How does Orbital Decay work? And why?

[Dr. Kerbal]

Why does orbital decay take place?

Edited February 11, 2021 by Dr. Kerbal

[JoeSchmuckatelli]

8 minutes ago, Dr. Kerbal said:

Why does orbital decay take place?

Not the sharpest tool in this shed - but AFAIK - its atmospheric drag as the primary culprit

 

"Space" as we know it, does not exactly have a sharp boundary with the atmosphere - thus some satellites can be in orbit, in space, but still experience atmospheric drag.  

 

Edited February 11, 2021 by JoeSchmuckatelli

[Apelsin]

What Joe said, plus gravitational influence of other bodies (ex: the moon). KSP uses the patched conics model, which ignores everything except the strongest influence at a given location (SOI). See the principia mod for a more realistic approximation of actual orbital mechanics.

[Pds314]

1 hour ago, JoeSchmuckatelli said:

Not the sharpest tool in this shed - but AFAIK - its atmospheric drag as the primary culprit

 

"Space" as we know it, does not exactly have a sharp boundary with the atmosphere - thus some satellites can be in orbit, in space, but still experience atmospheric drag.  

 

This is true in very low orbits but at intermediate altitudes, there are tidal effects of even slightly non-round bodies that begin to dominate as concentrations of mass in the object fly by underneath and interact gravitationally with the satellite. Objects in low lunar orbit without constant course corrections will eventually collide with the moon due to its non rounded shape.

Objects above a synchronous orbit will do the opposite, being slightly boosted by the non-round shape of the parent body, at least if their orbit isn't highly inclined/retrograde.

Unfortunately you cannot synchronously orbit the moon because it is tidally locked to Earth.

Edited February 11, 2021 by Pds314

[kerbiloid]

And solar light pressure.

[K^2]

1 hour ago, Pds314 said:

This is true in very low orbits but at intermediate altitudes, there are tidal effects of even slightly non-round bodies that begin to dominate as concentrations of mass in the object fly by underneath and interact gravitationally with the satellite. Objects in low lunar orbit without constant course corrections will eventually collide with the moon due to its non rounded shape.

I might have to ask for citation or strong argument on this. Non-spherical shape results in perturbed potential, but it's still a conservative potential, so while your orbit might drift, the energy isn't going to change, so no orbital decay.

The reason why Moon is being tidally accelerated by Earth isn't just because Earth is slightly non-spherical, but because Moon's gravity is deforming the Earth as it goes around. It's the time-dependent changes to the potential that leads to energy of an orbit not being conserved.^*

Does a satellite deform Earth or Moon as it orbits? Technically, yes. But that deformation is going to be so minute as to be essentially irrelevant. So while yes, there are tidal forces acting on a satellite always, they aren't going to be changing the semi-major axis of the orbit. In principle, you can have eccentricity drift, because that's coupled to angular momentum, which is conserved only for spherically symmetrical potentials. So in principle, your periapsis might drop low enough for collision, but even that seems unlikely for any practical setup that didn't have high eccentricity to begin with.

You are correct that a lunar satellite will eventually crash into Moon's surface, but it's because space is far from empty even up there. There's stuff evaporating from Moon's surface all the time, meaning that it has a residual atmosphere. But even without that being the case, there is solar wind putting all kinds of particles into interplanetary space. So there will always be drag of some kind. I just wouldn't count tidal forces as one of the sources for anything not massive enough to have its own gravity of note.

 

^* If you (or anyone reading) want a really deep dive into mathematics of conservation laws in orbital mechanics, Constants of Motion is a good start, and typical way of deriving these for orbital motion is via Hamilton-Jacobi Equation. And if all of that is Greek to you, good intro texts are Classical Dynamics of Particles and Systems by Marion and Thornton or Course of Theoretical Physics - Volume 1: Mechanics by Landau and Lifexcrementsz. Both assume that you have familiarity with basics of Newtonian physics and partial differential equations, but otherwise very readable, and first chapter of either is basically all you need for background. Landau Lifexcrementsz book actually does a deep dive into Hamilton-Jacobi in the last chapter. But then again, if you read and understand that entire book, you'll understand orbital mechanics better than most NASA engineers. Classical Mechanics by Goldstein, Pool, and Safko has a less compressed version of Hamilton-Jacobi in their final chapter, and is probably the text most NASA engineers actually read.

