# Calculating satellite movement in the arc.

From: John Locker (john@satcom.freeserve.co.uk)
Date: Thu Oct 23 2003 - 04:26:18 EDT

• Next message: Björn Gimle: "Re: Calculating satellite movement in the arc."

```Hi everyone ,

I have a question for the math minded members of the group.

Studying  recent images of the Eutelsat Hotbird satellites at 13 east I have
been trying to work out how far one of these birds moves  over the period of
an hour.
The target satellite is listed as having an inclination of 0.9
degrees.(Hotbird 3 : cat number 24931)

Comparing the position of the sat in two images taken  over 30 minutes apart
, and doing a few  rough calculations , I have come to the conclusion that
the bird drifts at a rate of about 28 km per hour  in the inclined plane.

Does this sound about right?   If it does , it suggests a geostationary
spacecraft in a near 1 degree inclined orbit will drift about 170km off the
theoretical arc in( 6 times 28 )  a 24 hour cycle.....and "Travel" nearly
700 km every day
(4 six hour legs of  170 km).

However....and this is where I seem to have messed up......if we assume a
radius to the Clarke belt of 38,000 km.... using 2 pi "r"  we get
238,761km. Divide this by 360 to find one degree of arc gives a result of
663km
...... four times my original figure of 170km....So either my calculations
are wrong , or my target satellite isnt HB3 , but one of the others , with
an inclination of about 0.25 degrees.

A small animation of the movement is available here :
http://www.satcom.freeserve.co.uk/ in the geostationary satellites section.

As you can see , I'm not exactly bright in the mathematic department , and
would apprecaite any help ironing out the figures.

Many thanks,

John [ confused ;O)  ]

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