9.4+Orbital+motion

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9.4 ORBITAL MOTION
[|IB Practice question on Orbital Motion]

9.4.1 State that gravitation provides the centripetal force for circular orbital motion. CENTRIPETAL FORCE: Orbital motion requires an accelerating force. This is provided by the gravitational attraction of the masses.

9.4.2 Derive Kepler’s third law. Assume the orbit is circular. The source of the centripetal force is the gravitational force of the Sun on the planet. Use F=ma a nd v=2πr/T

KEPLER’S THIRD LAW: The square of the time of revolution of a planet about the Sun is directly proportional to the cube of the mean radius of the planet’s orbit.

IB PRACTICAL AIM: To use the PHET simulation [|My Solar System] to investigate the relation in Kepler's Third Law. Use Sun and Planet preset, collect data in Excel and produce graphs to demonstrate the relation. You should also consider logarithmic scales to demonstrate the relationship.

9.4.3 Derive expressions for the kinetic energy, potential energy and total energy of an orbiting satellite.

9.4.4 Sketch graphs showing the variation with orbital radius of the kinetic energy, gravitational potential energy and total energy of a satellite. 9.4.5 Discuss the concept of “weightlessness” in orbital motion, in free fall and in deep space.

WEIGHTLESSNESS IN SPACE: True weightlessness would only occur an infinite distance from the Sun (and other stars). A body in freefall (eg in orbit) experiences no reaction force from another object (such as a spacecraft) which is also falling and so the body feels weightless.

9.4.6 Solve problems involving orbital motion.