Delta V}{\Delta r}

0 to R

The GFS is 0 at the centre and increases linearly until it reaches the radius of the planet.

Beyond the radius

GFS drops off rapidly as it is inversely proportional to the distance from the centre.

Escape velocity

The minimum velocity an object must be given to escape from a planet when projected vertically from the surface.

Escape velocity equation

\sqrt{\frac{2GM}{R}}

Radial velocity equation

v²=\frac{GMs}{r}

Geostationary orbits

A satellite that stays above the same point on the Earth equator as it orbits the Earth because its orbit is in the same plane as the equator, its period is exactly 24 hours and it orbits in the same direction as the Earth’s direction of rotation.