[Pds314]

Hmm... I was sure that the effect scaled down to even small satellites but that could be wrong. Obviously the ISS doesn't greatly distort Earth the way that, say, the moon does. I thought I remember reading a convincing argument that mascons would actually sap momentum from lightweight objects into the rotation of the planet by distorting their orbital path but it's been probably half a decade since I looked into it.

[mikegarrison]

I am pretty sure it's got something to do with forgetting to brush your orbits for at least two minutes twice a day.

[K^2]

17 minutes ago, Pds314 said:

Hmm... I was sure that the effect scaled down to even small satellites but that could be wrong. Obviously the ISS doesn't greatly distort Earth the way that, say, the moon does. I thought I remember reading a convincing argument that mascons would actually sap momentum from lightweight objects into the rotation of the planet by distorting their orbital path but it's been probably half a decade since I looked into it.

So like I implied before, in order for the energy of the satellite to change, you need a potential that varies in time. And even then it's not so simple. So for example, as Earth goes around the Sun, the tidal bulge rotates, so that's technically a time dependence, but I can trivially go into a rotating coordinate system where Sun stays still and the satellite will pick up an additional centrifugal and Coriolis forces, which will certainly affect the trajectory, but they can still not change the total energy of the craft. Coriolis forces never do work and centrifugal force is time-independent. So for a single planet orbiting a sun, energy of satellite in planet's orbit can never change due to any gravitational interaction. And that's even if planet is very asymmetrical one and tidal forces are significant. It can lead to some wild orbits, but they will maintain constant energy, and therefore, stay around roughly constant semi-major axis.

Now, we do also have the Moon and a tidal bulge and forces due to it. Because the moon goes around the Earth a lot quicker than the two go around the Sun, the two frequencies are different, and now we can say that the potential will have time dependence in any coordinate system. That's technically a foot in the door, but all that says is that energy can vary. It's far cry from showing that energy is going to be consistently increasing or decreasing for any choice of orbit. Usually, if you have a periodic perturbation like that, average energy will stay the same, and you'll just have an additional source of precession. But maybe you can come up with some wild resonance, which is why I've asked for a reference. It'd be interesting to see. But I do doubt that anything like this is worth considering for any practical case.

[paul_c]

Decay =/= perturb

 

[magnemoe]

2 hours ago, Pds314 said:

This is true in very low orbits but at intermediate altitudes, there are tidal effects of even slightly non-round bodies that begin to dominate as concentrations of mass in the object fly by underneath and interact gravitationally with the satellite. Objects in low lunar orbit without constant course corrections will eventually collide with the moon due to its non rounded shape.

Objects above a synchronous orbit will do the opposite, being slightly boosted by the non-round shape of the parent body, at least if their orbit isn't highly inclined/retrograde.

Unfortunately you cannot synchronously orbit the moon because it is tidally locked to Earth.

Think the issue with the moon is more regions with higher gravity, I guess this is because large iron asteroids has impacted the surface so you get spots with high mass and therefor higher gravity. 
At higher orbits this effect is far more noticeable 

[kerbiloid]

https://en.wikipedia.org/wiki/Mass_concentration_(astronomy)

[cubinator]

4 hours ago, K^2 said:

I might have to ask for citation or strong argument on this. Non-spherical shape results in perturbed potential, but it's still a conservative potential, so while your orbit might drift, the energy isn't going to change, so no orbital decay.

I can imagine the orbit getting more elliptical, driving the periapsis into the Moon without changing its energy. Remember, energy is equal to the area of the ellipse.

4 hours ago, K^2 said:

There's stuff evaporating from Moon's surface all the time, meaning that it has a residual atmosphere. But even without that being the case, there is solar wind putting all kinds of particles into interplanetary space. So there will always be drag of some kind. I just wouldn't count tidal forces as one of the sources for anything not massive enough to have its own gravity of note.

