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How does the lunar orbit compare to a circular path?
Question Date: 2012-09-16
Answer 1:

The lunar orbit is close to being a circle, but it is actually an ellipse. If the orbit were circular, the Moon would always be the same distance from the Earth, but instead, the distance varies by 13% during the orbit. On average, the Moon is 239,000 miles (385,000 km) from Earth and travels at an average of 2288 miles per hour (1023 m/s).

Circles and ellipses have similar mathematical equations:
Equation for a circle:
x2 + y2 = r2
Equation for an ellipse:
(x/a)2 + (y/b)2 = r2
The equation for the ellipse is like a circle with x and y stretched by different amounts, a and b.

An example of an ellipse and a circle are shown below.
click here

The center of the circle and ellipse are labeled with a “C”. The ellipse also has two additional points labeled F1 and F2. Each of these points is a focus of the ellipse. In the lunar orbit, the Earth is at a focus rather than the center of the Moon’s orbit.

The second diagram shows the orbit of the Moon (not to scale). When the Moon is closest to the earth, it as at the perigee and when it is farthest, it is at the apogee. The Moon’s orbit is every elliptical compared to the planets, which have orbits much closer to circles (but still ellipses).

figure 1
Figure 1: Example of an ellipse and circle (left). Diagram of the lunar orbit (right).

http://www.ifa.hawaii.edu/~barnes/ASTR110L_S03/lu narorbit.html

Images from:
http://www.algebra.com/algebra/homework/equations /THEO-20100329.lesson
http://scienceblogs.com/startswithabang/2012/05/0 5/a-feast-for-your-naked-eyes-su/

Answer 2:

You may have heard or read that the path of the Moon around the earth is elliptical not circular. This is true, but it is still reasonably close to being circular.

Because of this elliptical path, sometimes the Moon looks a little bigger and sometimes it looks a little smaller. It is not trivial to see this, but it is quite possible. Here is a picture from Wikipedia comparing the Moon at its largest and at its smallest.

See moon size comparison

One way to observe this is during a solar eclipse. Some eclipses of the Sun are total, with the Moon completely covering the Sun. While for other eclipses, such as the one this last May, the Moon was relatively far away and its apparent size was a little smaller so it did not quite cover the sun.

At its closest, the Moon is about 362,600 km away. At its farthest it is about 405,400 km away.

One might also measure the apparent size of the Moon with a telescope. For such a project see:

lunar orbit

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