Gravitational fields

Gravitational Potential and Orbital Motion

Work done is:

  • Positive when the displacement is in the same direction as the force

  • Negative when the displacement is in opposite direction to the force

  • Zero when the displacement is perpendicular to the force

Zero work is done as we move an object along one of these equipotential lines

ΔGPE = mgΔh only in a uniform field

IN A RADIAL FIELD:

Gravitational Potential:

This is the work done to bring a unit mass from infinity to a defined point in the field

V = -GM/r

where V = Gravitational potential (Jkg∧-1)

G = gravitational constant

M = mass of object producing the field

r = distance from the centre of the object

By convention, the formula is negative because the object is moving away from the field lines

The maximum value of GPE is 0 (at infinity)

Gravitational Potential Energy (Ep)

Ep = - GMm / r

Small m is there because it's no longer a unit mass

Graphs we need to know

Gravitational Potential against Distance

Distance isn't only from Earth's centre (any planetary body)

  • The graph is always negative

  • The tangent to the curve at any point is the gravitational field strength, g at that point.

Gravitational Field Strength against Distance

Force Distance Graph

ALL THESE GRAPHS ARE INVERSE GRAPHS

Derivations

Geosynchronous orbit

  • Also known as inclined orbit (at an angle to the equator)

  • Geosynchronous satellites orbit around the planet at the same speed at which the planet rotates around its axis.

  • If the satellite is orbiting Earth, the orbital period is 24 hrs

Geostationary Orbit

  • Positioned above the equator

  • Also orbits around the planet at the same speed at which the planet rotates around its axis.

  • If the satellite is orbiting Earth, the orbital period is 24 hrs

  • The satellite appears stationary from a position on Earth and will be visible all day