Why does a centripetal force not work in a circular orbit?
Expand a bit on Randy P's excellent answer. This is a subtle but very important point. What is "Work?" Suppose you got a job carrying 25 kg boxes up a flight of stairs. You can expend all the energy you wish doing "push-ups" and you will not get paid. To get paid you must do Work and carry boxes up stairs. Suppose you have a "frictionless cart" that moves on a level track. How much Work do you do moving 25 kg boxes one km at 1 km/hr? Again, except for the Force to accelerate the cart/box to 1 km/hr you do no Work. Even though the box is exerting 9.8 N (weight) down. That Force is at right angle to the direction of motion ===> does no Work.
Really confused about Centripetal Forces?
LET ME CORRECT YOU- Centripetal force is NOT a resultant of circular motion. Its the opposite. Circular Motion IS a resultant of Centripetal force. We provide that resultant force externally. EXAMPLES: The centripetal force can of the type, 1. a string (tension force) when a bob is rotated freely in the air by a string attached to it. 2. friction when a car takes a turn on a circular road. Bigger EXAMPLE: Earth rotates around the Sun. The Centripetal Force in this case is the GRAVITATIONAL FORCE OF ATTRACTION.
Why does the speed of a satellite remain constant in an orbit?
To have a satellite orbiting around the Earth the satellite needs to be imparted a particular horizontal velocity called the orbital velocity (if the velocity given by the launch vehicle is less than necessary, the satellite would fall back to Earth in a parabolic trajectory) by the launch vehicle. The satellite would then trace a circular or elliptical orbit around the Earth. The speed of the satellite would remain constant only if its orbit is perfect circular. This is because any object undergoes circular motion due to a force known as centripetal force. In this case the gravitational force of Earth provides the necessary centripetal force. Naturally an object at a particular height above the Earth must experience a downward force due to gravity. But in this case this downward force provides the necessary centripetal force for orbiting. The gravitational force of the Earth being a constant, the centripetal force also must be a constant. Centripetal force expression is F = mv²/R. This means for a constant radius of orbit, velocity will be a constant. This can happen only if the satellite is at a particular altitude with proper orbital velocity given in the correct direction.The satellite orbiting the Earth in an elliptical orbit will revolve around the Earth in a particular time, but its velocity changes at different points on the ellipse. The satellite will be faster closer to Earth and slower farther away from Earth such that the areal velocity (area swept in unit time) would be a constant. If the angular velocity (angle covered in unit time) of a satellite is equal to angular velocity of Earth, then the satellite appears to be fixed at a particular point above the Earth. Such satellites are called geostationary satellites. Obviously their speed has to remain constant so as to remain fixed in space with respect to Earth.
Centrifugal force? Centipetal force?
Centrifugal force is a force that involves spinning movement. A good example is a Tilt-a-Whirl ride at a carnival. If you sit in the ride and it spins around it forces your body into the back of the seat. This is centrifugal force. It is a force while spinning it pushes you to the outside. Another example is a washing machine on spin cycle. It spin really fast and the clothes end up on the walls of the tub. This is a centrifuge that helps ring the water out of your clothes. Centipetal force is the opposite of centrifugal force. Instead of forcing you to the outside of the center it brings you in toward the center. I imagine a bath tub drain or a black hole would be an example of this. It is a force that sucks you into the center. I hope this helps. Take care.