Kepler’s second law is a consequence of conservation of angular momentum. Angular momentum equals the (transverse speed of the planet) x (mass of the planet) x (distance from the sun). The transverse speed is the amount of the planet’s orbital velocity that is in the direction perpendicular to the line between the planet and the Sun. If the distance decreases, then the speed must increase to compensate; if the distance
Kepler’s second law is a consequence of conservation of angular momentum.
(mass of the planet) x (distance from the sun). The transverse speed is
the amount of the planet’s orbital velocity that is in the direction perpendicular to the line between the planet and the Sun. If the distance
decreases, then the speed must increase to compensate; if the distance
increases, then the speed decreases.
(a) Using this information derive an expression for how much greater
a planet’s velocity is at perihelion compared to aphelion. Hint: At
perihelion and aphelion all the planets orbital velocity is perpendicular
to the line between the planet and the Sun.
(b) If Mars has an orbital speed of 25 km/s at perihelion, what is its
orbital speed at aphelion?
(c) What is the ratio between the kinetic energy at perihelion and aphelion?
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