![](https://venautics.space/wp-content/uploads/2020/05/syntes-en-2-1024x578.png)
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.
Data
Earth’s standard gravitational parameter: mu=398 600 km3 s-2
Average Radius of the Earth: Rt=6,378km
Calculations
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
We can therefore calculate the geometrical data of the orbit that are the semi-major axis a and eccentricity e.
![](https://venautics.space/wp-content/uploads/2019/07/mecelieq16.png)
![](https://venautics.space/wp-content/uploads/2019/07/mecelieq17.png)
This data is used to calculate Sputnik’s time to circle the Earth.
![](https://venautics.space/wp-content/uploads/2019/07/mecelieq18.png)
We can also know the velocity at each point but we will be content to calculate at the extremes of the orbit that is to say the apogee and the perigee.
![](https://venautics.space/wp-content/uploads/2019/07/mecelieq19.png)
![](https://venautics.space/wp-content/uploads/2019/07/mecelieq20.png)
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.
![](https://venautics.space/wp-content/uploads/2019/07/mecelieq21.png)