Having a problem understanding orbits.....
Discussion
My problem is with the 'constantly falling' analogy used to describe why an object stays in orbit once enough velocity is achieved i.e. shooting a shell, parallel to the ground, faster and faster until the shell falls to earth at the same rate as the curvature of the earth so it never hits the ground (obviously in a vacuum).
Right, there are a lot of assumptions coming up, which is probably why I do not understand this. I assume that a body in orbit experiences the relatively constant attractive force of gravity at 90 degs to its orbit (i.e. straight down to the Earth’s surface). This then leads me to my second (probably incorrect) assumption; let’s unfold the circle of the earth into a plane that stretches to infinity (i.e you can keep on going around the earth, it never ends). If the plane provided the same force of gravity across its surface as the equivalent surface area of the Earth then I assume that this would be an equivalent model to the spherical Earth in terms of an orbiting object. Now shoot your bullet at escape velocity parallel to the plane. In my mind it still has to fall towards the plane as there is not an opposing force. As such I can't understand why orbits don't decay very very quickly?!
So where have I gone wrong? I did think that perhaps the ‘constantly falling’ analogy was a convenient simplification for the layman and the actual reason was the centrifugal force (let’s not go into the fictitious bit, a stone orbits on a string etc, seems like a real force to me!) generated by the velocity of the orbit. Can somebody explain what is really going on here?
Right, there are a lot of assumptions coming up, which is probably why I do not understand this. I assume that a body in orbit experiences the relatively constant attractive force of gravity at 90 degs to its orbit (i.e. straight down to the Earth’s surface). This then leads me to my second (probably incorrect) assumption; let’s unfold the circle of the earth into a plane that stretches to infinity (i.e you can keep on going around the earth, it never ends). If the plane provided the same force of gravity across its surface as the equivalent surface area of the Earth then I assume that this would be an equivalent model to the spherical Earth in terms of an orbiting object. Now shoot your bullet at escape velocity parallel to the plane. In my mind it still has to fall towards the plane as there is not an opposing force. As such I can't understand why orbits don't decay very very quickly?!
So where have I gone wrong? I did think that perhaps the ‘constantly falling’ analogy was a convenient simplification for the layman and the actual reason was the centrifugal force (let’s not go into the fictitious bit, a stone orbits on a string etc, seems like a real force to me!) generated by the velocity of the orbit. Can somebody explain what is really going on here?
I see it as a balance of gravity vs centrifugal force, which is no doubt incorrect. However, such a balance would have to be perfect so the mystery to me is how many objects manage to find themselves in orbit at all! There must be some kind of 'equilibrium well' that things fall into.
Centripetal force.
The fact that the object is travelling parallel to the curved surface of the object it is orbiting means that it can't hit the surface of the object as the surface is falling away at the same rate the object is falling..
The point it is actually rotating around is the graviatational centre of the object, usually close to the object's centre.
Orbital speeds are a balance between gravitational force and centripetal force.
If orbital speed is not reached, gravitational force wins and the object does eventually fall inwards and hits the surface.
If the speed is too high, it moves away from the object it is orbiting making a bigger orbit. If the speed reaches "escape velocity", the object can't hold on to it and it will drift out of orbit never to come back.
The fact that the object is travelling parallel to the curved surface of the object it is orbiting means that it can't hit the surface of the object as the surface is falling away at the same rate the object is falling..
The point it is actually rotating around is the graviatational centre of the object, usually close to the object's centre.
Orbital speeds are a balance between gravitational force and centripetal force.
If orbital speed is not reached, gravitational force wins and the object does eventually fall inwards and hits the surface.
If the speed is too high, it moves away from the object it is orbiting making a bigger orbit. If the speed reaches "escape velocity", the object can't hold on to it and it will drift out of orbit never to come back.
Edited by Eric Mc on Thursday 5th April 17:47
Simpo Two said:
I see it as a balance of gravity vs centrifugal force, which is no doubt incorrect. However, such a balance would have to be perfect so the mystery to me is how many objects manage to find themselves in orbit at all! There must be some kind of 'equilibrium well' that things fall into.
