# Do all orbits have a perigee and an apogee?

Feb 20, 2017

Yes. See explanation.

#### Explanation:

Perigee and apogee are used for nearest and farthest positions of a

( natural or artificial ) satellite, from its parent planet..

Any satellite orbit is an ellipse and and the the center of the

parent space body is at a focus of this ellipse.

The eccentricity of this ellipse is $e \in \left(0 , 1\right)$.

It is 0.055, nearly, for Moon orbit.

As of now, Moon/s perigee is 36400 km and apogee is 405400 km.

ISS ( international Space Station ) orbit eccentricity is 0.00115, nearly.

ISS perigee is 400 km and apogee is 410 km, nearly.

If these orbits are scaled down to an A4 paper, in a class room, they

would look like circles, and the focus of the ellipse would be

merged with the center of the ellipse.

The distance between the focus ( the Earth's center ) and the center

of the orbit is (405)(0.00115) = 5 km, nearly.

Compared to mean distance 405 km, this is 1 : 81.

So, on an A4 paper, the graphs of satellite orbits would appear as

circles.

graph{(x^2/(4.05)^2+y^2/(4.05)^2-1) = 0 [-10, 10, -5, 5]}

The miniaturized ISS orbital ellipse with semi axes a = 405 km

and b = a, rounded to km.

If it appears here as an ellipse, we have to state that it is a

not-to-scale graph. For teaching purpose, we show it as, what it

really is. an ellipse.