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Example from Physics, 7.1 Kepler's Laws of Planetary Motion
Kepler’s Second Law
Figure 7.6 shows the major and minor axes of an ellipse. The semi-major and semi-minor axes are half of these, respectively.
Figure
7.6
The major axis is the length of the ellipse, and the minor axis is the width of the ellipse. The semi-major axis is half the major axis, and the semi-minor axis is half the minor axis.
Earth’s orbit is very slightly elliptical, with a semi-major axis of 1.49598 × 108 km and a semi-minor axis of 1.49577 × 108 km. If Earth’s period is 365.26 days, what area does an Earth-to-sun line sweep past in one day?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Strategy
Each day, Earth sweeps past an equal-sized area, so we divide the total area by the number of days in a year to find the area swept past in one day. For total area use . Calculate A, the area inside Earth’s orbit and divide by the number of days in a year (i.e., its period).
Solution
7.2The area swept out in one day is thus .
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