Systems

For example, satellites in orbit around the earth are gravitationally bound to Earth since they can't escape Earth's gravity. By contrast, the Voyager spacecraft, which explored the outer solar system, was launched with enough energy to escape Earth's gravity altogether, and hence it is not gravitationally bound. The Moon, is gravitationally bound to the Earth, and the Earth to the Moon. The Earth is gravitationally bound to the Sun, and the Sun to the Earth. In fact, everything in our Solar System is gravitationally bound, which is why we are called a solar SYSTEM, because we are a gravitationally bound system, bound by the incredible mass of the Sun that keeps us all together.
When we think about the relationship between the Earth and the Sun, this is often the model we go to when we think about gravitationally bound systems. A very small something, like the Earth here on the right, the peppercorn at the end of the courtyard, circling around something very massive, the Sun. But there are also systems where the objects are about the same size.
For example, some stars circle around other stars. In this case, because both objects are approximately the same mass, neither one is orbiting around the other, they are both going around each other. More precisely, they are both orbiting around something called the center of gravity. The center of gravity is not a real thing, there is nothing there, but it is the place where the gravitational weight of a system acts as if it were concentrated. That is kind of complicated, but I think we may be able to figure it out using some examples. The center of gravity between two objects, for example, is always some place on a line between the two objects. It is going to be closer to the more massive object.
So for example in the Earth-Sun system, and remember that this picture is not to scale! We can draw a line between the Earth and the Sun. The center of mass of this system is somewhere along this line. Where do you think it might be? The Sun is so massive compared to the Earth, that the center of mass is inside of the Sun! It is not quite at the center, but it is so close, that the Earth basically looks like it is circling around the Sun, and the Sun is standing still. However, in fact the Sun is rotating around the center of mass too, making tiny little circles that we don’t even notice. Everything in a gravitationally bound system, falls toward the center of mass of that system.
We are gravitationally bound to the Earth. Where do you think the center of mass of the Earth is? It’s right in the middle, at the core.
When you have two stars that are the same mass, the center of gravity is going to be exactly in the center between those two stars. If one star is a little more massive, the center of gravity will be a little closer to the more massive star.
In this case, the orbits will look a little like this.
When you add even one more body, things get really complicated. One of the most famous problems in physics is exactly this, when you place a bunch of objects with various masses close together, with initial velocities, what will happen? What will their motions look like? How will gravity affect the way they move? Will they begin to orbit one another in a stable way, or will gravity swing them off into space? This is called the “n-body problem.”This link simulates a three body system.http://merganser.math.gvsu.edu/david/reed03/projects/salomne/index.htmlThis one a bunch of n-body systems.http://www.youtube.com/watch?v=gM4fmL6dLdY
Galaxy groups and clusters are the largest gravitationally bound systems that we have observed in the Universe. This is a picture of a galaxy cluster, one that our galaxy group, the local group, happens to be drifting toward right now, drawn in by its gravity. It is likely that in the distant future, we will become gravitationally bound to this cluster. Each of these galaxies is gravitationally bound to the center of gravity of the cluster, and so we have this big n-body system, with complicated motions, but all essentially orbiting around each other.Remember that in our doll metaphor, the cluster or group we belong to is called the local group. The local group is inside of the Virgo Supercluster, which is inside the Universe. But Superclusters and the Universe are NOT gravitationally bound. They are very much AFFECTED by gravity, but they are not tied to each other permanently by gravity, at least not yet. So when we talk about gravitationally bound systems, we are only talking about things from this doll on down. This doll, the galaxy clusters and groups, including our local group, are the largest gravitationally bound systems that we know about.
Galaxies are gravitationally bound systems. All the stars, dust, gas, etc, swirl around the center of the galaxy. For spiral galaxies, like ours, a very, very massive black hole anchors the rotation of the galaxy and is incredibly massive, so most things spiral around it.I have a question for you, is this photograph of our Milky Way galaxy, or is it of another galaxy? How do you know?You can’t photograph your house from inside of it! And we cannot get outside if the Milky Way.
Sometimes groups of stars are bound together gravitationally, but inside of galaxies. These are called star systems. Many star systems are only two stars, which we will talk about when we talk about stars. In fact, most stars are in systems with another star. But some stars systems are huge, like this one, which is called a star cluster. Clusters just like this one tend to be in the halo of the Milky Way, and you can see some of them even with your naked eye. They are really spectacular through a small telescope.
Solar Systems are gravitationally bound. This is not a drawing of our solar system, this is a drawing of a Solar System around another Star, not our Sun, called Kepler 11.
The Earth Moon system is gravitationally bound. This famous picture was taken in 1969, des anyone know what it is a picture of?Earthrise! The first Earthrise ever witnessed by humans.
Of course there are a lot of other things in Earth’s gravity, here is a map of some of the satellites around us right now. They are all also gravitationally bound to Earth.