1.6. Motion in a Gravitational Field (D1 - AHL)

A gravitational field is a region where a mass experiences a gravitational force.
The strength of the field is given by gravitational field strength g.
The gravitational force between two masses is given by Newton’s Law of Gravitation

Understanding gravitational fields allows us to:

Launch spacecraft: calculate the required escape velocity
Plan orbits: Use centripetal force and Newton's law of gravitation to determine orbital speed and period.
Navigate interplanetary travel: predict how spacecraft will move under gravitational influences of planets and moons.
Use gravity assists: slingshot maneuvers that use a planet's gravitational field to increase a spacecraft's speed.

Kepler's three laws of orbital motion
Newton's universal law of gravitation for bodies treated as point masses
conditions under which extended bodies can be treated as point masses
that gravitational field strength g at a point is the force per unit mass experienced by a small point mass at that point
gravitational field lines

HL Only

Gravitational potential energy of a system is the work done to assemble the system from infinite separation of the components of the system
Gravitational potential energy for a two body system
Gravitational potential at a point is the work done per unit mass in bringing a mass from infinity to that point as given by equation
Gravitational field strength as the gravitational potential gradient equation
Work done in moving a mass in a gravitational field equation
Equipotential surfaces for gravitational fields
The relationship between equipotential surfaces and gravitational field lines
Escape speed at any point in a gravitational field as given by equation
Orbital speed of a body orbiting a large mass as given by equation
The qualitative effect of a small viscous drag due to the atmosphere on the height and speed of an orbiting body