Kepler's Third Law
Kepler's third law defines the ideal relationship between elliptic orbital time
and mean orbital distance. It states that the square of the orbital time is porportional to the cube of the mean orbital distance. In terms that make sense numerically, this law can be expressed in the form of a simple, compact mathematical equation:
If it takes time (t1) to orbit a body at mean distance (d1), then it
would take time (t2) to orbit the same body at mean distance (d2).
Here, the mean orbital distance refers to the mean taken over the eccentric anomaly
of the orbit, which in this case, equates to the semi-major axis, or 1/2 the longer (major) axis of the orbital ellipse.
The above program is based on this equation, where time and distance
may be expressed in any convenient units.
The body being orbited generally refers to the sun, a planet or a star,
compared to which, the mass of the lesser satellite is insignificant.
Knowing any three variables, we may directly compute the unknown fourth
variable. The following equations, derived from the above, are used by
the program to compute the individual unknown variables.
© Jay Tanner - PHP Science Labs - 2012
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