# Orbiting-why doesn't it fall?

1. Jul 22, 2006

### superweirdo

This is a basic question I always had trouble understanding. As moon is orbiting earth, is it coming close? Now it might be for other factors but my point is, earth has some gravity force on it so even if something is orbiting earth, it should be coming to close to it unless it is fast enough to surpass earth's gravity in which case, there won't a orbit, there will be a curve. I just don't understand the fact that something can orbit earth in a circle(theoretically) and not come closure to it.

2. Jul 22, 2006

### pete5383

Weird...I just woke up thinking about this question and was going to ask it as well. Unfortunatly, I guess I don't know, so I can't be much help. You'd think something like the moon would fall into the eart since gravity points towards the center of the earth. I could see if it was a magnetic field..the only way I could figure when I was thinking about it was if the moon had some tangential velocity when it was captured by the earth's gravity, and it is falling towards the earth but also trying to move tangent to the earth.

That was kind of a messy post...haha, sorry. But yeah, I would like to know as well.

3. Jul 22, 2006

### nuts2546

The moon is actually orbiting away from earth, future eclipse wont block out as much light. In other words the moons orbit is spiralling away from earth. That is why the moon hasnt collided with us.

4. Jul 22, 2006

### Staff: Mentor

A satellite (like the moon) continuously falls towards the earth, but it also goes sideways fast enough that it continuously misses the earth.

5. Jul 22, 2006

### superweirdo

Guys, not helping, I know all that stuff, but WHY does moon not fall? In my mind, the velocity has to be exact for it to be able to remain totally circular to the earth, if it is greater, the moon will take a curve and go away, it is less, than moon will collide to the earth. But keep circuling and getting away, I just don't get that at all. I do get however keep circuling and getting closure but that is far from reality.

6. Jul 22, 2006

### pallidin

Sorry for the following long post, but this is from:
http://curious.astro.cornell.edu/question.php?number=192 [Broken]
Note, ignore the "suspended in air" That was from the poster.

"Your question has two answers: an elementary one and a rather subtle one. The elementary answer stems from Newton's laws of gravity. A complete answer, however, was only worked out by Einstein at the start of the last century.

A the simple answer to "why does the Moon stay suspended in the air?" is this: There is a gravitational force between the Moon and the Earth, that tries to pull the Moon toward the latter. This constant tug on the Moon as it moves around the Earth is called a "centripetal" force. This force is balanced by the "centrifugal" force, that pulls on the Earth and keeps the moon in motion. For a technical description of the (subtle) difference between centripetal and centrifugal forces check out this page. It is the balance between the centripetal and centrifugal forces that keep the Moon in orbit around the Earth.

One can be more persistent than that, however, and this is where the subtlety comes about. Why do the centripetal and centrifugal forces exactly balance each other? Because otherwise the Moon would come crashing into Earth. But why does the Moon not come crashing into Earth? Because the centrifugal force exactly balances the centripetal force. The reasoning here is circular: the simple explanation above provides a way of understanding how the Moon stays in orbit around the Earth, but not exactly why. The why was only supplied by Einstein in the early 1900s.

A more thorough answer to "Why does the Moon stay suspended in the air?" is the following. We think that Einstein's Theory of General Relativity explains the properties of space and time in the Universe. Within that theory, objects with mass curve spacetime in their vicinity, and this curvature influences the motions of other objects. The greater the mass and density of the object, the larger the curvature of spacetime that results. So, the Moon orbits the Earth because the Earth curves spacetime in the vicinity of the Moon. Though the Moon itself curves space as well (since it has mass), the curvature in the vicinity of the Moon is dominated by the Earth, which "tells" the Moon to orbit the Earth, given the Moon's current position and motion in the sky. It is this interplay between mass and curvature that causes the gravitational and the centripetal forces in the first place, and thus why the simple explanation holds.

