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Home : Math & Science : Physics Study Guides : Gravitation : Kepler : Problems on Kepler's First Law
Problems on Kepler's First Law
Problem 1.1:
Calculate the eccentricity of an ellipse with one focus at the origin and the
other at (- 2k, 0), and semimajor axis length 3k.
[Solution]
Problem 1.2:
For an ellipse with its major axis parallel to the x-direction and its
rightmost focus at the origin, derive the position of the other focus in terms
of its eccentricity ε and k, where k is defined as k = a(1 - ε2).
[Solution]
Problem 1.3:
The general equation for orbital motion is given by:
Where the k is the same k as in the last problem: k = a(1 - ε2) = ![]() Problem 1.4:
Derive the formula for the area of an ellipse by integration.
[Solution]
Problem 1.5:
Prove that for a point on an ellipse, the sum of the distances to each foci is a
constant.
[Solution]
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