Help: Circular motion at constant angular velocity (1 Viewer)
- Thread starter ThreeOne
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Because the gravitational field acts between two masses, and the centre of the Earth is its centre of mass I think that's why ...
Another thing, it's called orbital decay. Orbital decay occurs when the satellite isn't travelling fast enough at the required velocity to maintain orbit.
EDIT: Oh hang on
Satellites in low earth orbit or geosynchronous orbit move with uniform circular motion.
This is motion in a circular path at a constant speed. Obviously, although the speed is constant, the velocity is not, since the direction of the motion is always changing. It can be shown that for an object executing uniform circular motion (UCM), the acceleration keeping the object in its circular path is given by:
ac = v2/r
where ac is called the centripetal ("centre-seeking") acceleration, v = velocity of the object and r = radius of the circular path. As the name implies, centripetal (circular) acceleration is directed towards the centre of the circle. Remember from preliminary course ?
Too much acceleration and a satellite can possibly leave orbit path into space, too little and it can crash to the ground. Must be an equilibirium in centripedal force.
Clearly, the centripetal force, Fc, acting on an object undergoing UCM is given by: Fc=mv2/r and r is from the centre of the Earth.
Centripedal force is directed towards the centre in very short.
Feel free to ask more questions, it benefits everyone.
Another thing, it's called orbital decay. Orbital decay occurs when the satellite isn't travelling fast enough at the required velocity to maintain orbit.
EDIT: Oh hang on
Satellites in low earth orbit or geosynchronous orbit move with uniform circular motion.
This is motion in a circular path at a constant speed. Obviously, although the speed is constant, the velocity is not, since the direction of the motion is always changing. It can be shown that for an object executing uniform circular motion (UCM), the acceleration keeping the object in its circular path is given by:
ac = v2/r
where ac is called the centripetal ("centre-seeking") acceleration, v = velocity of the object and r = radius of the circular path. As the name implies, centripetal (circular) acceleration is directed towards the centre of the circle. Remember from preliminary course ?
Too much acceleration and a satellite can possibly leave orbit path into space, too little and it can crash to the ground. Must be an equilibirium in centripedal force.
Clearly, the centripetal force, Fc, acting on an object undergoing UCM is given by: Fc=mv2/r and r is from the centre of the Earth.
Centripedal force is directed towards the centre in very short.
Feel free to ask more questions, it benefits everyone.
Last edited:
twilight1412
Member
are you sure your talking bout the right thing? i think he means circular motion in generalf3nr15 said:
basically you know how the linear velocity is always tangential right?
well if you take 2 points on the circle and then find dv using vector 'subtraction'
as
a = v - u
t
disconerning time the acceleration is the final velocity minus the inital velocity
and as the 2 points you take get closer together then the acceleration is closer to the center so when t = 0 (when they are at the same point) then the instantaneos acceleration is at the center
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I'll use Jupiter as an example.
As Jupiter orbits the sun at a constant angular velocity, it is pulled by the gravitational attraction of the sun while on orbit, if it were to happen and not stop, Jupiter would be pulled into the Sun.
But however as Jupiter loses potential energy during the pull with the sun it gains kinetic energy.
With the kinetic energy it gains enough speed to pull out of the gravitational attraction, all the kinetic energy is lost and converted back into potential energy (Law of Energy Conservation) and it begins all over again.
Now you know when an object is held off a cliff by a person it has full potential energy and no kinetic energy ?
When it is dropped and when it falls half-way, half of its energy is potential and the other half is kinetic. When the ball hits the ground, it no longer has potential energy and it has transformed into kinetic energy, with sound energy as a product.
As Jupiter orbits the sun at a constant angular velocity, it is pulled by the gravitational attraction of the sun while on orbit, if it were to happen and not stop, Jupiter would be pulled into the Sun.
But however as Jupiter loses potential energy during the pull with the sun it gains kinetic energy.
With the kinetic energy it gains enough speed to pull out of the gravitational attraction, all the kinetic energy is lost and converted back into potential energy (Law of Energy Conservation) and it begins all over again.
Now you know when an object is held off a cliff by a person it has full potential energy and no kinetic energy ?
When it is dropped and when it falls half-way, half of its energy is potential and the other half is kinetic. When the ball hits the ground, it no longer has potential energy and it has transformed into kinetic energy, with sound energy as a product.
airie
airie <3 avatars :)
The ball will have a constant angular velocity when the force exerted on it is the same for all parts of its motion in an orbit; and since it's coming from the same source, the ball is at the same distance away from it at all times ie. it moves in a circle (constant radius) around the source, which is at the centre of this circle.ThreeOne said:
If the angular velocity is not constant, that means the path of the object is an ellipse, with the central body at one of its foci. The object will have a greater angular velocity when it's closer to the body, and less when it's further away. This is demonstrated by Kepler's second law, which states that a radius vector from the central body to the object sweeps out equal areas in equal time intervals.
rama_v
Active Member
OK here is a simple explanation.
We know everything will go in a straight line with a constant speed if not acted upon by a force.
Now, think about a body orbiting the Earth. What forces are on it? Only one, gravity. That acts directly between the object in orbit and the Earth. This force is only changing the direction of the body in orbit but not its speed (because if you take a snapshot of the body in orbit it is moving perpendicular to the gravity force).
So, the body's direction is changed by gravity and only the direction. BUT the body does not fall to Earth, it more misses the Earth and therefore continues to miss it and flies in a circle around the Earth.
If you have read Hitchhiker's Guide to the Galaxy, in some ways Douglas Adams was right. You do fly by missing the ground
I hope that helps.
We know everything will go in a straight line with a constant speed if not acted upon by a force.
Now, think about a body orbiting the Earth. What forces are on it? Only one, gravity. That acts directly between the object in orbit and the Earth. This force is only changing the direction of the body in orbit but not its speed (because if you take a snapshot of the body in orbit it is moving perpendicular to the gravity force).
So, the body's direction is changed by gravity and only the direction. BUT the body does not fall to Earth, it more misses the Earth and therefore continues to miss it and flies in a circle around the Earth.
If you have read Hitchhiker's Guide to the Galaxy, in some ways Douglas Adams was right. You do fly by missing the ground
I hope that helps.