The difference between the two answers is very subtle, but boils down to this:

First case: - Why does the Moon orbit the Earth? It just does. And you can understand how it does by analyzing the forces on the Moon caused by its orbit and finding the forces pushing in and out are equal.

Second case: - Why does the Moon orbit the Earth? Because the Earth distorts spacetime in the vicinity of the Moon, and causes it to orbit the Earth the way it does and the balance of forces to come out the way it does."

Last edited by a moderator: May 2, 2017
7. Jul 22, 2006

### Born2Perform

would not be simpler saying that: "it doesn't fall because its centrifugal force is equal to the gravity force at that distance"

8. Jul 22, 2006

### Gokul43201

Staff Emeritus
Yes, to a good approximation, the velocity is just right that it maintains a virtually constant orbit. That's all for now. You'll learn more when you take a high-school physics class.

9. Jul 22, 2006

### rcgldr

There is a big range of velocities that allow an object to orbit the earth, depending on the initial position and velocity vector, most of these will end up creating an elliptical orbit. The moons orbit is slightly elliptical, not circular. As long as the orbit doesn't intersect the atmosphere or the earth, the object won't slow down, and will maintain it's orbit.

10. Jul 22, 2006

### rcgldr

There is a big range of velocities that allow an object to orbit the earth, depending on the initial position and velocity vector, most of these will end up creating an elliptical orbit. The moons orbit is slightly elliptical, not circular. As long as the orbit doesn't intersect the atmosphere or the earth, the object won't slow down, and will maintain it's orbit.

As the initial velocity isn't equal or greater than the escape velocity for that position the object will orbit, unless it's slowed down.

11. Jul 22, 2006

### Parlyne

This is just totally wrong. If there were really multiple forces acting on the moon which all cancelled out exactly, the moon would move in a straight line. This is the essence of Newton's first law (although we can see it just as well by looking at the second law).

Ignoring the (small) effects of the rest of the solar system, the only force acting on the moon is the gravitational force between it and the Earth, which is directed along a line between the centers of the two bodies.

The confusion here stems, not from an additional force, but from a misunderstanding of the connection between forces and motion. Newton's second law tells us that the sum of all the forces acting on an object will be proportional to its acceleration. In other words, forces change motion. In this case, since gravity is attractive, the basic change in the moon's motion will be for its path to curve towards the earth instead of remaining a straight line (which it would be if there were no forces).

In Newton's theory of gravity, it turns out that there are four different shapes that an objects orbit can take, depending on how fast it's moving and how close it comes to the gravitating object. These, however, are relatively difficult parameters to use, so we generally talk about the energy and angular momentum, instead (but, we could transform directly from one of these sets of parameters to the other).

For any given angular momentum, the lowest energy orbit will be a circle. All orbits between this energy and a mechanical energy of 0 will be elliptical. 0 energy orbits are parabolas and posive energy orbits are hyperbolas.

From this, it's clear that any orbit with negative mechanical energy (or, equivalently any bound state orbit) will be a closed path. So, no orbits will lead the moon to progressively spiral towards the earth. If its orbit is already large enough that it doesn't hit the earth, it will stay that way.

To understand why these stable orbits are allowed, we can think about what physically happens in each type of orbit. First, we consider a circular orbit. In this case the object is always moving perpendicularly to the force of gravity. This means that the object must have just exactly the right velocity that it will always fall towards the ground at just the same rate that the ground falls away below it, due to the curvature of earth's surface.

An elliptical orbit is what happens when the velocity is not just right for that to happen. Let's say it starts off moving too slowly. Then, as it falls in its orbit it gets closer to the earth. But, as it gets closer, it must also speed up due to the conservation of energy. The closer you are to a gravitating object, the more negative your gravitational potential energy becomes. So, for your total energy to be conserved, kinetic energy must increase, meaning increased speed. Eventually a speed will be reached such that the object is falling slower than the ground curves away below it. At this point, it will start moving farther away from the surface. At least until it reaches a point when it is too slow.

