If you hover above Earth (in a helicopter or something) within the pull of gravity will you rotate with the Earth because of gravity or would you stay in one position and watch the Earth rotate beneath you (i’m not worried about taking into consideration wind resistance or anything like that)?..and why?
It’s actually pretty complicated because the helicopter has some horizontal velocity when it takes off from the ground. So, unless that velocity was somehow concelled, the copter would not just hover.
Think about the famous Galileo thought experiment. You’re riding a horse with a ball in your hand. You throw the ball straight up, but the ball continues to move forward after it leaves your hand, maintaining the forward velocity it had before you threw it.
It is true that the helicopter keeps the momentum it has from the rotation of the earth when it moves up. But when it ascends, it increases its distance from the axis (around which the earth rotates), so the same tangential velocity now translates to a slightly lower radial velocity. Thus, if you ascend high enough or wait long enough, the helicopter will fall behind in rotation compared to the earth.
Gravity has nothing to do with it. You are dealing with a movement that is perpendicular to the gravitational force.
Assuming a no-wind situation, you are stationary w/r to the air mass. If your airspeed is zero and the wind speed is zero, then you will remain over the same spot on the surface of the Earth. If the wind speed is 20 knots and your airspeed is 20 knots, then you will remain over the same spot.
You have answered your own question. “Hover” implies maintaining a given altitude above a point on the rotating Earth, thus you are moving with the Earth (at low altitudes at least, your question isn’t specific). At high altitudes (relatively speaking), can you really be at a fixed point anymore? Relative to what? I think the question is ambiguous, although I like MartinL’s answer best.
And since no one has said it, welcome to the SDMB. Enjoy your stay, and try the veal!
Me too although it should be noted that wind will be pushing you around more than anything you are likely to notice from a change in your radial velocity (I know the OP said ignore wind resistance but try telling that to a helicopter pilot).
The OP should be glad for this aspect of physics. Were it not so letting go of something in your car would see the object fly out the back window at 60 MPH. Or worse, you’re on a plane and jump and shoot through the back bulkhead at 600 MPH.
It’s gonna be hard to hover outside the pull of the earth’s gravity - properly speaking, every object in the universe is within the graviational field of every other object.
To a first approximation, the earth’s rotation has no meaningful effect on any flying or hovering object. The pilot of your helicopter will do pretty much the same thing when hovering at the equator or one of the poles. The effect that MartinL notes is valid, but minuscule (even at the equator, where it’s at a maximum).
There is also a tidal effect, which would be so microscopic on something the size of a helicopter that you probably couldn’t find it–but it’s not the wind! That would eventually slow you down so that the earth turns under you.
Gravity only pulls you towards the center of the earth. It doesn’t speed up or slow down your horizontal speed.
If you ignore air resistance, a helicopter would fall out of the sky. But if you consider a rocket hovering above an airless planet, you can either hover above a fixed spot, or stay fixed relative to the rest of the universe[li] and let the planet rotate beneath you. Both are almost equally easy. (Actually, staying above a fixed point is slightly easier, because you are rotating with the planet and the centrifugal force does some work to keep you afloat.)[/li]
i.e. in an inertial frame, as opposed to a rotating frame.
If you’re riding in an airliner and you drop your dinner roll, does it fall straight downwards, or does it race back towards the back of the plane at 400mph?
Also, if you climb to the top of a 300 mile tall tower, your weight is only down by 10% or so, yet you can wave to the space shuttle as it zips by below you, and the people inside are “weightless.”
A geostationary orbit is about 35,000 km (cite). So on any tower lower than that, you will be pulled down, but on any tower higher than that, you will be hurled away from earth (on or above the equator only, but you get the point).
Not that you could build a tower that high, I just wanted to point out that by moving away from earth (and remaining fixed above a certain location on the surface) the centrifugal force will be more important than the decrease in gravity caused by increased distance to the earths mass.
Nitpick: Centrifugal force doesn’t exist. What you’ve actually got is angular momentum. You’d fly off in a straight line at a tangent to your orbit – not along the radius – if gravity stopped abruptly.
