How to Decide Centripetal Forces

[kuikaili]

A satellite is in a circular orbit around Earth at an altitude at which air resistance is negligile. Which one of the following statements is true?
A. There is only one force acting on the satellite.
B. There are two forces acting on the satellite and their resultant is 0.
C. There are two forces acting on the satellite and their resultant is NOT 0.
D. There are three forces acting on the satellite.
E. None of the preceding statements are correct.

I'm teetering between A and B. My problem is just that I seem to be able to justify anything to myself and it confuses me. Here's what's going through my mind:

Force 1: Gravity. The Earth pulls on the satellite.

Possible Force 2: Centripetal Force.
Why yes: If there were no force to counteract gravity, the satellite would succumb to gravity and accelerate toward the center of earth. Therefore, a second force is necessary.
Why no: (Maybe this is just a lame excuse for logic that's just stuck in my mind.) While the Earth currently pulls the satellite (gravity), it's actually a force which previously propelled the satellite to such a velocity to reach a free fall state that keeps the satellite in orbit. The satellite tends to stay on its instantaneous trajectory, because as inertia explains, it just does. In each instant, the Earth pulls it onto a slightly different trajectory.

Possible Force 3: Gravity. The sun pulls on the satellite.

Possible Force 4: Centripetal Force. Orbit around the sun.

Infinitely More Forces: Gravity (each planet in the universe). Centripetal Force (motion of galaxy through universe).

I realize that I'm probably just making this more complicated than it needs to be, but it seems that I never understand what my teacher is trying to ask. If I decide to zero in on just the satellite and earth, he includes the sun. If I include the sun, he's only looking at the satellite and earth. Not so fun on my multiple choice assignments.

 

[cepheid]

Welcome to PF,Centripetal means "towards the centre." Centripetal force is not a specific kind of physical force, like gravity, or the electric force. Centripetal force is just a kinematic *requirement.* In other words, if an object is undergoing uniform circular motion, then there must be some force on it that is pulling it towards the centre of that circle (i.e. something that acts as a centripetal force). So, some actual physical force that is specific to the situation in question must *provide* the centripetal force in that situation. For example, if you twirl an object on a string in a circle above your head, then there must be a force acting on the object that pulls it towards the centre of that circle (this is *required* simply by virtue of the fact that the object is undergoing circular motion. If there were no such force, then the object would not move in a circle). In this example, the tension in the string is that force.

In the situation given in your problem, gravity IS the centripetal force. It acts towards the centre of the orbit. Gravity is what provides the centripetal force necessary to keep the planet moving in a circle. Remember Newton's 1st law (the law of inertia): an object in motion wants to remain in motion in a straight line at a constant speed (and an object at rest is just a special case of this). So, if you suddenly removed gravity, the planet would fly off in a straight line tangent to the circular orbit it was just part of. To keep it in a circle, you have to constantly change the direction of its velocity (i.e. accelerate it), which is what the centripetal force (in this case gravity) does. Without gravity, the orbit would not happen.

The reason why gravity causes the object to "fall" in a circular orbit around the sun, instead of straight into it, is because the object is also moving "sideways" as well. So, in pulling towards the centre, gravity continuously changes the direction of this "sideways" velocity vector, leading to the circular path.

EDIT: Okay, so I was talking about this in the context of a planet orbiting a star, but the same thing applies to a satellite orbiting a planet, which is the situation you were given

EDIT 2: Yes, you are right that any other object with mass will, in theory, also exert a gravitational force on the satellite. HOWEVER, all of those other objects are much farther away from the satellite than the Earth is, therefore their gravitational influence on the satellite is negligible in comparison to the gravitational influence of the Earth on the satellite.

 

[jedishrfu]

Since the satellite is not moving in a straight line, we can conclude a force is causing it to move in a circle. That force is the Earth's gravity. If gravity was suddenly turned off the satellite would continue its motion in a straight line away from the earth.

Remember the satellite is actually falling toward the Earth but its speed is sufficient to make it orbit instead. If it moved any faster its orbit would expand and it would spiral away from the earth. If it moved slower then its orbit would get smaller until it hit the earth.

Also in your complication of the problem you forgot to mention the moon. :-)

I think cepheid says it better!

 

[kuikaili]

So, if we're isolating our system to just the Earth and satellite, it really is just gravity at work and gravity happens to be the centripetal force or force which is pulling toward the center of the orbit.

Then, similarly, the tension force of a string, in the classic ball on a string moving in a circle scenario, is the centripetal force, right? And the track of a roller coaster through a loop exerts the centripetal force?

 

[cepheid]

So, if we're isolating our system to just the Earth and satellite, it really is just gravity at work and gravity happens to be the centripetal force or force which is pulling toward the center of the orbit.

Then, similarly, the tension force of a string, in the classic ball on a string moving in a circle scenario, is the centripetal force, right? And the track of a roller coaster through a loop exerts the centripetal force?

EXACTLY. Now you've got it. In each of these situations, there is some force that its giving rise to a circular motion, because that force acts centripetally. But the nature of that force differs from situation to situation.

By the way, what I said in EDIT 2 in my previous post is not quite right. It's probably right for other solar system objects like the other planets: they exert a negligible influence on the satellite. However, it's not correct to say this about the sun. The sun may be really far away, but it's also really really huge (massive). And if you think about it, the entire system of (Earth + satellite) moves together in an orbit around the sun. So it's clear that both the Earth and the satellite feel the gravitational influence of the sun, and are therefore pulled into an orbit around it. However, as you said, this is not relevant to your problem, in which you're considering the Earth + satellite system in isolation.

 

[kuikaili]

This makes so much more sense now. I hadn't consider "centripetal" as an adjective on its own which could be applied to different types of forces before. I always thought of "centripetal force" as a physical force, but it didn't makes sense.
I really appreciate your help, Cepheid and Jedishrfu.