PHY C8: Circular Orbits

What is Kepler’s Third Law?

States that the square of the periods of revolution (T²) of planets is directly proportional to the cubes of their mean distances (r³) from the Sun (T² ∝ r³).

What is the formula for Kepler's Third Law (relating to central mass M)?

T² = (4π²/GM)r³.

Does the period in Kepler's Third Law depend on the mass of the orbiting body?

No, it is independent of the mass that is orbiting.

What force provides the centripetal force for a planet/satellite in circular orbit?

The gravitational force from the central body.

What is the kinetic energy (EK) of a satellite in circular orbit?

EK = ½ mv² = GMm/(2r).

What is the potential energy (EP) of a satellite in circular orbit?

EP = -GMm/r.

What is the total energy (ET) of a satellite in circular orbit?

ET = EP + EK = -GMm/(2r).

What is the total energy of a bound system (like an orbiting satellite)?

Negative.

What is a Geostationary Satellite?

A satellite that remains at a fixed position in the sky as viewed from any location on the Earth's surface.

What conditions must a Geostationary Satellite satisfy?

1. Orbital period same as Earth's rotation (24 hrs)

2. Direction of rotation same as Earth's (West to East).

3. Plane of orbit lies in the same plane as the equator (above equator).

What is the approximate radius (r) of a Geostationary Orbit?

Approximately 42,250 km.

What are the Advantages of a Geostationary Satellite?

Continuous surveillance, easy communication for ground stations (antennas fixed), transmits/receives signals over a large area (high altitude).

What are the Disadvantages of a Geostationary Satellite?

Significant loss of signal strengths (high altitude), poorer resolution in imaging, time-lag in telecommunication.

What is a Binary Star System?

Consists of two stars that are gravitationally bound and orbit around the center of mass of their system.