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]
= (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]
where va and vp are the speeds at
the apogee and perigee respectively?
[Solution]
= 
, 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]
