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# RE: Osculating element sets and secular effects

```Some good humorous answers -- let me try to be factual

> I have seen the terms "osculating elements" and "secular effects"
> mentioned in orbital mechanics texts, but can't for the life
> of me figure
> out how kissing can possibly have anything to do with
> satellite tracking.
> And if there are secular effects, are there also religious effects?
>
> Where do these terms come from?
>
> Joe KM1P

In celestial mechanics the "two-body" problem can be solved exactly -- the
orbit of a satellite around a single, isolated object is completely
predictable. Except for effects like atmospheric drag, the orbital elements
from "now" can forecast where a satellite will be into the distant future.

But when three or more objects are involved in the system, the orbital
properties cannot be perfectly predicted. If you have perfect knowledge of
the state of the "N-body" system, then the future can be calculated only by
numerical integration of the equations of motion. An example of this problem
that we all remember is that AO-13 was launched into what was thought to be
a stable orbit (AO-13 and earth = two bodies), but the combination of the
AO-13 inclination and eccentricity and the gravitational tugs of the sun and
moon (making for an N=4 body system) caused the satellite to crash in 10
years.

The ancient astronomers (i.e., those in the era after Newton but before Cray
computers) worked out a "patch" on the 2-body problem that allowed for an
approximation to the N-body problem. It involved having the proper orbit
"kissed" by the other planets. This resulted in orbits that change with time
reflecting the effects of the other bodies in the system. Therefore
osculating orbits change with time.

To get more detail than you ever wanted to know, do a Google search on
"osculating elements". The first hit you get will be a pointer to
http://www.xylem.f2s.com/kepler/osculate.html which will give you more
detail than you ever wanted to know!

73, Tom

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