Understanding Centripetal and Gravitational Forces in Orbital Motion

[cdotter]

I'm having some trouble understanding this (not a homework question by the way.)

A satellite orbits the Earth with a certain angular velocity. Centripetal acceleration is directed radially inward. Acceleration due to gravity of the Earth is also directed radially inward. If I draw a free body diagram for this I get two forces directed radially inward. But the satellite doesn't fall towards the Earth because it has sufficient angular velocity. Where in the free body diagram would the acceleration pointed radially outward (to counter acceleration due to gravity and centripetal force) be and how does it come about?

 

[NobodySpecial]

Centripetal acceleration is directed radially inward.

You may wish to rethink that

 

[D H]

I'm having some trouble understanding this (not a homework question by the way.)

A satellite orbits the Earth with a certain angular velocity. Centripetal acceleration is directed radially inward. Acceleration due to gravity of the Earth is also directed radially inward. If I draw a free body diagram for this I get two forces directed radially inward.

Centripetal acceleration is a kinematical result. We know that some planet is undergoing a centripetal acceleration because we can see the planet's behavior over time. The same goes for an object stuck to the rim of a spinning wheel in space. That object too is undergoing a centripetal acceleration; we can once again see that the object is accelerating.

Centripetal acceleration is just a descriptive term. It does not say what causes that acceleration to occur. Once you have found the underlying that is responsible for that acceleration does not mean you suddenly have two forces on hand. In the case of the planet, there is only one force involved: Gravitation. Gravitation is what causes that centripetal acceleration.

 

[cdotter]

Centripetal acceleration is a kinematical result. We know that some planet is undergoing a centripetal acceleration because we can see the planet's behavior over time. The same goes for an object stuck to the rim of a spinning wheel in space. That object too is undergoing a centripetal acceleration; we can once again see that the object is accelerating.

Centripetal acceleration is just a descriptive term. It does not say what causes that acceleration to occur. Once you have found the underlying that is responsible for that acceleration does not mean you suddenly have two forces on hand. In the case of the planet, there is only one force involved: Gravitation. Gravitation is what causes that centripetal acceleration.

When the satellite is orbiting Earth with sufficient rotational velocity then the sum of the forces = 0, correct? Gravitation is always pulling the satellite towards Earth. Then where does the equal/opposite force (and acceleration) come from?

 

[D H]

A zero net force would mean the satellite has to follow a straight line trajectory, something it obviously is not doing. So, think about what you wrote for a bit. How can the sum of forces possibly be zero?

 

[cdotter]

A zero net force would mean the satellite is moving in a straight line, which it is not doing. So, think about what you wrote for a bit. How can the sum of forces possibly be zero?

Now I understand. Thank you.