I’m trying to get my head around planetary orbits and tidal forces.
I get why we have (ocean) tides on earth, and why smaller bodies can become tidally locked to larger bodies if they’re close enough.
What I don’t get is why the rotation of the larger body has an effect on the orbital path of the smaller body.
On reading about this topic, a few sources have pointed out that Venus’ slow and retrograde rotation would cause any moon to fall in towards Venus, and either get broken up, or collide. This is thought to be why Venus doesn’t have any moons. But why is this?
[ol]
[li]The moon raises a tidal bulge on the earth.[/li][li]Because the earth is rotating faster than the moon is orbiting it, the tidal bulge “pulls ahead” of the moon. I.e. the centre of the bulge is no longer directly under the moon, but a few degrees forward of its position.[/li][li]The gravity of the tidal bulge, because it is ahead of the moon now, pulls the moon forward through gravity.[/li][li]This pull speeds the moon up (and slows the earth down). The extra speed of the moon transfers it to a higher orbit.[/li][/ol]
If the earth rotated in the other direction (and the moon still orbited in the same direction), the tidal bulge would be pulled behind the moon and would slow it down instead of speeding it up, forcing it into lower and lower orbits until it splats.
A satellite that is in geosynchronous orbit would be orbiting at exactly the speed of the tidal bulge - so the gravity from the bulge would neither accelerate or decelerate the satellite in its orbit.
A satellite below geosynchronous orbit is orbiting faster than the bulge - so the bulge pulls back on the satellite, leading it to lose altitude. This is the situation that Mars’ moon Phobos is in Phobos (moon) - Wikipedia - someday Phobos will crash into Mars due to tidal deceleration.
A satellite above geosynchronous orbit is orbiting slower than the bulge (like Earth’s moon is) and as leachim said, the gravity of the bulge thus accelerates the satellite into an even higher orbit.
Because Venus rotates very slowly, the "geo"synch orbit for Venus is very far out (probably far enough out that the Sun would interfere with any satellite that did orbit there) - thus it’s very likely that any (hypothetical) satellite of Venus would be well inside the Venus-synch orbit, and would therefore be continually slowed, and drawn into even lower orbits, leading to a crash. Thus Venus has no satellites (and the same applies to Mercury for the same reasons).
I had a read about this a while ago, so my memory is a bit muddled but here is my stab at the problem.
As we know that planets are not perfectly spherical so its not a good idea to model the gravitational forces by assuming a point mass, IE gravity not uniform. Depending rotational speed of the planet and the orbit speed of the satellite it may get pulled into the planet or swung into higher orbit.
For example in Earth-Moon system the tidal bulge rotate faster then the moons orbit due to Earth rotation so the bulge “drags” the Moon along. This results in Earth passing on so of its rotational energy on to the Moon giving it higher orbit. So the Moon is moving away from us and our days get longer. The opposite could happen as well under different circumstances.
From my understanding orbit system reach some sort of equilibrium eventually or they smack into each other or get flung out. Now my turn to pose a question, are the bulge caused by the planet rotation about its own axis or the gravitational effect of the stateliness or its it both?
OK, thanks guys it makes a lot more sense to me now.
I see why it would not be a stable situation for Venus to have a moon now. But for how long might it last? Let’s say we give Venus an earth-sized moon. Its orbital velocity is 1km/s (like our moon), opposite the direction of Venus’ rotation.
But we set its distance such that, absent tidal forces, it would be a stable orbit.
How long does it last? (don’t bother if this is too hard a question, I’m just curious)
Consider 3 small satellites in a straight line from the center of the earth, all in circular orbits. The closer one would orbit faster, the outer one slower.
So instead, we attach the 3 together with a long, thin wire so the all orbit at the same speed as the middle satellite. The closer one is going too slow, and wants to fall inward - but doesn’t, because the wire holds it. The further one is going too fast for its orbit, and wants to fly away. Essentially, he result is a string of 2 weights orbiting so that the wire always points directly to the earth. this is the equivalent of tidal bulge… the close part is pulled in, the further part is wanting to flay out.
It’s too hard for me, because while it’s easy to determine the sign of the gravity effects (i.e. whether the effect will be to push the moon out or pull it in), calculating the size of the effect depends on how much the planet and the moon deform under gravity - if both the moon and the planet are perfectly rigid, there is no effect on the orbit, and likewise if both the moon and the planet are perfectly fluid there is again no effect on the orbit, but since the planet and moon are neither, the problem gets difficult. Sorry.
Gravity has more of an effect the closer two objects are, doesn’t it? So how close could a moon get to the surface of a planet before it starts falling? I know it can’t just fall straight down because of it’s orbital speed but could you have a moon that’s orbiting at only say, 1000 miles above the planet? 100? Or would the orbit just get more elliptical and less stable until it slams into the surface?
You could have a moon orbiting at 1m above the surface for the right kind of moon and the right kind of planet. The big things would be that the moon be small enough not to raise significant tides (I’m thinking boulder-sized), and the planet not have any atmosphere to slow the moon down through friction (and of course not have any raised topography for it to slam into).
Basically, to the extent that you can approximate the planet-moon system as a Newtonian-gravity two-body problem, there is no requirement for the bodies to maintain any particular distance for the orbit to remain stable.
Yes. There is “Roche’s Limit” (Roche limit - Wikipedia) which pertains to satellites that are held together by their own gravity (as the Moon is) - get too close to the primary, and tides will tear the satellite apart.
But even that’s not a hard limit. There are currently satellites of Jupiter and Saturn which orbit within Roche’s limit. Certainly my boulder-sized satellite is held together by more than just its self-gravity.
Absolutely - I did not intend to disagree with you, but just to add more info; I agree completely boulders (and space stations, for that matter) survive tidal forces because they are held together by other forces than gravity.