# Explain an Orbit: Simple Definition & Example

• hottytoddy
In summary: In addition, their examples are usually more illustrative and easy to follow. In summary, an orbit is the set of all possible positions that an element can take in a group, with the action of that group being the operation that's used. It can be found in books like Introduction to Abstract Algebra, and examples can be found on Wolfram MathWorld.
hottytoddy
I'm trying to study a proof for a quiz right now, and even though I have the answer, I don't get it because I don't understand what an orbit is. I got no definition in class, and can't find anything in the book. I looked on wikipedia, but that was completely over my head.

Can someone please explain an orbit as simply as possible, and perhaps with an example?

Thank you!

http://img98.imageshack.us/img98/6195/orbit2oj8.gif

hmm looks like the image code is broken

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This sentence from Wikipedia basically sums up an what an orbit is as briefly as possible...

The orbit of a point x in X is the set of elements of X to which x can be moved by the elements of G.

So a few questions for you. What's a G-set? What's an action? Where is all of this coming from?

I'm curious, what book are you using for your class? I've used Introduction to Abstract Algebra by Keith Nicholson, and it provides a pretty decent discussion on this material. Also, what proof are you looking at right now?

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Somehow, everyone in my class gets this, but me. I don't know how I missed it, but I've never learned this stuff... I'm past the proof, but now I have another problem and just don't understand what it means.

The book we're using is the third edition of Abstract Algebra, I.N. Herstein. The only references in the book, according to the index, are problems.

So a few questions for you. What's a G-set? What's an action? Where is all of this coming from?

The wiki sentence: Is it saying that if X is {1,2,3,4,5} then, for some G, O(x) for x=1 could be {2,4}? I don't know what a G-set is, and I can only assume an action refers to a function?

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Well the orbit of x will include x itself, but I think you're starting to get the idea. Basically the orbit is all of the possible values that you can achieve when operating the element x with all of the elements in G, where G is a group. The action is the operation that's used, so yeah basically a function.

Another resource that you can look at is Wolfram MathWorld. They usually provide defintions, with a few extra information about the topic.

## 1. What is an orbit?

An orbit is the path that an object takes around another object in space due to the force of gravity.

## 2. What is the difference between orbit and rotation?

Orbit refers to the movement of an object around another object, while rotation refers to the spinning motion of an object around its own axis.

## 3. How does gravity affect an orbit?

Gravity is the force that keeps objects in orbit. It pulls objects towards the center of the larger object, causing them to continuously move in a circular or elliptical path.

## 4. What are some examples of orbits?

Examples of orbits include the Earth's orbit around the sun, the moon's orbit around the Earth, and the planets' orbits around the sun.

## 5. Can an orbit change over time?

Yes, an orbit can change over time due to various factors such as the gravitational pull of other objects, changes in the mass of the objects involved, and external forces such as solar winds.

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