# How would one obtain the longitude of satellite at the apogee?

I know that apogee longitude is a design point in Molniya orbits. Given the classical orbital elements, how can I find this value?

Molniya orbits are designed to have satellites hang out most of the time at very northern latitudes, which means having the apogee at the point furthest away from the equatorial plane.

Thus, the apogee of a Molniya orbit is 90 degrees ahead of the ascending node, so $$\Omega + 90º$$ in terms of the classical orbital elements.

I want to generalize this for any given inertial state. If you have a state in some inertial frame you could do the following with a few key assumptions/info which I will list below.

Assumptions:

• Spherical Shape Model

Known Inputs:

• Rotational Information of your center body (this can be as simple as pole orientation and a rotation rate) (check this reference from the International Astronomical Union)
• State information in some inertial frame (I am assuming it is inertial since you are characterizing it with COE)

Procedure:

1. Get your state in classical orbital elements to cartesian coordinates.
2. Given your rotational data of your body, you can construct a rotation matrix to transform your state from your inertial frame to fixed frame.
3. From this state represented in your fixed frame, you can get the azimuth (longitude) and elevation (latitude) of your position unit vector