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This question already has an answer here:

What force other than gravity acts on objects in Earth orbit? Without such force, continued orbit would be impossible, as the object would be drawn to the Earth.

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marked as duplicate by John Rennie, CR Drost, dmckee Jan 5 '16 at 19:04

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The "force" in question is a so-called "fictitious force" called the "centrifugal force". It is "fictitious" because it comes from a choice of accelerating coordinates; this particular fictitious force is one of two that exist in any rotating reference frame, for example, the reference frame that co-rotates with the orbiting object. So in those rotating coordinates where we seen the object simply suspended in midair at a fixed location, the centrifugal force is created by the coordinates and pushes the object up, balancing out the gravity pulling the object down.

What's a fictitious force?

Fictitious forces are very easy to understand: you are in a car that turns sharply and you feel a force slamming you into the door! Or it brakes sharply and you feel "flung forward". Or, you're in a train or plane that hits some sort of uneven track/air, and you feel jostled about by the train or plane.

These are fictitious forces which exist because your coordinates (the reference points of the car, train, plane) are not in a state of constant, uniform motion, but are instead accelerating out from under you. So for example if you start pulling a wagon and there is a ball in the wagon, the ball rolls into the back of the wagon. Common sense. But if you look very carefully at the ball from a reference point of the ground, say lining it up with some line on a sidewalk, you will see that it does not travel backwards relative to the ground, in fact moving the wagon forwards will drag it slightly forwards, just not fast enough to stay where it was relative to the accelerating wagon. The back of the wagon is crashing into it, it's not spontaneously moving backward to crash into the wagon.

Why do fictitious forces matter for orbit?

A ball wants to go at a constant speed in a straight line, if there are no forces upon it. An orbit is not a straight line -- it loops around on itself! It is therefore possible for a force to draw something into an orbit, but without needing anything to balance it out.

The easiest way to see this is to attach an object to a rope and start swinging it around in circles. If you let go of the rope, the object will go off in some straight line from wherever it was going: so if you're swinging it in a horizontal plane around you, clockwise when viewed from the top (left-to-right when you look forward at it) then to make it travel straight forward you need to release it when the ball is immediately to your left, so that it is moving straight forward right when you release it.

But because you are pulling it in with a constant force, it does not fly away: it orbits you.

How stable are gravitational orbits?

So, to stay in orbit, we need a deviation from the orbit to not change the gravitational force so much that the object falls into the thing it's orbiting. This is called "stability".

It turns out that for satellites around the Earth, this sort of thing is pretty robust against everything except friction -- and there is no friction in space except for against space dust or, as you get closer, Earth's atmosphere. The reason is that the 1/r^2 force law does not just allow orbiting circles but in general orbiting ellipses. There are only two rules: (1) the velocity needs to be lower than the "escape velocity" otherwise Earth isn't strong enough to keep it in orbit; and (2) the ellipse needs to not collide with the Earth itself (since the Earth is not a point particle but is really big!). Any orbit which fits between those two regimes will keep orbiting, and little perturbations like a collision with space dust will knock it into some other orbit which is relatively stable, until these small random collisions start to knock the satellite into contact with Earth's upper atmosphere: then air drag will start to slow the object down and pull it into the Earth and heat it up until it vaporizes.

By contrast, there is a place where the gravity of Earth balances out the gravity of the Sun and the co-rotating (with Earth around the Sun) centrifugal force. This is called a Lagrange point, there's actually a bunch of them (one 60 degrees ahead of the Earth's orbit, one 60 degrees behind, one on the far side of the Earth from the Sun, one on the far side of the Sun from the Earth). This particular one is called the L1 point, and there are orbits around it, but they are unstable: any collision will tend to increase either the Earth or the Sun's attraction to the thing, and that attraction will eventually pull it into an orbit around the Earth or the Sun instead of around the L1 point, as the respective gravity "wins out". So when we want to park a satellite at the L1 point, it has to have little rockets and some fuel to actively maintain its orbit.

On the flip side, the ones 60 degrees ahead of and behind us (L4 and L5) turn out to be stable again: orbits about these points should lead to other orbits around these points under little jiggles. This is a mixed blessing for satellites: there are probably therefore some clouds of space dust living at our L4 and L5 points, so any satellites we'd send out there would have to deal with frequent collisions with space dust!

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The object that has found it's way into orbit has momentum, and the momentum is balanced against the force of gravity so that the objects direction is changing in response to gravity, with the momentum holding it some distance from the earth.

When an object is launched into orbit if it has too great an acceleration it will continue off into space, too little it will fall back to Earth. The force that put the object into orbit is whatever caused it to accelerate and end up near the Earth.

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Tidal forces also act on objects in orbit and rotation from the Earth actually forces the moons orbit farther out. Ultimately no orbit is stable forever. I agree with what ANIXX said on the Duplicate link posted above when they said: "The Moon does not fall towards Earth right now because Earth rotates itself. The energy from the Earth's own rotation around its axis is gradually transferred into energy of the Moon's orbital motion. That's why the Earth's rotating speed decreases but the distance to the Moon increases.

This process will continue until Earth's proper rotation will slow to the point where it has the same angular velocity as the Moon's orbital motion. From that moment on the Moon will start to gradually approach Earth.

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