I am very confused about this...please help me?

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Joe

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So if a planet has an elliptical orbit with an orbital speed of 20 km/s when it is at its AVERAGE distance from the sun, which is most likely to be the planet's speed when it is farthest from the sun:

30 km/s; 25 km/s; 20 km/s; or 15 km/s

Please help me understand this. And when you do solve it, please explain to me how you got it. Thanks
 
It would be 15 km/s. Think of it this way: a planet speeds up as it gets closer to the Sun, so it moves more slowly when it's farthest from the Sun.

A helpful analogy is to think of the elliptical orbit as an elliptical pie. You want to produce equal sized pieces of pie by cutting it into pieces with the Sun as the narrow end of each piece. "Equal pieces of pie in equal times." So the perihelion pieces will be wider than the aphelion pieces, which means that the planet has to travel faster close to perihelion.
 
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