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). Components of unit vector P over 364 days, Z-> green Y->blue, X->red

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

  • 2
    $\begingroup$ 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. $\endgroup$
    – Tristan
    Commented Feb 15, 2019 at 21:55
  • $\begingroup$ 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.sstatic.net/asvzm.png) Please correct me if I am wrong or not accurate. Much appreciated. $\endgroup$
    – Ray
    Commented Feb 15, 2019 at 22:37
  • $\begingroup$ @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. $\endgroup$
    – Roy
    Commented Feb 16, 2019 at 0:04
  • $\begingroup$ What force model/propagator are you using in STK? $\endgroup$
    – Chris
    Commented Feb 16, 2019 at 0:43
  • 1
    $\begingroup$ @Chris I'm using J4Perturbation. $\endgroup$
    – Roy
    Commented Feb 16, 2019 at 1:17

1 Answer 1


What you are seeing is precession of the orbital plane due to the use of nonspherical gravity sources in your propagator -- that's what the J4 stands for. The precession is primarily due to the J2 harmonic, which represents, generally speaking, the oblateness of the body.

As to why this happens, think of it this way:

An oblate spheroid results in a gravity vector that doesn't point at the center of the planet in general. That means that the gravity vector also is not in the orbital plane. The result is that when the orbiting body is in northern latitudes, it experiences a larger than normal southern component in its gravity vector and vice versa. The constant pulling of the orbiting body towards the equator of the central body creates a net torque on the orbit, causing the orbital plane to precess about the North-South line running through the central body's poles, in much the same way a tilted toy gyroscope does.

The rate of precession depends on both the altitude and inclination of the orbit. Equatorial orbits experience none whatsoever, nor do perfectly polar orbits. The 51.6°, 400 km orbit ISS uses goes through one cycle about every two months.

This effect can be used to specific benefit. On earth, a 98°, 700ish km orbit precesses in reverse at the rate of precisely once per year. This means that an orbit with these parameters will maintain the orientation of its plane with respect to the sun, meaning that a satellite in this orbit will always pass over the same areas at the same time of day -- particularly useful for photoreconnaissance satellites. This is called a "sun-synchronous" orbit.


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