On October 26, 1957, a modified semiorka R-7 ballistic missile opened a page of history by launching the first satellite in history, sputnik-1. We will use this example to use the calculations related to the elliptical orbit.
Earth’s standard gravitational parameter: mu=398 600 km3 s-2
Average Radius of the Earth: Rt=6,378km
As the altitude is not usable as such, it is converts altitudes into a radius.
Perigee radius: rp=hp+Rt=215+6,378=6,593km
Apogee radius: ra=ha+Rt=939+6 378=7 317km
This data is used to calculate Sputnik’s time to circle the Earth.
With a perigee at only 215km altitude, Sputnik was braked at each pass. The velocity decreased, the semi-major axis to decrease and the orbit became circular. After 3 months the perigee velocity fell below the minimum orbital velocity at that altitude (calculated below) and could no longer maintain its orbit, it disintegrated in the atmosphere.