How Do Satellites Stay in Orbit with Centripetal and Gravitational Forces?

[Elmorshedy]

I'm really confused I have learned at school that the satellite remains in it's orbit because it's in an equilibrium state due to Centripetal force and the gravitational force but how?
Doesn't the centripetal force and the the gravitational force both of them act toward the the earth?
And what is the role of the centrifugal force?

 

[SandeshPhy]

Centrifugal force acts away the center(frugal meaning to flee) while centripetal force acts towards the center(petel means to seek).

Centrifugal force is simply a pseudo force due to use of non inertial frame of reference

 

[Doc Al]

I'm really confused I have learned at school that the satellite remains in it's orbit because it's in an equilibrium state due to Centripetal force and the gravitational force but how?

A satellite in orbit is accelerating centripetally--towards the center of the earth--and thus requires a centripetal force. Gravity provides that force. (A satellite is not in equilibrium--it's accelerating.)

 

[Tricks67]

whats the difference between an inertial and non inertial frame of reference?>

 

[DrStupid]

whats the difference between an inertial and non inertial frame of reference?>

An inertial frame of reference complies with Newton's laws of motion. This is the case for a non rotating system where the satellite orbits earth. The gravitational force between satellite and Earth is consistent with all three laws. In a rotating frame of reference the first two laws would be violated because the satellite is at rest even though the gravitational force is acting on it. If you assume the first two laws to be fulfilled you will get pseudo forces (e.g. centrifugal force) violating the third law.

 

[D H]

I'm really confused I have learned at school that the satellite remains in it's orbit because it's in an equilibrium state due to Centripetal force and the gravitational force but how?
Doesn't the centripetal force and the the gravitational force both of them act toward the the earth?

For now, I'll consider just circular orbits. Kinematics tells us there must be some net force acting on the satellite that is directed radially inward: A centripetal force. Kinematics doesn't say anything about the source of the centripetal force that causes uniform circular motion. A rock tied to a string that is swung around in a circle, a train running on a circular track, a satellite in circular orbit: As far as kinematics is concerned, these are all uniform circular motion.

It is dynamics that explains the source of the force that causes the uniform circular motion. From kinematics, we can derive the magnitude of the centripetal force. The dynamical considerations must necessarily yield the exact same force. So in a sense, this is a "balance" -- but not in the context of Newton's third law. In the case of the orbiting satellite, kinematics says the centripetal force is $mv^2/r$ while Newton's law of gravitation says the gravitational force is $GMm/r^2$. Equating these requires that $v^2=GM/r$. What if the dynamics say the force is something else? For example, what if the satellite is moving at some velocity other than the circular orbit velocity?

The answer is simple: You don't get a circular orbit. The satellite instead follows an ellipse, or a parabola, or a hyperbola. Explaining orbits in terms of centripetal force only works in the case of circular orbits. Circular orbits are nice fictions that make the behavior a bit easier to understand. In nature, there is no such thing as a perfectly circular orbit. Deviate one iota from the circular orbit conditions and you no longer have a circular orbit. You still do have an orbit, however. It's just not circular.

And what is the role of the centrifugal force?

In terms of looking at things from the perspective of an inertial frame of reference, there is no such role. There is no centrifugal force in an inertial frame.