The essence of this argument comes down to the conservation of the orbiting body's energy and angular momentum. Only if there is some outside interacting which progressively changes one or both of these parameters is it possible for a stably orbiting body either to crash or to escape.

Last edited by a moderator: May 2, 2017
12. Jul 23, 2006

### Dr.Brain

Infact from my knowledge , if we go back in cosmological time , when debris and stones shot out fromt he sun , moon was one of them and so was earth , both travelling away from the sun . Earth's gravitational pull helped in confining the motion of moon in an orbit .Infact the centripedal force exerted by earth on moon does make moon fall closer to earth.But not in the sense you think it to be.

The earth's pull , makes moon's motion curvature fall or 'deviate' from the straight line path moon must have taken in absence of earth , so if you try visualising it on the paper , at any particular time moon's motion would be tangent to the orbit it inhabits , but it falls below that straightline path due to earth's pull maintaining a closed path not exactly circular , at the same time not able to retain its straightline path.

13. Jul 23, 2006

### rcgldr

This is true only because earth is spherical and the object would hit the atmoshpere or the earth it self in a low orbit if the orbit wasn't circular. However, if the earth were shaped like an ellipse, with it's cener of mass concentrated at one of the centers of the elliptical shape, then the lowest energy orbit would also be an ellipse.

An orbits energy doesn't depend on it's shape (as long as it's an orbit). You can start with an object in a circular orbit, and then apply a force to that object that is perpendicular to the path it's traveling. This will change the shape of the orbit, but since no work is done, the new elliptical orbit has the same energy as the circular orbit it had before.

The size of the earth doesn't mattter as long as there are no collisions. All of it's mass could be concetrated in a 1 meter sphere, and the orbit of the moon would remain basically the same. The path of the orbiting object is not related to the shape of the earth's surface (as long as there are no collisions).

You can find out more at wiki

http://en.wikipedia.org/wiki/Orbit_equation

14. Jul 23, 2006

### krab

Simplest demo is to take a pendulum. With no sideways velocity, it passes through centre. This is equivalent to moon hitting the earth. If it has just the right sideways speed, it will travel in a circle with this sideways speed continually. That's analogous to what the moon is actually doing. HTH, weirdo

15. Jul 23, 2006

### BoTemp

If you're mathematically inclined, find a newtonian mechanics textbook. "Classical Dynamics" by Thornton and Marion is decent; I don't particularly recommend it but it'll have the answer in this case.

The moon had some initial angular momentum. For a rotating body in a gravitational field, weird things happen. The effective force on the body is a sum of three terms: The normal gravitational term, -GMm/r^2, a centrifugal force, -mw x (w x r) = mw^2r = mv^2/r, and the Coriolis force -2m w x v_r (assuming w = angular velocity is constant). The coriolis term isn't important for the moon's orbit, in fact I think it's 0.

Anyway, the gravitational and centrifugal forces can balance (given proper initial conditions) leading to stable elliptical (or circular, which is a special case of elliptical) orbits. It's the same force which keeps the planets orbiting the sun, and every star in the galaxy orbiting the galaxy's center.
There's also a solution for a body which comes in and then leaves; a hyperbolic orbit.

It's not necessary to use GR to explain this, btw. While quantitatively, there will be some small corrections to actual orbits due to Einstein, stable orbits exist in both cases.

16. Jul 23, 2006

### Parlyne

But, that changes the angular momentum, which is something I wasn't addressing. For any given angular momentum, my characterization of the orbits will hold. The only additional information needed is that the energy of the circular orbit depends the value of angular momentum. (Specifically, a circular orbit has energy $$E = \frac{-G^2 m^3 M^2}{2L^2}$$, at least in the limit where the large mass, M, doesn't move.)

