Having a problem understanding orbits.....
Discussion
When you linearise your model, you straighten out the orbit to a straight line, with gravity acting in a purely normal direction towards the new linear plane you are deffining as the gravity source. However, you have failed to adjust the direction of forces on your object in the same way. Effectively the force that acts on the objects inertia now attempts to "maintain momentum" with a vector that now points "uphill". This replaces the Centripetal acceleration in the 2 dimensional model. The complication being that we have now lost the nice easy relationship between the objects velocity (used to be rotational velocity in rad/s) and the magnitude of this new "uphill" force.
Better all round i think to keep things "simple" and just use a 2 dimensional circle model, where the force of gravity and the objects inertial forces act in equal and opposite directions.
Better all round i think to keep things "simple" and just use a 2 dimensional circle model, where the force of gravity and the objects inertial forces act in equal and opposite directions.
Simpo Two said:
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.
In actual fact, the hammer thrower DOES have enough mass to attract the hammer. However, his gravitational pull is so small that his gravitational attraction loses out completely to his own muscle strength and the gravitational pull of the earth.Being a small bloke, I blame lack of gravitational pull for my lack of success with the ladies i.e. my pulling power is swamped by bigger blokes.
Inertia isn't a force. The string is the mechanism by which the force is applied to the object at it's end, gravity can replace this force as it doesn't need anything to transmit it. You can show it just as easily with a bike going round a wall of death, remove the wall and the bike flies out wards it was only being kept on a circular path by the reaction between the tyres and the wall.
Bedazzled said:
Inertia isn't a force, it describes an object's resistance to change its motion unless it is acted upon by a force (such as gravity).
True; what I meant was that the object's inertia (tendency to travel in a straight line) is countered by the tension in the string, which forces it to travel in a circle. You could argue therefore that as the ball's inertia is placing tension on the string, it is a force, but I'm probably wrong 
rjben said:
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.
Like I said before, it is a matter of visualising what is happening. Here is the equation that describes a circular orbit:
a is acceleration - in this case due to gravity, which remains constant.
v is velocty, and r is the radius of the orbit.
As you can see, there is only one force involved - centrifugal force doesn't exist, it only appears to exist if you look at the system from the orbiting body's frame of reference.
http://spaceplace.nasa.gov/how-orbits-work/
have fun
have fun
Edited by SystemParanoia on Friday 6th April 16:29
Can I have a go, it used to confuse me also.
The object moves tangentially away from the earth x meters in x minutes. In the same x minutes gravity pulls it x meters back. So its 'height' remains the same. Like this
This is why people feel weightless in orbit. Actually they are nowhere near far enough away to escape the effect of gravity, they are merely falling at full gravitational rate.
The object moves tangentially away from the earth x meters in x minutes. In the same x minutes gravity pulls it x meters back. So its 'height' remains the same. Like this
This is why people feel weightless in orbit. Actually they are nowhere near far enough away to escape the effect of gravity, they are merely falling at full gravitational rate.
Bedazzled said:
You can lead a horse to water...
If you can't accept that 'falling' simply means accelerating toward the centre of mass due to gravity then you are doomed to forever misunderstand the analogy; and centrifugal force isn't a real force it describes the effect of inertia, see Newton's first law. If an object is in free fall it means the only force acting on it is gravity.
It's not about 'accepting', I don't think I'm right and have made this clear all the way through my posts. I'm trying to understand it. I now understand the fact that there is only gravity involved and that the fictitious centrifugal force is an effect of inertia. I'm still struggling with the free fall concept though.If you can't accept that 'falling' simply means accelerating toward the centre of mass due to gravity then you are doomed to forever misunderstand the analogy; and centrifugal force isn't a real force it describes the effect of inertia, see Newton's first law. If an object is in free fall it means the only force acting on it is gravity.
I seem to be attracting a little bitterness on this thread. My way of understanding requires me to create a mental model and then use the model to understand what is happening. If it does not work then I ask questions and update the model. Sorry if this rubs some of you up the wrong way, I'll leave you to it.
Otherman - your diagram really helped, thanks.
Edited by rjben on Friday 6th April 21:54
rjben said:
My way of understanding requires me to create a mental model and then use the model to understand what is happening. If it does not work then I ask questions and update the model. Sorry if this rubs some of you up the wrong way, I'll leave you to it.
I often work in the same way, but occasionally creating an analogical mental picture can get in the way of really understanding. It's a bit frustrating when that happens because you can easily get stuck with the 'wrong' picture, and it makes it harder to let go of that and form an accurate picture.Ok, after much contemplation I now think I understand! It feels right and I'm happy with the free fall / constantly falling analogy. There have been two important leaps:
1) understanding that there is no such thing as centrifugal force and that it is merely a side effect of gravity I.e the trajectory is a function of velocity and gravity, and the balancing force is in fact a bodies propensity to continue whilst being affected by gravity.
2) the definition of freefall as provided.
Now I have another concern. In my simple brain this model has effort that is being expended I.e. the constant bending of a bodies orbit. If there is effort being expended then what is the cost? Will the velocity of the body reduce? Also, is gravity being 'usedl' like a resource? Will the source of the gravity slowly 'evaporate', will the earth lose mass? This whole thing has opened a can of worms for me!
Thanks for all your help.
(sent from my phone, sorry for typos and formatting)
1) understanding that there is no such thing as centrifugal force and that it is merely a side effect of gravity I.e the trajectory is a function of velocity and gravity, and the balancing force is in fact a bodies propensity to continue whilst being affected by gravity.
2) the definition of freefall as provided.
Now I have another concern. In my simple brain this model has effort that is being expended I.e. the constant bending of a bodies orbit. If there is effort being expended then what is the cost? Will the velocity of the body reduce? Also, is gravity being 'usedl' like a resource? Will the source of the gravity slowly 'evaporate', will the earth lose mass? This whole thing has opened a can of worms for me!
Thanks for all your help.
(sent from my phone, sorry for typos and formatting)
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