There are lots of "equilibrrium" points. Orbits can be at all sorts of distances from the parent object and can be all sorts of shape - from virtually perfectly circular to wildly elliptical to retrogade, equatorial, polar and all points in between.Natural objects end up in orbits due to a process of elimination over millions (even billions) of years. TYhe solar system we see today is the product of 4.5 billion years of objects smashing, crashing, bashing, falling and bumping into each other leaving us with a "REASONABLY stable set of orbiting bodies. However, there are still lots and lots of items out there orbiting the planets and the sun in cockeyed and wayward orbits and occasionally they do indeed fall or crash into a planet, a moon or the sun.
rjben said:
OK, thanks all, so it seams that my hunch is right, the 'constantly falling' analogy is incorrect, and the missing force is the fictitious centrifugal force.
It's not really incorrect, it just requires thinking about.Velocity is a vector quantity - it contains both speed and direction. According to Newton's first law, an object travelling at a particular velocity will continue to travel at that velocity, unless an external force acts upon it.
Gravity is that external force. When you apply an external force to an object, it accelerates. If you take an object and drop it, it will accelerate towards the ground at 9.8 ms^-2. Since it has no horizontal velocity to start with, it just goes straight down and will hit directly below where it started from.
If you take the same object and throw it sideways, it still accelerates downwards at 9.8 ms^-2 and because you can't throw very hard it will take almost exactly the same time to hit the ground. Now if you greatly increase the speed at which you throw the object sideways, it will travel a lot further before it will hit the ground - but because the earth is not a flat plane it also has to fall further. If you keep increasing the speed at which you throw sideways, eventually the object will travel far enough sideways that by the time it would have hit the ground, the ground is no longer there and the object keeps going on its curved trajectory. If you get the speed exactly right it will enter a stable orbit. Too slow, and eventually it will fall to earth. Too fast and it will fly off into space.
tank slapper said:
It's not really incorrect, it just requires thinking about.
Velocity is a vector quantity - it contains both speed and direction. According to Newton's first law, an object travelling at a particular velocity will continue to travel at that velocity, unless an external force acts upon it.
Gravity is that external force. When you apply an external force to an object, it accelerates. If you take an object and drop it, it will accelerate towards the ground at 9.8 ms^-2. Since it has no horizontal velocity to start with, it just goes straight down and will hit directly below where it started from.
If you take the same object and throw it sideways, it still accelerates downwards at 9.8 ms^-2 and because you can't throw very hard it will take almost exactly the same time to hit the ground. Now if you greatly increase the speed at which you throw the object sideways, it will travel a lot further before it will hit the ground - but because the earth is not a flat plane it also has to fall further. If you keep increasing the speed at which you throw sideways, eventually the object will travel far enough sideways that by the time it would have hit the ground, the ground is no longer there and the object keeps going on its curved trajectory. If you get the speed exactly right it will enter a stable orbit. Too slow, and eventually it will fall to earth. Too fast and it will fly off into space.
Yes, I understand the analogy but it just does not make sense. The object is not falling as it does not get any closer to earth. It is travelling at a velocity that allows gravity to be cancelled out by centrifugal force. Velocity is a vector quantity - it contains both speed and direction. According to Newton's first law, an object travelling at a particular velocity will continue to travel at that velocity, unless an external force acts upon it.
Gravity is that external force. When you apply an external force to an object, it accelerates. If you take an object and drop it, it will accelerate towards the ground at 9.8 ms^-2. Since it has no horizontal velocity to start with, it just goes straight down and will hit directly below where it started from.
If you take the same object and throw it sideways, it still accelerates downwards at 9.8 ms^-2 and because you can't throw very hard it will take almost exactly the same time to hit the ground. Now if you greatly increase the speed at which you throw the object sideways, it will travel a lot further before it will hit the ground - but because the earth is not a flat plane it also has to fall further. If you keep increasing the speed at which you throw sideways, eventually the object will travel far enough sideways that by the time it would have hit the ground, the ground is no longer there and the object keeps going on its curved trajectory. If you get the speed exactly right it will enter a stable orbit. Too slow, and eventually it will fall to earth. Too fast and it will fly off into space.
rjben said:
Yes, I understand the analogy but it just does not make sense. The object is not falling as it does not get any closer to earth. It is travelling at a velocity that allows gravity to be cancelled out by centrifugal force.
Here's a diagram.
Ignore air resistance for the moment because it just makes things annoying, and the curvature of the earth for the moment too.
Take a cannon to the top of a very high mountain and fire it horizontally. What happens? The shell falls to earth a distance away. The faster you fire the shell, the further away it will fall.
