# Why is Angular Momentum of Satellite Rotating in ECI Frame?

Summary: The angular momentum per unit mass of satellite is rotating in ECI x-y plane and I can't understand why. I'm very new to orbital mechanics.

What I'm doing: I'm taking the cross product of satellite position by satellite velocity in ECI frame; Turn this vector into a unit vector and plotting components of this unit vector over one year.

$$P = \frac{Pos \times Vel}{|Pos|*|Vel|}$$

Satellite orbit data is generated using AGI STK's orbit wizard with the following parameters: Circular orbit, Inclination 75 deg, Altitude 700 km, RAAN: 30 deg

What I'm expecting: Since the frame is ECI, I was expecting the orbit plane to be constant over time and so the unit vector orthogonal to this plane (P) to be constant as well.

What I'm observing: The orthogonal unit vector P is rotating in x-y plane suggesting orbit is rotating around the earth.

The graph shows the components of unit vector P ($$\hat P_z$$ : green, $$\hat P_y$$ : blue, $$\hat P_x$$ : red) over 364 days ( horizontal axis is in UNIX time format i.e. seconds).

Question: How is this constant rotation explained? What is the rate of change?

• What are the units on the graph? Is this actual state vector data from an actual satellite? Inclined orbits do precess, primarily as a function of the $J_2$ gravity harmonic associated with Earth's equatorial bulge. That appears to be what this looks like, but I don't really know what the time frame I'm looking at is. Feb 15, 2019 at 21:55
• Having the same issue. I am guessing in ECI frame, the change pattern of the angular momentum P is a circle like the attached graph. ![sat position](i.stack.imgur.com/asvzm.png) Please correct me if I am wrong or not accurate. Much appreciated.
– Ray
Feb 15, 2019 at 22:37
• @Tristan thanks for your comment. I updated the question with orbit information and time frame. Specifically this is a circular orbit with 75 degrees inclination over 364 days. I would appreciate it if you can explain this precession a bit more.
– Roy
Feb 16, 2019 at 0:04
• What force model/propagator are you using in STK? Feb 16, 2019 at 0:43
• @Chris I'm using J4Perturbation.
– Roy
Feb 16, 2019 at 1:17