36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

Objective:Study the orbital parameters of a geostationary satelliteand its orbit after a misfiring of the apogee engine.

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

Definitions of energy and angular momentum

Question 1: Determination of orbital parameters,velocity, energy, and angular momentum of a satellite in a

geoestationary orbit.

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

Question 2: Determination of orbital data after a misfiring of the engine; orientation, maximum and minimumradii, and period.

Third Kepler law

Provided as a hint

m

M

rl

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

Energy conservation.

Angular momentum conservation.

Polar equation for conics (hint).

Determination of the minimum boost parameter that allows the satellite to escape and the resulting orbital data (orienta-tion, impact parameter, minimum distance to the Earth).

Questions 3 and 4:

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

Physical requirements:

Mechanics:

Newton’s laws. Conservation of energy and angular momentum. Centripetal acceleration, Kepler’s laws.

Geometry of conics.

Mathematical hints:

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005

On the record:

XI International Physics Olympiad (Moskow, 1979):....Moon landing.

XXX International Physics Olympiad (Padova, 1999):....A space probe to Jupiter.

(Precedents in previous editions)

36th International Physics OlympiadTheoretical competition, Tuesday July 5, 2005