# Optimal transfer between non-circular orbits

The orbits are given:

     alt (km)
no.  peri  apo     inc   AOP   RAAN     notes
---  ------------  ---   ----  ----   ------------------
1.  200   200     65°   ---    0°    basis orbit
2.  700   10000   65°   290°   0°
3.  800   40000   65°   270°   0°
4.  100   40000   65°   270°   0°    atmospheric decay


What would be the optimal trajectories to minimize the fuel consumption (1->2, 2->3, 3->4), considering the mission time of maximum 10 days? Impulsive maneuvers are assumed.

I supposed to use the Hohmann transfer orbit for 1->2, however, the second orbit is not circular. Also, for the 2->3, the AOP is different. I would appreciate the links where the calculations are described.

Definition of AOP: the angle from the ascending node to the periapsis.

UPDATE

I'm going to solve the Lambert problem (boundary value problem), considering 2 impulses. Is this a good idea, or there is a better way?

• By convention, perigee and apogee are normally given as altitudes above Earth's surface (or a reference sphere) rather than radius from barycenter, despite the fact that radius is far more convenient when doing the math. You might want to edit to make it clearer that your "atmospheric decay" perigee altitude is 100km. – Russell Borogove Nov 6 at 16:02