In this case, the changes in their speed are not too large over the course of their orbit.įor those of you who teach physics, you might note that really, Kepler's second law is just another way of stating that angular momentum is conserved. The orbits of most planets are almost circular, with eccentricities near 0. A planet is moving faster near perihelion and slower near aphelion.Since velocity is distance divided by time, and since the distance between A and B is shorter than the distance between C and D, when you divide those distances by the same amount of time you find that: If you look at the distance along the ellipse between A and B, it is shorter than the distance between C and D. Since the areas of these two sectors are identical, then Kepler's second law says that the time it takes the planet to travel between A and B and also between C and D must be the same. That is, the sector between C and D on the right contains the same amount of area as the sector between A and B on the left.Ĭredit: Dr. These slices that alternate gray and blue were drawn in such a way that the area inside each sector is the same. When the planet is close to perihelion (the point closest to the Sun, labeled with a C on the screen grab below), the line drawn between the Sun and the planet traces out a shorter, fatter sector between points C and D. The image below links to an animation that demonstrates that when a planet is near aphelion (the point furthest from the Sun, labeled with a B on the screen grab below) the line drawn between the Sun and the planet traces out a long, skinny sector between points A and B. The line joining the Sun and a planet sweeps through equal areas in an equal amount of time.In their models of the Solar System, the Greeks held to the Aristotelian belief that objects in the sky moved at a constant speed in circles because that is their “natural motion.” However, Kepler’s second law (sometimes referred to as the Law of Equal Areas), can be used to show that the velocity of a planet changes as it moves along its orbit! The Sun is offset from the center of the planet’s orbit.The distance between a planet and the Sun changes as the planet moves along its orbit.Kepler’s first law has several implications. Note that if you follow the Starry Night instructions on the previous page to observe the orbits of Earth and Mars from above, you can also see the shapes of these orbits and how circular they appear. The elliptical orbits diagram at "Windows to the Universe" includes an image with a direct comparison of the eccentricities of several planets, an asteroid, and a comet. For an animation showing orbits with varying eccentricities, see the eccentricity diagram at "Windows to the Universe." Note that the orbit with an eccentricity of 0.2, which appears nearly circular, is similar to Mercury's, which has the largest eccentricity of any planet in the Solar System. In reality the orbits of most planets in our Solar System are very close to circular, with eccentricities of near 0 (e.g., the eccentricity of Earth's orbit is 0.0167). Studies have shown that astronomy textbooks introduce a misconception by showing the planets' orbits as highly eccentric in an effort to be sure to drive home the point that they are ellipses and not circles. So you can think of a circle as an ellipse of eccentricity 0. In the limiting case where the foci are on top of each other (an eccentricity of 0), the figure is actually a circle. The larger the distance between the foci, the larger the eccentricity of the ellipse. ![]() In the image above, the green dots are the foci (equivalent to the tacks in the photo above). The line that is perpendicular to the major axis at its center is called the minor axis, and it is the shortest distance between two points on the ellipse. The line that passes from one end to the other and includes both foci is called the major axis, and this is the longest distance between two points on the ellipse. However, in an ellipse, lines that you draw through the center vary in length. We know that in a circle, all lines that pass through the center (diameters) are exactly equal in length.
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