These weird questions sometimes occur to me when I am sleeping - clearly I need a life!
Are there any physical laws governing which way something can orbit our planet? It is always east to west? Could it go west to east? Could it orbit the planet north to south?
All sorts of orbits are possible in all sorts of directions, not necessarily circular with the Earth in the middle, either.
One thing that isn’t possible, however, is an orbit around the Earth that would make the object appear to move from east to west once every 24 hours, because that’s actually more or less the same as staying still, while the earth rotates below - such an object would fall like a stone, unless some force was acting on it to keep it aloft.
I feel obliged to add that any object in orbit is falling like a stone, but also moving parallel to the Earth’s surface so that it never gets any closer. That’s what an orbit is. At the risk of being whooshed by Mangetout, the Sun is following such an orbit. (Technically, the Sun and the Earth are orbiting around each other.)
To answer the OP, any direction or angle of orbit is possible. Many satellites have a polar orbit, for example, where they circle the North and South pole, following a line of longitude. Others are geosynchronous, meaning they follow a line of latitude.
Not quite; that orbit has a period of 360-something days, not 24 hours.
Even the one Mangetout pointed out?
Good call on all the orbits really being an “infinite” fall.
Is it true that the plane of the orbit must include the center of the earth? In other words, it would be impossible to have a satellite perpetually directly over the tropic of Cancer for example.
And wouldn’t orbits above the geosynchronous radius have what would appear from earth to be retrograde motion (rise in west, set in east)?
No, the Sun appears to move from east to west in (about) 24 hours, which was what the proposition was. A satellite of Earth not in orbit around the Sun would not need to be 93,000,000 miles away to have an orbital period of one Earth year, of course; I make it about 860,000 miles as a rough guess. That gives it a transit time across the sky of one solar day; one sidereal day is harder to manage. 
Yes, that’s quite right. Gravity is always pulling the satellite towards the centre of the Earth, so it must always trace a Great Circle route (in any of an infinite number of orientations). If it were trying to orbit over the Tropic of Cancer there would always be a gravitational pull to the southwards.
Yes.
Basically, Kepler’s Laws apply to an object orbiting around another (much larger) object. So the orbit of a satellite is an ellipse, with the Earth at one of the foci. (Actually it’s slightly more complex than that, because the earth isn’t a point mass, but it’s pretty close.)
Anyway, that’s why you can’t put a broadcast satellite above North America. You have to put it in a geostationary orbit above the equator, or put it in an inclined orbit so it moves north/south over the course of the day. (Sirius uses such an orbit, so at least one of their satellites are north of the equator at any time, i.e. higher up in the sky than geostationary satellites.)
Yes. But if Earth were all by itself, the satellite would have to be infinitely far away for it to rise/set every 24 hours. It basically means the satellite is staying still in space.
However if we take into account the sun, there are points in space where the gravity from the sun and earth interact to create stable “orbits,” called Lagrange points. A satellite in a Lagrange point would rise in the east and set in the west every 24 hours. In fact there are a few such satellites, mostly astronomical satellites.
Still missing the point, and on purpose now. The point is: an orbit that is nothing more than an illusion fostered by the rotation of the earth on its axis is not possible.
The OP is clearly referring to objects that orbit our planet in comparatively close proximity; artificial satellites, maybe also the moon.
:smack:
I see what Mangetout is saying. Yes, the Sun is orbiting the center of mass of the Earth-Sun system - but that orbit manifests as the change in the position of high noon from one day to the next (as seen here.)
So we want something orbiting with the Earth such that it appears to move across the sky once a day. Without going through the math, I think the existence of the Moon is proof that it’s possible. The rising and setting of the moon is due to the Earth’s rotation, yes, but the Moon does go around the Earth once a month. So by adjusting the distance you could get that down to once a day. (Kepler’s third law says the square of the period is proportional to the cube of the semi-major axis of the ellipse.)
scr4, putting a satellite at a Lagrange point (which just to be clear, is actually an orbit), would create the same illusory once a day rotation as the Sun has. It would move across the sky because the Earth is rotating, not because it’s going around the Earth once every 24 hours, because the very definition of a Lagrange point is that it’s stationary relative to the Earth.
shrug I’m sorry you want to take it that way.