In climbing up your unreasonably tall tower, or ascending in a space elevator, you need to gain angular momentum, which you can do in one of two ways: by giving yourself a shove in the appropriate direction with a rocket engine, or by being pulled forward by the tower (which has to be rigid as well as unreasonably tall). This is fairly obvious: at Earth’s surface you were whipping around a 6500km-radius circle once per day, but at geostationary altitude it’s a 40000km-radius circle, so you must be travelling about six times as fast.
As for your helicopter, it’s ascending in air, which is moving around with the lithosphere (on average), so presuming that air isn’t frictionless you will pick up the necessary shove from the air. The rotation of the planet slows by an infinitesimal fraction
What force exists that would hurl you away from the earth? An object in geostationary orbit still has to feel a gravitational force in order to be in orbit. It is not true that the force is zero, as you imply.
Even pickier nitpick:
I have heard scores of physicists stress this argument. I understand their point, but I do not agree.
Centrifugal force is observed inside rotating, hence accelerated systems. For every part of that system, this force is its push to break out of the system. That’s what we see from the inside, and that’s also where the name “centrifugal force” comes from.
Of course, for an outside (resting) observer it appears that there is a force that keeps the parts of the spinning system on track, or else they would follow a straight line: centripetal force. Although only the centripetal force can be observed, by Newton’s third axiom actio = re-actio we need to conclude that there must be a centrifugal force as well. In this special case it is easy to distinguish between actio and re-actio, but very often this turns into a hen-and-egg problem.
So centrifugal force may not exist in a very narrow minded approach about what a force is (I would not use it in a diagram showing forces in a system), but it is a valid term to describe the centripetal force necessary to keep the rotating system intact, or just to describe what mass inertia means in a rotating system (like the one we live in).
IMO, the sentence Centrifugal force doesn’t exist. is plain wrong without further elaboration on nomenclature.
When you are moving along with the “tower” above a fixed location on the earths surface, then earths gravity will be strong enough to pull you down again if you are below that geostationary altitude; it will keep you just in place if you are right at that height; and it will not be strong enough to keep you if you are higher, so you will move away from earth.
Maybe the word hurl was wrong, as it may imply that you would be pushed away by some extra force. This is certainly not the case.
Of course, “motion” is relative. Imagine you are floating in the most desolate part of of empty space. There are no planets nearby, no stars, no galaxies. Just you in your space suit. As far as you are concerned, you are completely motionless. As you sit there, you see a light approaching and it turns out to be another space traveller. Maybe you wave to each other as he passes. You say, “That space traveller moved past my motionless self at 5 knots.” But switch the perspective to the other space traveller. From his point of view, he is motionless and you are the one approaching him at 5 knots. Which perspective is valid? Both are equally valid. “Motion” only has meaning when there is a reference point. That is, you are moving relative to another object.
So back to the helicopter. “Hovering” means to fly a helicopter over one spot. That is, the helicopter is motionless relative to the Earth. But the Earth is spinning at about 1,000 miles per hour; therefore, the helicopter is travelling through space at 1,000 mph from the point of view of someone who is above the Earth’s axis. And the Earth itself is moving along its orbit at – what? 65,000 miles per hour? (I don’t know). So from the point of view of someone who is in a fixed position relative to the sun, the helicopter is going very fast indeed! And of course, the sun is speeding along in a galaxy, which is speeding along in the universe, which is expanding rapidly…
So if a helicopter is motionless w/r to the surface of the Earth, then it’s motionless. Or as Malacandra said, you are gaining your angular momentum by virtue of being inside something that is “connected” to the Earth (the still air mass, or the air mass that is moving at a certain speed relative to the surface for which you are compensating) and is moving with it.
MartinL, most likely you haven’t heard scores of physicists make that argument; you’ve heard scores of introductory physics students make it. Centrifugal force is exactly as real a force as is gravity. Care should be taken in when to use centrifugal force, as it’s only valid in a rotating frame of reference, but in that rotating frame of reference, it’s perfectly right to use centrifugal force, and perfectly wrong to use centripetal force.
You do have a misconception there about action and reaction, though. Action and reaction refers to Newton’s 3rd Law, and is always true. But centripetal and centrifugal forces are not a 3rd law pair. You can, maybe, consider them to be a second-law pair, but you can only form second-law pairs in the special case of non-accelerating bodies, and that’ll depend on your reference frame.