Now add in the curvature of the earth, but take gravity out of the equation. Fire that shell horizontally, and it will stay on that course. However due to the curvature of the earth, the distance of the shell from the earth will increase.
Make sense?
You can see from the diagram what happens. as the shell is fired with a higher and higher velocity, the further and further it gets before hitting the planet, partially due to the force equation (more along compared to the same amount of down), but also because relatively speaking the earth is falling away beneath it.
At some point you'll be going so fast that the earth is moving away quicker than gravity can pull you towards it.
rjben said:
Yes, I understand the analogy but it just does not make sense. The object is not falling as it does not get any closer to earth. It is travelling at a velocity that allows gravity to be cancelled out by centrifugal force.
It's a little difficult to get your head round, but it is still falling. If the surface of the earth were an infinitely long plane, then no matter how fast you throw the object sideways, it will always hit the ground at the same time as an object which is dropped. But the earth is not a flat plane, and nothing says an object in orbit has to remain the same distance above the earth.If the object were stationary above a point on earth (it makes it easier to forget that the earth is spinning for a moment), gravity would cause the object to accelerate straight down.
Now if the object is pushed slowly sideways, it will accelerate towards the ground but hit slightly along from the point above which it was released.
Looking down, the earth looks like a circle. As you gradually increase the speed at which you push sideways, the closer to the edge of the circle it will hit. Eventually, if you push fast enough the object will miss the circle altogether.
The earth isn't a flat circle though, it's roughly spherical. So as you are pushing sideways faster, the distance the object has to fall increases. When you reach the very edge of the circle, the object is hitting the earth a quarter the way around and landing virtually sideways.
When you push fast enough to miss the edge of the circle, the object doesn't actually hit the earth at all but carries on straight past it - gravity is still affecting the object, so eventually it gets pulled back and hits the other side of the planet.
If you keep increasing the speed sideways, you get to the point where the object is going so fast that it misses the earth on the way out, and it misses on the way back too, impacting on the side you can see again.
Slightly faster and it misses on the way out, on the way back and again on the way out.
Faster still and eventually it misses every single time - congratulations you are in orbit. But it's not a circular orbit, it is elliptical - the height above the earth varies as the object travels around. If you want the orbit to be circular, you have to push sideways at a very specific speed.
This is why when a space craft in orbit wants to return to earth, all it has to do is fire its engines to slow itself down to a point where it no longer misses the earth.
It's just ballistics. You can work it out on the back of an envelope.
http://en.wikipedia.org/wiki/Astrodynamics
http://en.wikipedia.org/wiki/Astrodynamics
Honestly, I understand the analogy, I just think it is flawed as it completely misses the essential notion of centrifugal force and as such is misleading the layman.
I don't think that a body in orbit is in free fall, as free fall implies that the body has succumb to the force of gravity. I think an object in orbit has reached the balance between gravity and centrifugal force (when I say 'think' I mean 'makes sense to me' not 'fact'). I understand that an object in orbit is accelerating in the same way that a car going around a roundabout at constant velocity is accelerating. It's just not falling as in the cannon ball analogy.
It's all magic I say!
I don't think that a body in orbit is in free fall, as free fall implies that the body has succumb to the force of gravity. I think an object in orbit has reached the balance between gravity and centrifugal force (when I say 'think' I mean 'makes sense to me' not 'fact'). I understand that an object in orbit is accelerating in the same way that a car going around a roundabout at constant velocity is accelerating. It's just not falling as in the cannon ball analogy.
It's all magic I say!
One reason you are struggling to understand Orbits is you believe in Centrifugal force, the force isn't pushing out it is pulling in. Look at the hammer throw or spin a weight on a string above your head let go of or cut the string where does the weight go? It will fly off at a tangent to the circle it was spinning in. So Gravity is the only force required, because the object is falling towards the centre of the object and missing also all orbits decay eventually they will slow and fall to the centre.
Engineer1 said:
Look at the hammer throw or spin a weight on a string above your head let go of or cut the string where does the weight go? It will fly off at a tangent to the circle it was spinning in. So Gravity is the only force required, because the object is falling towards the centre of the object
But in your example one force is inertia and the other is gravity. A hammer thrower does not have sufficent gravity to attract an iron ball, and things in orbit are not connected to the Earth by string.Gassing Station | Science! | Top of Page | What's New | My Stuff