The orbit Sirius uses is called a Highly Elliptical Orbit which increases the dwell time (i.e. the total part of the sidereal day it spends above a particular latitude) to give maximum access to the satellite from ground. There are also specific classes of HEOs like Molniya orbits and Tundra orbits that accomplish specific dwell requirements.
A satellite in an Earth-Moon Lagrange point would be in orbit of the Earth just as the Moon is. (Technically, it’s orbiting the common barycenter of the system as are both bodies, but this is generally dismissed for first order analysis.) A satellite at a Sun-Earth lagrange point would be in orbit of the Sun, not the Earth.
Also note that Keplerian motion only applies to orbits of an essentially massless satellite aboud a point mass. Kepler doesn’t account for the effect of local gradients, gain or loss of rotational inertia from a close swing-by, other sources of perturbation, or (of course) relativistic frame dragging. Kepler is fine for charting the overall orbits of planets and (most of the time) moons and small satellites, but when you start dealing with three-body and n-body systems there are no general closed form solutions, and you either start making simplifying assumptions or start integrating numerically to characterize celestical mechanical behavior.
I’m not sure what other way there is to take it. The illusionary “orbit” of the Sun about the Earth is not an orbit at all, which would be clear by taking careful observations over the course of the year. The added rotational velocity of the Earth will cause apparent retrograde velocity changes in the “orbit” of the Sun; they won’t cause the Sun to actually move backward, as is apparent with the apparent motion of Mars, but it is discernable to a careful observer, especially when you factor in the ascension of the Sun due to the rakish angle of Earth’s axis to the ecliptic. The Sun cannot be said in any sense, other than apparent (illusionary) to orbit the Earth.
Stranger
You know, I thought to mention Lagrange points and the Earth-Sun system when posting my first answer in this thread, but I didn’t, because I really think the OP is talking about what can be done with conventional artificial satellites. Maybe I’m wrong about that.
Um, why can’t you put a conventional artificial satellite at a Lagrange point? And what’s so unconventional about WMAP (at L2) and SOHO (at L1)?
<sigh> OK, but again, this isn’t what I understand the OP to be talking about.
Or to put it another way - all these nitpicks are admonishing me to remember to include things I have deliberately omitted for the sake of simplicity.
It’s inherent in the nature of the Dope: If you (or I) omit anything for the sake of simplicity, someone else will inevitably pop in to include it.
As for the original questions, most satellites orbit west to east (the same way the Earth turns), but there’s no physical reason why an object couldn’t orbit east to west (this is called a retrograde orbit). But they’re rare, because the natural processes which form planets and satellites tend to cause everything to turn in the same direction; and for artificial satellites, it’s cheaper to launch west-to-east, and there’s only rarely any benefit to a retrograde orbit.
It’s actually way cheaper to launch west-to-east. Putting a satellite in a westerly orbit would require enough total impulse to cancel out the momentum from the Earth’s rotation imparted before launch and then getting it up to orbital speed. Add to this that it’ll be going the opposite direction of most debris and therefore in the worst orientation for orbital impact. I can only think of a sparse handful of retrograde satellites, and I don’t think any of them were long term orbits.
Stranger
Indeed, the only reason I could think of to desire a retrograde orbit was if you wanted more impacts, whether for purpose of cleaning up space junk, or for attacking rival satellites. Why were the sparse handful you know of launched?
Due to the fact of unfriendly neighbors to the East, Israel launches all its satellites into retrograde orbit:
http://www.satobs.org/faq/Chapter-09.txt
I also believe that there are some American military satellites that are in retrograde orbit. (Looking for a cite).
