Please help with kelpers second law?

Question

I have now fully understood the kelpers first law.
I now trying to learn kelpers second law.
i have seen that it states : A line joining a planet and the sun sweeps out equal areas during equal intervals of time as the planet travels along its orbit or in other words each "wedge" has the same surface area.
Does this mean that planets dont travel at the same constant velocity along their orbit?
What about a satellite in GEO orbit travelling in a circuler orbit, does it travel in constant velocity(speed) through out in its orbit?
another thing which is the correct spelling is it KELPER or KEPLER
Thanks alot in advance.

Answer 1

Omar -

Yes, the object will speed up or slow down relative to the planet it is orbiting, depending on the distance from that planet. When a comet in an elliptical orbit is out near the Oort cloud, it moves slowly. When it swings past the sun, it moves quickly, then slows again as it leaves the region of the inner planets.

A circle is just a special case of an ellipse (both vertices are coincident), so the rule applies to a circle as well. This results in a constant speed, which is why an object in a near-circular, geosynchronous orbit appears to stay in one place in the sky. If it were in an elliptical orbit, then as it approached apogee, the earth would spin beneath it, then it would tend to catch up as it swung in close. This would make it tough on all those TV dishes!

Answer 2

Kepler's 2nd law applies more fully to elliptical orbits. The closer a planet get to the sun, the faster it's orbital speed. But since it's closer to the sun, the pie-shape it sweeps in equal periods will be the same as when it's farther away and moving slower.

Answer 3

You're right--It is also know as the law of equal areas. When the earth is at apahelion (farther from the sun, our velocity slows, creating an imaginary long triangle with a short base. At perahelion our velocity increases (the closer to the sun the faster a planet orbits--eg. Mercury-This creates a shorter imaginary triangle with a larger base. Over the same period of time, whether closer or farther from the sun, these imaginary triangles are the same area.

It's Kepler.

Answer 4

The velocity of a planet in an elliptic orbit is not constant, it travels fastest when it's closest to the sun

A circular orbit is at constant velocity

Kepler

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Answer 5

Kepler's Law applies equally to elliptical or circular orbits.