I don't think that's the dominant effect. Exhaust from the LEM rocket engines caused a significant addition to the lunar atmosphere. Sure, there is solar wind and photon pressure, but the reason Moon orbits are especially unstable is that the Moon has irregularities in its mass distribution. The largest one that comes to mind is the planetoid chunk buried under the Aitken basin.

[wumpus]

12 hours ago, Apelsin said:

What Joe said, plus gravitational influence of other bodies (ex: the moon). KSP uses the patched conics model, which ignores everything except the strongest influence at a given location (SOI). See the principia mod for a more realistic approximation of actual orbital mechanics.

I'm pretty sure that air resistance is the key to any decay that you might live long enough to see fall out of orbit (Vanguard 1-c was the second satellite the US launched.  It is expected to decay to Earth in 2240).  The moon will certainly mess with any satellite outside of Low Earth Orbit, and geosynchronous satellites need some sort of engine to remain in position, but not really prevent decay.  Those geosynchronous satellites are required to boost to a "graveyard orbit" somewhat higher than geosync and are expected to remain there indefinitely.  At that point, it seems much more likely that lunar effects are more likely to eject the satellite into solar orbit than to send it back to Earth.  I'd also suspect that any case where lunar gravity > air resistance is more likely to eject the body from orbit rather than reduce Pe to sufficiently within the atmosphere for inevitable decay, but have no real evidence for it.

[magnemoe]

16 minutes ago, wumpus said:

I'm pretty sure that air resistance is the key to any decay that you might live long enough to see fall out of orbit (Vanguard 1-c was the second satellite the US launched.  It is expected to decay to Earth in 2240).  The moon will certainly mess with any satellite outside of Low Earth Orbit, and geosynchronous satellites need some sort of engine to remain in position, but not really prevent decay.  Those geosynchronous satellites are required to boost to a "graveyard orbit" somewhat higher than geosync and are expected to remain there indefinitely.  At that point, it seems much more likely that lunar effects are more likely to eject the satellite into solar orbit than to send it back to Earth.  I'd also suspect that any case where lunar gravity > air resistance is more likely to eject the body from orbit rather than reduce Pe to sufficiently within the atmosphere for inevitable decay, but have no real evidence for it.

This, satellites in high orbits like GTO or sun synchronous need to adjust their orbit because of various gravity pulls because they need to stay in the position to do their work. 
Low earth orbit is cheap and also lower on radiation so you go here if you just want to be in space. Using an ion engine to keep attitude is cheap. 

[K^2]

5 hours ago, cubinator said:

Remember, energy is equal to the area of the ellipse.

I don't know if you're mis-remembering something, but it's trivial to show that this isn't true. Take a brick and drop it with zero orbital velocity from some apoapsis height r. The energy is -μ/r, the area of ellipse is zero. In fact, energy is always -μ/2a. So it depends on the major axis only. Doesn't change your point, but it seemed worth pointing out.

But yeah. I've mentioned the fact that eccentricity can drift and that can cause collision with the surface. It's not really de-orbiting, but that just makes the crater bigger, so maybe we shouldn't be splitting hairs on this one. And while it seems rather unlikely for any given orbit, it can technically happen. Perhaps, I should even say will eventually happen, but it should take an exceptionally long time unless you're intentionally trying to chose an orbit which will quickly drift to collision.

[cubinator]

3 hours ago, K^2 said:

I don't know if you're mis-remembering something, but it's trivial to show that this isn't true. Take a brick and drop it with zero orbital velocity from some apoapsis height r. The energy is -μ/r, the area of ellipse is zero. In fact, energy is always -μ/2a. So it depends on the major axis only. Doesn't change your point, but it seemed worth pointing out.

You're right, I must have been thinking of some other things. Let me try to get it right this time: 

 

E=−GMm/(2a).

So, the correct statement is: Orbits with the same semi-major axis have the same energy, even as eccentricity changes. 

And area varies by cos(e) or something along those lines.

Edited February 11, 2021 by cubinator