Why do objects fall towards the center of their orbit?

[fastforded]

falling objects and gravity?

i need help understanding...im under the impression that even though the moon orbits the earth, and the Earth the sun, that the moon is falling towards the earth, and the Earth ius falling towards the sun...im confused? if it orbits, then how is it falling? any info/explanation appreciated, thanks

 

[tiny-tim]

Welcome to PF!

Hi fastforded ! Welcome to PF!

That is what Isaac Newton worked out when he watched the apple falling.

He thought "If I throw the apple sideways, it will go a short distance. If I throw it hard enough, it will disappear over the horizon before it comes down. And if I throw it even harder, it will go into orbit, and come back into my hand! In all three cases, the apple is falling all the time. And that's why the moon doesn't hit the Earth … it's falling towards the earth, but it's going so fast sideways that it keeps missing the Earth and returning to where it started!"

(Conversely, even when Isaac Newton threw the apple a short distance, technically it was in orbit … but the orbit was a highly elliptical one, which intersected with the earth. Anything in free-fall is in orbit … until it hits the earth!

In other words: orbiting and free-falling are the same thing. )

 

[Ken G]

And to that excellent answer I would add, imagine that you swing a rock, tied to a rubber band, around your head. The rubber band will stretch, yes? A stretched rubber band is pulling on its ends, so your hand feels a force, and the rock has a force on it too, pulling it inward. How can the rock be pulled inward if it gets no closer to your head? Because motion in a circle at constant speed requires such a force-- the "falling" is needed to keep the Moon from flying off into space, even though it makes the Moon get no closer to us.

 

[fastforded]

(Conversely, even when Isaac Newton threw the apple a short distance, technically it was in orbit … but the orbit was a highly elliptical one, which intersected with the earth. Anything in free-fall is in orbit … until it hits the earth!

In other words: orbiting and free-falling are the same thing. )

the difference between the moon orbiting and a meteor hitting? the direction of the orbit?

or anything coming close to a "body" like the Earth would have its direction altered by gravity? or its direction/course is what led it into a atmospheric entry?

and how does this relate to when NASA figured out how to "slingshot" a man made satellite around a planet? ( using gravity?)

and that moon moving sideways very fast so that its circles the Earth is also moving towards the center of the Earth at the same time? and if that orbit slows down it re enters the atmosphere?

thanks,

 

[MeJennifer]

i need help understanding...im under the impression that even though the moon orbits the earth, and the Earth the sun, that the moon is falling towards the earth, and the Earth ius falling towards the sun...im confused? if it orbits, then how is it falling? any info/explanation appreciated, thanks

As Wheeler once remarked the term free-float would have been more accurate than free-fall for an object that is not accelerating. Objects in orbit are free falling (or free floating if you prefer that terminology), but note that in GR the Moon is as much in orbit around the Earth as the Earth is in orbit around the Moon.

Two orbiting masses in isolation will eventually have their worldlines merge, which means that they eventually come together, as a very small amount of gravitational radiation is dispersed.

 

[tiny-tim]

the difference between the moon orbiting and a meteor hitting? the direction of the orbit?

Basically, yes.

or anything coming close to a "body" like the Earth would have its direction altered by gravity? or its direction/course is what led it into a atmospheric entry?

Yes … there are two types of approach … "fly-by", which is a hyperbola or parabola … and orbit, which is an ellipse.

Both a fly-by and an orbit can lead to a crash, if they're close enough to the Earth's atmosphere!

and how does this relate to when NASA figured out how to "slingshot" a man made satellite around a planet? ( using gravity?)

Well, the satellite is "free-falling" the whole time. It starts in a very elongated orbit round the Earth, which just happens to go near Venus. If it didn't go near Venus, it would just return to near the Earth again. But the gravity of Venus at first distorts the original orbit, and then takes over.

and that moon moving sideways very fast so that its circles the Earth is also moving towards the center of the Earth at the same time? and if that orbit slows down it re enters the atmosphere?

That's right … the moon's acceleration is always towards the Earth. Only its speed keeps it at a safe distance!

 

[D H]

As Wheeler once remarked the term free-float would have been more accurate than free-fall for an object that is not accelerating.

MeJennifer, that is just a tad too advanced given the nature of the OP's misunderstanding. I think we should to stick to classical physics here, not relativity. fastforded, you really shouldn't have posted this in the relativity forum.

but note that in GR the Moon is as much in orbit around the Earth as the Earth is in orbit around the Moon.

The exact same pertains to classical physics. The Moon and Earth orbit each other about the Earth-Moon center of mass.

tiny-tim and Ken G gave an excellent answers:

Imagine that you swing a rock, tied to a rubber band, around your head. The rubber band will stretch, yes? A stretched rubber band is pulling on its ends, so your hand feels a force, and the rock has a force on it too, pulling it inward. How can the rock be pulled inward if it gets no closer to your head? Because motion in a circle at constant speed requires such a force.

Suppose the rubber band breaks at some point. Per Newton's first law, the rock will fly away from you with the tangential velocity it had at the point where the rubber band broke. The unbroken rubber band provides the necessary force needed to keep the rock moving circularly. Gravity works much the same way. The Moon is always falling toward the Earth, which brings us to tiny-tim's answer:

And that's why the moon doesn't hit the Earth … it's falling towards the earth, but it's going so fast sideways that it keeps missing the Earth and returning to where it started!

the difference between the moon orbiting and a meteor hitting? the direction of the orbit?

The shape of the orbit. The Moon is in a nearly circular orbit (ignoring perturbations such as those caused by the Sun, the Moon's orbit is an ellipse). A meteor's orbit is a different shape: a hyperbola. One characteristic of an orbit is the point on the orbit closest to the body being orbited. In the case of the Moon, this closest point to the Earth (perigee) is not that much different from the furthest point. A meteor that hits the Earth simply has its perigee smaller than the Earth's radius. Orbits come in circles, ellipses, parabolas, and hyperbolas. These shapes are related in that they are all conic sections.

 

[russ_watters]

If I could try to be a little more succinct: an object in a circular orbit around the Earth is said to be in freefall because it is accelerating at g toward the earth. It never gets closer to the Earth because the acceleration is perpendicular to its direction of motion.

Btw, this is classical physics...

 

[fastforded]

If I could try to be a little more succinct: an object in a circular orbit around the Earth is said to be in freefall because it is accelerating at g toward the earth. It never gets closer to the Earth because the acceleration is perpendicular to its direction of motion.

still not understanding?

 

[tiny-tim]

Hi fastforded!

It's like driving a car in a circle on a flat road …

the acceleration (caused ultimately by turning the steering wheel) is always towards the centre of the circle, but the car never gets closer to the centre because it is always moving pependicularly.

If instead the car is on a "wall of death" (a bowl), and the steering wheel isn't turned, the car still goes in a circle, this time because it is "free-falling" towards the centre, but again never getting closer because it is always moving pependicularly.

(perhaps this is a bit more obvious with a ball-bearing )