The orbit of a planet is an ellipse with the sun at one focus. The sun’s gravitational force acts along the radial line from the planet to the sun (the dashed lines in Figure 16), and by Newton’s Second Law, the acceleration vector points in the same direction. Assuming that the orbit has positive eccentricity (the orbit is not a circle), explain why the planet must slow down in the upper half of the orbit (as it moves away from the sun) and speed up in the lower half. Kepler’s Second Law, discussed in the next section, is a precise version of this qualitative conclusion. Hint: Consider the decomposition of a into normal and tangential components.

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Planetary motion a N N N a a Sun