MadSci Network: Astronomy

Re: What are the equ's of the postition of moon WRT earth and earth WRT sun?

Date: Wed Jul 26 20:04:10 2000
Posted By: Bryan Mendez, Grad student, Astronomy and Astrophysics, University of California at Berkeley
Area of science: Astronomy
ID: 963163092.As

Hello Josh,

In principle, this is a "simple" problem to solve. The orbit of the Earth about the Sun is an ellipse (with the center of mass between the Earth and Sun at one focus) and the orbit of the Moon is also an ellipse about the Earth (with the center of mass between Earth and Moon at one focus). In the simplest case these orbits are closed and lie in a plane. The Moon's orbit is inclined to the Earth's orbit about the Sun by about 5. This introduces some difficulty into the equations once a coordinate system is set. Also, since you want to know when they will be in a given configuration we need to introduce a parameter of time. This is done using Newton's laws of motion. In the end the equations get much more complicated. Of course, the real solar system has more complications due to gravitational interactions between planets and tidal forces between Earth, Moon, and Sun. So there are more messy details to be added, but they are small effects over short periods of time.

There are many fine planetarium programs that make these calculations for you. Several of them also allow you to view the entire solar system in 3-D. Here is a list of programs from the Students for the Exploration and Developments of Space (SEDS):

If you would like the gory details of the calculations I'd be happy to talk you through them in email.

Bryan Mendez

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