# Can an orbit rotate around a non-orthogonal axis?

I'll attempt to draw a mental example, in case images are not kind (if they are kind, you can likely skip this first paragraph). Let us say that the Earth is at it's aphelion (arbitrary choice), and that the moon is at the midpoint of it's perihelion and aphelion. That is, the moon is at the point in its orbit about Earth that is perpendicular to the line drawn from the Sun to the Earth. Now, let us take the orbit of the moon and rotate it pi/2 radians about the axis that is perpendicular to the line drawn from the Sun to the Earth (an inclination of 90 degrees). The result is an orbit that will have the moon in perpetual sunlight, never being hidden behind the Sun.

Now if the Earth orbits the sun and reaches an equinox (the midpoint between its aphelion and perihelion), the moon will instead be blocked by the earth for (somewhat less than) half its orbit, and directly in sunlight for the other half. The questions then is this: is it possible for the moon's orbit to rotate during the Earth's orbit, such that the moon is always perpendicular to the line drawn from the Sun to the Earth (or alternatively tangential to the orbit of the Earth around the Sun).

To my knowledge, it is possible for an elliptical orbit to effectively rotate in a manner that makes a "flower petal"-like pattern, so if it were orbiting on the "x/y" axes (about the "z" axis), it could also rotate on the "z" axis. However, I'm curious if it's possible for such an orbit to rotate on the "x" or "y" axis, effectively changing the axes upon which it's orbiting. (An orbit revolving around the "z" axis, but rotating around the "x" axis, would inevitable shift to revolving around a combination of the "z" and "x" axes, then solely "x", then a combination again, then solely "z" again, cyclically)

Simply, is is possible for an orbit to rotate about a non-orthogonal axis.

Here are some images to hopefully shed further light on my query.

First is the "start state" of the aforementioned orbital system. Is it possible to have an orbit that has an inclination of pi/2 radians (90 degrees), such as this: that then rotates to one of the following states: perpendicular to the Sun, or tangential to the Earth's orbit, ending up with an orbit at its perihelion that is effectively a mirror of the aphelion. As far as I'm aware (and I could be mistaken), a rotation that is orthogonal to the orbit is possible, such as this: The question is whether non-orthogonal rotation of an orbit is possible.

• The locations of the equinoxes have nothing to do with the symmetry of the ellipse. They are determined by the direction of axis of the earth's rotation, which plays a negligible role in the geometry of the earth's orbit. Aug 10 at 18:43
• The moon's orbit can't rotate like you've shown - it's like a gyroscope, the plane of the orbit won't change (conservation of angular momentum) unless there's a continuous force applied to change it. It can perfectly well have an orbit in a plane perpendicular to the earth's orbit, but the orientation of that plane will not change (other than slightly due to perturbations).
– J...
Aug 10 at 22:01
• @TonyK, you are correct, I misused the term equinox. I was thinking of the aphelion and perihelion being the summer and winter solstices respectively (at least in the northern hemisphere), and thought of the equinox as "halfway between". It'd be more accurate for me to say "one/three quarters through the orbit", or "perpendicular to the Sun compared to the start point". I appreciate you keeping me straight. @J, I thought it might be possible either due to force from the Sun, or from other solar bodies. The question was largely to determine what would be necessary should it be possible. Aug 11 at 2:53
• @DefaultCube For the moon's orbital plane to rotate continuously in sync with the earth's rotation around the sun would require a specific continuous thrust applied to the moon normal to its orbital plane.
– J...
Aug 13 at 13:38

Sort of. They rely on additional forces to move the orbit around/create points of stability.

Sun synchronous orbits (SSO) use the oblateness of the Earth around the equator to change the satellites orbit over time so that over time it maintains the same relative position the Earth-Sun System. But there is still part of the orbit that will end up being eclipsed by the Sun because of the inclination and the orbital height of a SSO. (explanation vid if you're curious)

Lagrange point halo orbits orbit the combined Earth-Sun System. If you can find a constant significant force, then you can probably create an weird orbit that stays in the same place. For instance with solar sails you could probably design a satellite to orbit consistently above the ecliptic plane (or at widen the range of area of stable Lagrange orbits).

• Can't find it now but somewhere I read about a concept of using a solar sail above a pole to keep a satellite above the pole. Aug 10 at 14:18
• @user253751 That (solar sail to keep above the pole) is called a statite. It's not in orbit at all. Aug 10 at 20:40
• I think non-eclipsing SSO is pretty much possible. It can always go over the night/day boundary on Earth. Aug 10 at 21:53

If your elliptical orbits are around realistic rotating bodies like the Earth or Jupiter or anything with an equatorial bulge, then it will precess.

The most common kind of precession we hear about is around the Earth's axis. For example in a Sun-synchronous orbit the plane of an inclined orbit will precess around Earth's axis once per year to maintain its relationship with the direction of the Sun.

But that's a rotation of the inclined orbital plane; the orbit pretty-much stays the same within the plane.

### You can also get the orbit to precess within its plane!

From

here are plots of the Juno spacecraft around Jupiter with a roughly 90 degree polar orbit. In this case the apsidal precession is in-plane:  above x2: plots of Juno's orbit around Jupiter as described above, data from JPL Horizons.

• I think the sun-synchronous orbit is exactly what OP is looking for. Aug 10 at 18:05
• @2012rcampion after a night's sleep and morning coffee I think that you are right. Juno's in-plane recession is the "orthogonal" situation in the question, and an inclined orbit's precession around the central body's rotation axis due to equatorial bulge is a "non-orthogonal" to the orbital plane.
– uhoh
Aug 10 at 23:47

To my knowledge, it is possible for an elliptical orbit to effectively rotate in a manner that makes a "flower petal"-like pattern, so if it were orbiting on the "x/y" axes (about the "z" axis), it could also rotate on the "z" axis.

Neither this, nor the setup you propose, are possible in any conic section based models for orbital mechanics, like in Kepler orbits, the two-body problem, or the patched conics approximation.

Once you allow for perturbations, any kind of orbital deviation can be achieved. But these effects are usually much smaller than the acceleration due to gravity from the primary parent body.

Some examples of such perturbations:

• The Moon's orbit has changing axis due to being significantly influenced by both the Sun and the Earth. n-body systems are complex systems.
• Mercury's orbit is precessing due to relativistic effects.
• LEO satellites have changing axis due to drag and the oblateness of the Earth.