**Previous message:**Michael McCants: "OIG Catalog Action Report for the week ending December 14"**In reply to:**James: "Perigee & Apogee Height"**Next in thread:**James: "RE: Perigee & Apogee Height"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

James asked: > Can someone explain how the Perigee & Apogee Height of a sat > is calculated from a TLE? The method required depends on the required accuracy. Assuming that approximate values at the epoch (date and time) of the elements will suffice, here is a quick method: 1. Compute semi-major axis a = (8681663.653 / n0) ^ (2/3) Where a = semi-major axis, km n0 = mean motion at epoch, rev/d 2. Compute perigee height hp = a(1 - e0) - 6371 where hp = perigee height, km e0 = eccentricity at epoch 6371 = Earth's mean radius 3. Compute apogee height ha = a(1 + e0) - 6371 where ha = apogee height, km e0 = eccentricity at epoch 6371 = Earth's mean radius Applying this method to the following satellite's orbit: USA 129 15.0 3.0 0.0 5.3 v 1 24680U 96072A 02233.10391782 .00026000 00000-0 30679-3 0 04 2 24680 97.8820 295.4481 0500000 269.2694 90.7304 14.81194991 02 where e0 = 0.0500000 n0 = 14.81194991 rev/d results in hp = 283 km and ha = 983 km, both rounded to the nearest km. To get the most accurate result, requires taking full account of Earth's oblateness, in which case the results nearest the epoch of the above elements are hp = 304 km and ha = 989 km, both rounded to the nearest km. Here is a brief explanation of the role of Earth's oblateness in determining perigee and apogee height. Due to its oblateness, Earth's equatorial radius is 6378 km and its polar radius is 6357 km (both rounded to the nearest km), so a given perigee distance relative to the centre of the Earth, will result in different perigee heights relative Earth's surface, depending on the latitude over which perigee is located. Further complicating matters, Earth's oblateness causes the long axis of a satellite's orbit to rotate (or precess) about the Earth. For the above orbit, one complete rotation takes 110 days. Still further complicating matters, Earth's oblateness causes a satellite's orbital eccentricity to oscillate as its long axis rotates. Eccentricity is greatest when the perigee is at its most northerly point, and least when the perigee is at its most southerly point. For the above orbit, the perigee and apogee distance relative to the centre of the Earth, varies over a range of about 15 km, over a period of 55 days. To fully account for Earth's oblateness, requires the use of the SGP4 and SDP4 orbital models, which are the basis of the tles, and an algorithm to compute height relative to Earth's oblate surface. The calculations require the use of a computer. Ted Molczan ----------------------------------------------------------------- Unsubscribe from SeeSat-L by sending a message with 'unsubscribe' in the SUBJECT to SeeSat-L-request@lists.satellite.eu.org http://www.satellite.eu.org/seesat/seesatindex.html

**Next message:**James: "RE: Perigee & Apogee Height"**Previous message:**Michael McCants: "OIG Catalog Action Report for the week ending December 14"**In reply to:**James: "Perigee & Apogee Height"**Next in thread:**James: "RE: Perigee & Apogee Height"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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