Orbiting Satellite

[Ginger Ale]

Do orbiting satellites do work/ have work done on them? If work = force x distance, is centripetal force x distance of orbital = work?
Thank you!

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[justhanging]

Centripetal force never does work because its always perpendicular to the motion.

 

[MT Headed]

To elaborate a little, your physics book says either

work (scalar) = force (vector) DOT displacement (vector)

or simply

work = force x distance x cos(theta)

The important issue is that in circular motion, theta is always 90 degrees, cos(theta) is zero, and no work is performed.

Another way to approach the problem is to realize that neither the mass nor the speed change, so the kinetic energy does not change. No change in kinetic energy -> no work performed.

 

[Ginger Ale]

Thank you!

 

[GreenRabbit]

If the orbit isn't circular, yes work is done on the satellite. But not by that formula. It's not centripetal force, but gravitational force that does the work.

 

[Ginger Ale]

so if it's orbiting in an elliptical pathway....?

 

[GreenRabbit]

Sorry if I wasn't clear, but when I said non-circular orbits, I meant elliptical orbits. Yes, positive and negative work is done on the satellite. After all, without work being done on the object, it's speed can't change. And we know for elliptical orbits, the speed does change.

 

[plzNOCarribbean]

So, Does UCM apply only when the circle/circular path is a perfect or nearly perfect circle?

Also, I think this pertains to the subject so I wanted to avoid starting an entirely near thread on this but....When one object (say satellite, planet, whatever) orbits another in an elliptical fashion, or a fashion whether the circular path is not a perfect circle, is the point at which the two objects are closest to one another correspond to the objects maximum tangential velocity, max force, and max centripetal acceleration?

please correct me if i'm wrong, but my though process was that anytime one object is orbiting another, the force allows for this orbit occur is the GRAVITATIONAL FORCE, which PROVIDES the Centripetal Force. This is why we set Fg= Fc, and Fc in this case is acting like the Net force. Well, since the distance between the two objects is the least (ie. r decreases) then Fg must increase. Since the gravitational force between the two bodies is max at this point, then the speed of the orbiting object must be the max, the ac must be max, and Fc must be max according to

Fc= Fg
m(V)^2/r = GMm/(r)^2

so basically, anytime one object orbits another, the point where the orbiting object experiences the max speed, max Fc, and max centripetal acceleration is when the orbiting object is CLOSEST to the object its orbiting, and the reverse is true when their farthest?

 

[MD Odyssey]

So, Does UCM apply only when the circle/circular path is a perfect or nearly perfect circle?

Yes. Not only must it be in a circle, but it must also be moving at a constant speed.

Also, I think this pertains to the subject so I wanted to avoid starting an entirely near thread on this but....When one object (say satellite, planet, whatever) orbits another in an elliptical fashion, or a fashion whether the circular path is not a perfect circle, is the point at which the two objects are closest to one another correspond to the objects maximum tangential velocity, max force, and max centripetal acceleration?

The point of closest approach, known as the perigee, is the point at which the kinetic energy is the highest and the gravitational potential energy is the lowest. The point of furthest separation, the apogee, is the point at which the kinetic energy is the lowest and the gravitational potential energy is the highest. Kepler's law of equal areas is based upon this and it is largely a simple application of energy conservation.

please correct me if i'm wrong, but my though process was that anytime one object is orbiting another, the force allows for this orbit occur is the GRAVITATIONAL FORCE, which PROVIDES the Centripetal Force.

Perhaps this will clarify things for you. If you were in a completely isolated system where the only force was the gravitational force AND you neglected the force on the planet by the satellite, then you get perfect circular motion. In real systems, this is invalid. In a real solar system, you have multiple planets, moons, non-negligible masses, etc. It's far more complicated. This is why the planets move in elliptical orbits. However, the deviations are small, on a cosmic scale, so we make the approximation that energy is conserved and Kepler's laws of planetary motion fall out of that.

Ultimately, know that the gravitational force is exerting a centripetal force on the satellite, that energy is conserved, and be mindful of the definitions of apogee and perigee.

 

[plzNOCarribbean]

Great! thanks MD odyssey.

One other thing, I get what your saying about how in real life there are all these other forces, but with regarding to just one object orbiting another and you neglecting everything except the Fg between them.

Then the point at which the two bodies are closest to one another, or the perigee, does that also correspond to max speed (v), acceleration (a), and force (F)?

 

[MD Odyssey]

Then the point at which the two bodies are closest to one another, or the perigee, does that also correspond to max speed (v), acceleration (a), and force (F)?

Well, the maximum speed is easy. The kinetic energy at perigee is at a maximum, so clearly, the speed is also a maximum.

For the force and the acceleration, I'm not exactly sure. For a real gravitational system with N number of particles, no closed-form solutions exist. Approximations for systems with three bodies (e.g., the sun, the earth, and a spacecraft) exist, but extending that to anything more complicated is something which can only be done numerically. Which is to say, it's not something that you'd be able to do on the MCAT - such a thing is something that would likely be found in a graduate celestial mechanics course. The complexity all comes about because you have multiple objects all exerting a force on each other, which in turn changes the direction of the net force on the spacecraft.

In short, finding the maximum force and acceleration on a body where you have more than two bodies at work (even if one has a negligible mass) is far beyond the scope of anything that would be seen in undergraduate physics.

This really showcases the power of energy arguments. If you were to try to use Newton's law of gravitation and the kinematic equations to calculate acceleration, velocity, and position, and then figure out the maxima, you would be forced to do some pretty heavy numerical analysis. But, if you assume energy is conserved and are told the orbit is elliptical, you can easily find the maxima and minima of the velocity. Powerful, indeed.

I guess what I'm trying to say is that the nature of the net force and acceleration on a body in a system with more than two bodies is not straightforward in any way and far, far beyond the scope of the MCAT. I might even go so far as to say, if you see a question with elliptical orbits, think of energy and Kepler's empirical laws first.

Make sense?

 

[plzNOCarribbean]

yes thanks