Gravity and Circular motion

[emzz]

Hi,

 

Could someone please explain to me how satellites orbit the earth? I know about gravity providing the centrepetal force and all that, but I still don't quite get it.

If one were to launch say, an apple or something horizontally from some peak with a high velocity, how come it'll fall straight back down in projectile motion?

How come some things orbit the earth when launched whereas some things don't? Is there a like minimum distance or velocity that an object has to be launched with in order for it to orbit and not fall straight back down?

 

Thx

[insane_alien]

its quite easy, they just fall in souch away that they miss the ground.

 

lets take the example of your high peak. but lets make it 300km tall. well out of the atmosphere. if you fired a gun it would travel a good distance but still fall back to earth.

 

so, we replace it with a gun with a higher muzzel velocity. this gun will fire the bullet further. perhaps far enough that the earth starts to curve away under it.

 

now, we get an even bigger gun that fires the bullet at around 7.2 kilometers per second. this bullet would hit you in the back if you stood there for about 45 minutes.

 

the bullet IS falling but the earth is curving away at the same rate. that mens it can never reach the surface.

 

there is a minimum distance but that is because of the atmosphere.

if the earth was a perfect sphere with no atmosphere then you would only be limited by the ground.

[emzz]

Ooh I see. All this while I had the idea that it worked like a mass being whirled around with a string. I'm a Year 12 student and my textbook kinda just grouped tension, friction, gravity and electrostatic force together as sources of centrepetal force without really explaining each one individually.

 

Could you explain a bit more about the atmosphere bit? How does the atmosphere affect it?

[insane_alien]

well, the atmosphere slows you down. thats why planes have their engines running all the time you're in flight. the spaceshuttle or a sattelite doesn't have any engines that can provide thrust against the atmosphere for very long. so they have to go up to where the atmosphere is so thin it hardly matters. though given enough time (it can vary from hours to millenia depending on altitude) they would still come don due to atmospheric drag.

[swansont]

Ooh I see. All this while I had the idea that it worked like a mass being whirled around with a string. I'm a Year 12 student and my textbook kinda just grouped tension, friction, gravity and electrostatic force together as sources of centrepetal force without really explaining each one individually.

 

Well, it does; conceptually it's all the same. In a circular orbit, gravity provides the centripetal force. But not all motion under the influence of gravity gives you an orbit: if you don't satisfy F = mv²/r, you don't get a circular orbit, you get something else, like escape or crash and burn. The force is not toward the center, and so the path isn't a circle (centripetal = "center-seeking") (And then there are (non-circular) elliptical orbits, which are more complicated)

[iNow]

I like simple animations and graphics to help. Per the point above, if you don't fire the object fast enough, it will fall "into" the curve of the earth. However, if you fire it at just the right speed, it falls at the same rate that the Earth curves away.

 

 

http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

Suppose we fire a cannon horizontally from a high mountain; the projectile will eventually fall to earth, as indicated by the shortest trajectory in the figure, because of the gravitational force directed toward the center of the Earth and the associated acceleration. (Remember that an acceleration is a change in velocity and that velocity is a vector, so it has both a magnitude and a direction. Thus, an acceleration occurs if either or both the magnitude and the direction of the velocity change.)

But as we increase the muzzle velocity for our imaginary cannon, the projectile will travel further and further before returning to earth. Finally, Newton reasoned that if the cannon projected the cannon ball with exactly the right velocity, the projectile would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the projectile falls. That is, the cannon ball would have been put into orbit around the Earth. Newton concluded that the orbit of the Moon was of exactly the same nature: the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit.

[emzz]

I see...

What if it's projected with a too high velocity? Will it fall back to earth as well?

[iNow]

I see...

What if it's projected with a too high velocity? Will it fall back to earth as well?

 

More likely, it's orbit would form an ellipse, or, if fired hard enough, it could break away entirely in a tangential line (like letting go of a rock while spinning quickly in a circle).

[Sisyphus]

If you fire it faster than the speed for circular orbit, your firing point will become the perigee of an elliptical orbit. If it's faster than a certain threshold (escape velocity), it will escape the orbit altogether.

 

If you fire it slower than the speed for a circular orbit, your firing point will become the apogee of an elliptical orbit. This is what is happening when it hits the ground, actually, just the surface of the planet is getting in the way.

 

If you fire it non-horizontally, your firing point will be some other point on an elliptical orbit, or it will escape, depending on trajectory and velocity.

[Norman Albers]

If you fire it faster than the speed for circular orbit, your firing point will become the perigee of an elliptical orbit. If it's faster than a certain threshold (escape velocity), it will escape the orbit altogether.

 

If you fire it slower than the speed for a circular orbit, your firing point will become the apogee of an elliptical orbit. This is what is happening when it hits the ground, actually, just the surface of the planet is getting in the way.

 

If you fire it non-horizontally, your firing point will be some other point on an elliptical orbit, or it will escape, depending on trajectory and velocity.

 

Thus an orbiting craft can boost itself to a farther circular orbit by one firing of rockets to create an ellipse, and then at the perigee, another similar firing to make the ellipse a circle.