How are the properties of a gravitational field quantified?
How does an understanding of gravitational fields allow for humans to explore the solar system?
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.
that bodies moving along a circular trajectory at a constant speed experience an acceleration that is directed radially towards the centre of the circle—known as a centripetal acceleration
that the motion along a circular trajectory can be described in terms of the angular velocity ω which is related to the linear velocity v by the equation as given by v = 2πr T = ωr.
that circular motion is caused by a centripetal force acting perpendicular to the velocity
that a centripetal force causes the body to change direction even if its magnitude of velocity may remain constant
Situations should involve both uniform and non-uniform circular motion in both horizontal and vertical planes.
Analysis of forces on bodies in non-uniform circular motion in a vertical plane at points other than the top or bottom is not required.
For calculations involving orbital motion the orbits will be assumed to be circular.
Newton’s universal law of gravitation should be extended to spherical masses of uniform density by assuming that their mass is concentrated at their centre.
Determination of the resultant gravitational field strength will be restricted to points along a line joining two bodies.
Sketching and interpretation of gravitational field lines is required.
Gravitational potential is defined as being zero at infinity.
Problems may include, but are not limited to, determining the: speed to maintain orbit, changes in energy when a satellite changes orbit, energetics of a satellite going into orbit around a non-rotating planet starting from rest on its surface, energy conditions for an orbiting satellite to escape the gravitational influence of a planet.
Gravitational fields will include the radial fields around point or spherical masses and the (assumed) uniform field close to the surface of massive celestial bodies and planetary bodies.
The orbital motion of a satellite around a planet is restricted to a consideration of circular orbits.
An ability to map fields using potential is required.
All students should be able to deduce Kepler's third law using centripetal and gravitational force relationships for circular orbits.
Simulations: