Understanding Planetary Orbits: The Role of Gravitational Force and Rotation

[kyin01]

We started learning about gravitational force and how gravity is different everywhere. But than we talked about circular orbits and how we can find its period and such

So to remain in circular orbit the gravitational force between 2 planets pull each other, but doesn't those opposite reaction force cancel each other out?

 

[dst]

No, both attract each other - the gravitational attraction is a multiple of BOTH their masses (i.e. f=\frac{GMm}{r^2}).

The equal and opposite force works in that planet A pulls with force F on planet B while planet B pulls on A with the same force F.

 

[Danger]

Planets don't generally orbit each other, unless you count a large moon as a planet. Rather, they all orbit a host star. It's based upon conservation of angular momentum. While there is some uncertainty as to exactly how solar systems form, it's pretty much acknowledged that there is a spinning dust cloud at the root of it. That spin remains after the dust has aggregated into planets.
As a side note, most orbits are elliptical rather than round.

 

[Redbelly98]

So to remain in circular orbit the gravitational force between 2 planets pull each other, but doesn't those opposite reaction force cancel each other out?

They don't cancel because those two forces are acting on different objects. One acts on Planet #1 (due to Planet #2), and the other force acts on Planet #2 (due to Planet #1).

Force cancellation is used when two or more forces are acting on the same object.

 

[russ_watters]

Consider the tension on a rope held by you and a friend, when both are pulling on it. Do any forces cancel?

 

[Redbelly98]

Consider the tension on a rope held by you and a friend, when both are pulling on it. Do any forces cancel?

Of course. The two forces on the rope, due to me and my friend, are equal but opposite, so they cancel.

 

[Danger]

Is that really a cancellation? The rope still feels the effect, as do your muscles.

 

[Redbelly98]

Is that really a cancellation? The rope still feels the effect, as do your muscles.

What is the acceleration of the rope? Recall F=ma

 

[Danger]

I might be using the wrong terminology (I'm not educated in science). To me, that situation implies that the forces are balanced, but still exist. Cancellation would result in no tension in the rope. Sorry if I confused the issue.

 

[malty]

What is the acceleration of the rope? Recall F=ma

You can't just slap the formula F=ma onto everything, you first need to identify the systems involved. It is important to know that only one of the two forces connected by Newtons Third Law may appear in equations of motion, this will alway depend on the system we chose.

Consider a donkey and a kart in contact with the ground.If the donkey pushes against the kart the kart will push back against with and equal and opposite force, so the the two forces will cancel and there will be no net motion - this isn't what we observe in everyday life. So clearly we can't just use Newtons laws unless we are absolutely clear what our system(s)are. See if you can understand the flaw in the Donkey Dilemna.

 

[russ_watters]

Of course. The two forces on the rope, due to me and my friend, are equal but opposite, so they cancel.

Sorry, maybe I wasn't clear, but that was for the OP, not directed at you. The force you impart on the rope does not cancel with the force your friend imparts on the rope, to end up with zero force, like the OP suggested for gravity.

What is the acceleration of the rope? Recall F=ma

The scenario was an analogy. There are other forces in the system, namely the friction between your feet and the ground. I wanted to focus only on the common force between the two people.

If you want to be particular about it, if you and a friend got on roller skates, you could orbit each other at your common center of gravity and then the only forces would be between each of you and the rope and there'd be an acceleration. It works just like gravity.

 

[Redbelly98]

russ, malty, danger:

Looks like I misunderstood russ's question in more ways than one!

Consider the tension on a rope held by you and a friend, when both are pulling on it. Do any forces cancel?

I thought russ was asking me, as one of my posts came just before this one.

Also, in what we mean by saying that forces "cancel". I was thinking in terms of the net force (i.e. vector sum) of all forces acting on a particular object (the rope), when that object is either stationary or more generally not accelerating. The vector sum of the forces acting on the rope is zero in that case. If you'd rather say the forces balance instead of cancel then okay.

Yes, definitely there is tension in the rope due to the people pulling on it, and that's a different situation than if nobody were pulling on the rope.

Sorry about the confusion.

 

[Redbelly98]

You can't just slap the formula F=ma onto everything, you first need to identify the systems involved.

I was talking about just the rope, and just the forces acting on the rope. Sorry if that wasn't clear.

It is important to know that only one of the two forces connected by Newtons Third Law may appear in equations of motion, this will alway depend on the system we chose.

Agreed. I tried making a similar point in post #4 of this thread.

Consider a donkey and a kart in contact with the ground.If the donkey pushes against the kart the kart will push back against with and equal and opposite force, so the the two forces will cancel and there will be no net motion - this isn't what we observe in everyday life. So clearly we can't just use Newtons laws unless we are absolutely clear what our system(s)are. See if you can understand the flaw in the Donkey Dilemna.

As I tried pointed out in post #4, one must be clear about the forces acting on a particular object. I think we agree on this.

 

[kyin01]

Okay I kinda get it

but why do they (planets or whatever it is that is orbiting e.g. satellites around Earth or something) rotate and not just sit there?

 

[Danger]

They don't have to rotate, although most natural satellites do because of angular momentum retained from their formation. Most man-made ones don't, because they're designed to have sensors or transceiver antennae aimed at a specific target.

 

[jobyts]

What's the explanation of the Earth's elliptical orbit, rather a circular orbit?

 

[Danger]

It still has to be based upon the initial configuration of the dust cloud and conservation of momentum, but I don't know the real answer. Stand by for an Astronomy specialist to respond.

 

[russ_watters]

A circle is a special case of an ellipse, one that happens to have 0 eccentricity. So except in an impossibly perfect situation, no orbit would have exactly 0 eccentricity. You'd need perfect starting conditions and no perturbations from other objects nearby.

 

[DavidWhitbeck]

Okay I kinda get it

but why do they (planets or whatever it is that is orbiting e.g. satellites around Earth or something) rotate and not just sit there?

Why is it that if you jump off a building you fall to the ground? Both questions have the same answer. The satellites are in free fall. If they were to sit there they would just fall to the Earth. We give them enough fuel when they launch so that they have enough speed to be placed in a stable orbit and not fall back to the Earth. Sometimes their orbit deteriorates though and they come crashing down.

The same thing happens if you have water in a bucket. Tie a rope to the handle of the bucket. Now whirl the bucket around in a circle in the vertical plane. If you whirl it fast enough the water will stay in the bucket as you bring it to the top, else the water will come out, right? The same thing goes for these satellites.

 

[Danger]

Why is it that if you jump off a building you fall to the ground? Both questions have the same answer. The satellites are in free fall. If they were to sit there they would just fall to the Earth. We give them enough fuel when they launch so that they have enough speed to be placed in a stable orbit and not fall back to the Earth. Sometimes their orbit deteriorates though and they come crashing down.

The same thing happens if you have water in a bucket. Tie a rope to the handle of the bucket. Now whirl the bucket around in a circle in the vertical plane. If you whirl it fast enough the water will stay in the bucket as you bring it to the top, else the water will come out, right? The same thing goes for these satellites.

The only problem with that answer was that he asked about rotating, not revolving. There is no law that I'm aware of that requires rotation of an orbital body.

 

[DavidWhitbeck]

The only problem with that answer was that he asked about rotating, not revolving. There is no law that I'm aware of that requires rotation of an orbital body.

Well you inferred that he was speaking of the object spinning about it's own axis, but I don't think that was what he meant. I think that when he said rotating, he meant rotating about the Earth, especially since he contrasted it with "not just sit there" implying that it was stationary. The word "rotation" can refer to any type of motion about a fixed axis, so I am puzzled as to why you are distinguishing between the words "rotating" and "revolving".

Regardless of which of us interpreted his post correctly, he has an answer for both cases and that is what is important.

 

[Danger]

Rotation specifically refers to spinning around one's own axis. Circling something else is revolving.