Last edited: Jul 24, 2006
17. Jul 23, 2006

### rcgldr

The total energy of an object in orbit is fixed, it's the sum of it's kinetic energy (frame of reference would be the object being orbited, like the center of the earth in this case) and gravitational potential energy (also from the center of the earth).

As long at the total energy is less than the maximum gravitational potential energy, the path is an orbit.

If you consider the more accurate case of a pair of objects orbiting each other, then the sum of the kinetic energies and gravitational potential energies is constant.

In the case of an elliptical orbit, these "forces" aren't in balance, as the object is constantly changing speed, exchanging kinetic energy for gravitational potential energy. Only in the case of a circular orbit do both components of energy remain constant. Also, the only real force here is gravity, which is always accelerating the object; in the case of a circular orbit, always perpendicular to it's path, in the case of an elliptical orbit both perpendicular and in the direction of it's path.

Last edited: Jul 23, 2006
18. Jul 24, 2006

### superweirdo

alright I get it, however, one thing I don't get is that how can an object make an orbit like hyperbola?

19. Jul 24, 2006

### pallidin

I have no evidence here, but I would pressume that the hyperbolic orbit of the moon is due to the fact that the earth itself is revolving around our sun(therefore causing a natural distortion of the orbiting path of our moon), and perhaps also due to the gravitational influences of the other planets.
Just a guess, though.

20. Jul 24, 2006

### BoTemp

The orbit of the moon is not hyperbolic. Hyperbolic orbits pass the body around which they are orbiting and the escape to infinity.

I've been trying to track down a picture of the effective potential energy of a rotating body, but I haven't been able to find it (and my scanner isn't working for some reason). Veff ~ -1/r + 1/r^2. As r -> 0,
Veff -> + infinity, as r -> + infinity, Veff - > 0 (any constant, actually, but taken to be 0 by convention). Moving from r = 0 to r = +infinity, Veff(r) comes from + infinity to a relative minimum , and then increases to asymptotically approach 0.

That minimum value is where a circular orbit would taken place. An elliptical orbit can be seen as purturbations from that minimum. Picture a ball rolling back an forth when fixed to a 2-dimensional U-shaped track. A planet (or moon) does the same thing in this potential, only its radius is what oscillates.

Hyperbolic orbits occur where the body has enough energy to escape the potential well altogether. The analogy here would be throwing a ball down a U-shaped track hard enough that it flies out the other side.

21. Jul 24, 2006

### rcgldr

There's a maximum gravitational potential energy, this is the limit of the energy of an object as it approaches an infinite distance away from the gravitational source. If the total energy of an object, the sum of it's kinetic energy (related to it's speed) and it's gravitational potential energy (related to it's distance from the gravitational source) are greater than the maximum gravitational potential energy, the path is a hyperbola. If the total energy is the same, the path is a parabola (although having the energy exactly equal probably doesn't happen in reality, it's just a thought exercise). If the total energy is less, then you have an orbit. All of these cases assume that there are no collisions.

Last edited: Jul 25, 2006
22. Jul 24, 2006

### pete5383

So, let me get this straight, if the Earth and the moon had just been set the distance apart that they are now out in empty space, away from any other gravitational pull, and neither had an velocity in any direction, then they would collide? That is, the moon orbiting now depends on some straight initial velocity of the moon?

23. Jul 24, 2006

### Parlyne

Exactly right

24. Jul 25, 2006

### superweirdo

THx a lot guys, I get it, but wait a sec., what would the diff. b/w a parabola orbition and hyperbola b/c aren't all the things always orbiting for some other object? Wait a sec, is the sun orbiting?(by sun, I mean the whole solar system, like how earth and moon together are orbiting the sun)

25. Jul 25, 2006

### HallsofIvy

No, "things" are not necessarily orbiting other "things". It just happens that the solutions to the gravitational equations, with $F= -\frac{GmM}{r^2}$ are conic sections: circle, ellipse, parabola, hyperbola (and "degenerate" conics such as a straight line).