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  Home : Math & Science : Physics Study Guides : Gravitation : Kepler : Problems for Kepler's Second Law
Kepler and Gravitation
  
 
Problems for Kepler's Second Law
Problem 2.1: What is the angular momentum of Mercury when it is located at
= (45×106km, 57×106km, 0)
relative to the sun and has velocity
= (140m/s, 125m/s, 0)
, and a mass m = 3.30×1023 kg? [Solution]
Problem 2.2: Use Kepler's Second Law to explain why planets travel faster near the sun. [Solution]
Problem 2.3: If an Inter-Continental Ballistic Missile (ICBM) is launched into an elliptical path, where in its trajectory will it be traveling the slowest? [Solution]
Problem 2.4: Mercury has an aphelion distance of 69.8×106 kilometers and perihelion distance of 45.9×106 kilometers. What is the ratio
where va and vp are the speeds at the apogee and perigee respectively? [Solution]
Problem 2.5: Beginning with
=
, which is just an expression of Kepler's Second Law, prove Kepler's Third Law. Use the facts that A, the area of an ellipse, is equal to πab and that the semimmajor axis length is given by a =
. [Solution]
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