Since the last human mission to the moon, all of our explorations in space have focused on low Earth orbit. But what’s so special about LEO?

Low Earth orbit is not very high.

Yes, we think about LEO as being way up there in space—and it is indeed very high. The International Space Station orbits 400 km above the Earth’s surface. However, in terms of orbits, that’s not that far. Take a look at this python model (using trinket.io) that shows the path of the ISS around the Earth. Just so you can see it, I made the space station about 2,000 times larger than it actually is. Oh, and this is a python program so that you can look at the code and change it if you like. Also, you can rotate and zoom in and out of the view with right-click and scrolling.

As you can see, LEO is not very far from Earth. You can barely see it at all. But what about a geostationary orbit? A geostationary satellite is at an orbital distance such that its angular speed is the same as that of the Earth. This means that as it orbits it appears to be above the same spot on the equator of the Earth. Here is another simulation to show the distance of a geostationary satellite.

Humans don’t really go to a geostationary orbit. It’s all about LEO (for now).

LEO is more about speed than altitude.

Let’s pretend like there is no air on the surface of the Earth. Now you want to launch a satellite into low Earth orbit. There are two things you have to do (while holding your breath since there is no air). First, you have to raise the altitude of the satellite up to 400 km above the surface of the Earth. Second, you have to increase the horizontal speed of the satellite such that as gravity pulls it curves into a circular orbit. But which requires more energy? Here is a super quick tutorial on orbital energy.

Suppose I want a spacecraft orbiting at a distance of r from the center of Earth (which has a radius R). The only force on the spacecraft is the gravitational force which decreases with distance from the center. This force has to make the object move in a circle of radius r such that it has an acceleration. So, I get (G is the gravitational constant and M E is the mass of the Earth):

The change in energy to get something in orbit would be the sum of the changes in kinetic energy and the changes in gravitational potential energy (going from the surface to orbit). Both of these depend on the distance from the center of the planet.

Substituting in for the velocity of an orbiting object:

That first term in the is the kinetic energy (in terms of orbital radius) and the other terms are due to the change in gravitational potential energy. If I put in a value of r corresponding to a 400 km altitude, then the kinetic energy is 89 percent of the total energy needed for orbit with the gravitational potential energy just being 11 percent.

But what about different orbital distances? The higher you go, the less kinetic energy you need and the more gravitational potential energy is needed. Here is a plot showing the energy needed for different orbits (starting from the surface of the Earth).

Yes, this plot ignores energy loss due to air drag in the atmosphere as well as the boost you could get from the rotation of the Earth.

LEO is not permanent.

When a spacecraft goes into low Earth orbit, it won’t stay there forever. As objects orbit the Earth, they interact with the atmosphere. There is a small air drag force similar to the forces a on a bullet shot from a gun—well the big difference is the size of the drag force. In LEO, the air is really thin and exerts just a tiny force on objects.

Generally, bigger objects have lower effects from drag since they tend to also have very large masses. The drag force is proportional to the cross sectional area of the object but the mass is proportional to the volume. So, if you double the length of a spacecraft (and scale all dimensions up too) then the area will increase by 4 but the volume will increase by 8. With a larger mass, the force is a lower influence.

How do you keep a spacecraft in low Earth orbit? They need a little help from a friend. For the ISS, this help can come from ESA ATV when it uses it’s thrusters to reboost the space station.

LEO is still the first step into space.

Even though low Earth orbit is lacking in many ways, it does offer something very useful—time. Once you get into LEO, you have time to make your next move. Yes, it’s not permanent but it is permanent-ish. Low Earth orbit is sort of like the lowest rung of a ladder. It doesn’t get you very far but you have to take that first step.

But what is the next step? The next rung of the ladder is probably getting all the way out of Earth’s gravitational well. Starting from the surface of the Earth with a speed of 11.2 km/s, you would have enough energy to leave and never come back—we call this speed the escape velocity.

Of course once you get out of Earth’s influence, you are still interacting with the Sun (just like the Earth). If you want to escape the whole solar system (starting from the position of the Earth), you would need an initial velocity of 42.1 km/s. Which leads to the last question: Where would you go from there?