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I was watching a Fehnman lecture on YouTube, where he used Kepler's second law as an example of something he was explaining.

He was showing geometrically why a line joining a planet and a Sun sweeps out equal areas during equal intervals of time.

I followed his explanation for when the Sun has no pull on the planet. Then, I'm just solving the area of obtuse angles.

His explanation begins here and he loses me when he says that the triangular area swept out when the Sun has a force has the same height.

I understand that both triangles have the same base, but I don't understand how to see that they're the same height.

His explanation was, "...and do they have the same altitude? Sure, because they're included between parallel lines and so they have the same altitude."

That doesn't explain it for me, and so can someone show me how it's done?

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    If you take the baseline to be one of the parallel lines, then the corresponding heights of the triangles is just the distance between the two parallel lines. (the "other" parallel line passes through the vertices of the triangles opposite the baseline). Drawing a picture should help.2012-02-14
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    @David, since the picture is in the video, it didn't appear to help the OP. The key point of confusion must be that in the first half of the argument we too the _orbit_ to be the base of the triangles, and in the second hand we switch to considering the middle one of the sun-planet radii to be the base.2012-02-14
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    @HenningMakholm so if the middle of the sun-planet radii is now the base, I can see that the height is the 1 second measure, since the lines are parallel. But then I'd have to show that the 'radius base' is the same as the height of the previous triangle, for the areas to be the same. That's what I don't know.2012-02-14
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    You know what? I just got it. I had to look at it in a different way. I was trying to see how the base of the 3nd triangle was the same as the height of the 1st triangle. But what I really had to do was see that the base of the 3rd triangle was the same as the base of the 2nd triangle. Then I could say that the 3rd triangle had the same area as the 2nd triangle, and I already knew that the 2nd triangle had the same area as the first. Done. Thanks!2012-02-14

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