Today I'd like to briefly discuss various common types of orbital trajectories that many satellites above your head use to complete their missions. Since a given orbit defines the location and velocity of a satellite at any given time, different orbits are used by different spacecraft to accomplish different tasks.

If you aren't very familiar with orbits, check out part 1 over here, which should help get you up to speed on the very basic conceptual aspects of orbital trajectories.

Fundamental Types of Orbits

When it comes down to it, there are only four types of orbital trajectories for an object orbiting a single large mass (and two of them re really just special cases of the other two): The conic sections - ellipses, circles, parabolas, and hyperbolas.

The four conic sections starting on the left define the four types of orbits with a single central gravitational object.
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Circular orbits are really just special cases of elliptical orbits (with eccentricity equal to zero) and parabolic trajectories ("perfect" escape trajectories) are really just special cases of hyperbolic trajectories (with eccentricity equal to one). Under the approximation that only one planet/star/asteroid/object influences the orbit (a very good approximation when you are close to Earth), every orbit comes down to one of these four types.

But that's not really what this post is about. I'd like to discuss more specialized types of the above four fundamental orbits that accomplish certain tasks. Where a spacecraft orbits Earth determines its mission lifetime, the environment it will be in, and how it can complete its mission, so orbit types matter quite a bit.

Equatorial Low Earth Orbit

What is probably the simplest possible realistic orbit is an equatorial, circular orbit near Earth. Such an orbit has an inclination values of zero degrees, meaning that a spacecraft in such an orbit will be constantly over the equator of the planet. If you stood on the equator and aimed an antenna upwards, you would be able to detect a spacecraft in an equatorial low Earth orbit about once every 90 minutes, every 90 minutes. Since the orbit is circular, an object in such an orbit is always travelling at the same speed, and is always at a fixed altitude above sea level.

Funnily enough, this special kind of orbit essentially never occurs (I had an undergrad orbital mechanics project a few quarters ago for which I was trying to find an example of an equatorial LEO object and simply couldn't find one). The reason for this is because most launch sites are not at the equator, so putting a spacecraft into a an equatorial orbit would require an excessive amount of fuel. Most Low-Earth orbit objects are at higher inclinations, usually above 30 degrees.

The blue region shows where an equatorial low-Earth orbit could occur.
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Low Earth Orbit also happens to have a somewhat damaging environment for spacecraft. While you are most certainly in space, there is still enough gas from the atmosphere left over that a spacecraft in a low orbit will have to occasionally fire a thruster to prevent itself from being slowly dragged back into the planet by aerodynamic drag forces (once an object reaches about 100km above the surface, it will be rapidly pulled back down due to the increasing air density before being quickly destroyed by re-entry heating). The bright side of a low orbit above the equator is that the radiation levels are reasonable, since any such object would still be well within Earth's protective magnetic radiation shielding.

Polar Low Earth Orbit

A similar orbit that actually get used extremely often is a polar orbit. Polar orbits are orbits that have inclinations near 90 degrees, allowing a polar-orbiting object to pass over both the north and south pole of the planet below. Since Earth rotates at a constant rate (giving us our 24 hour days), a satellite in a perfect polar orbit (Inclination = 90 degrees) can pass over every single point on the face of the Earth. Think about it like this - as you pass over the north pole, the planet is rotating, so from the point of view of someone on the ground the spacecraft is actually taking a slightly curved path over the surface to get back to the south pole.

This result makes polar orbits extremely useful. If you, for example, want to map the surface of a planet, your spacecraft simply needs to go into an orbit as close to polar as possible and it will eventually pass over every single square inch of land on the planet. This means that spy satellites, Earth science missions, and weather satellites will often be placed into polar orbits.

Examples of satellites in polar orbit trajectories.
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The other advantage of polar orbits is that satellites can be launched into them, theoretically, directly from any point on the planet by firing the rocket north or south. I currently live a few hours north of Vandenberg Air Force Base, California, which has several rocket launch pads that regularly (every month or so) send up satellites into polar orbits, producing some really nice views as you can see the rockets takeoff from hundreds of miles away in the right conditions.

Other than the ability to see anywhere on the planet given enough time, polar low-Earth orbits are similar to equatorial low-Earth orbits. One environmental difference is that polar orbiting spacecraft pass into regions near the poles where much more ionizing radiation is present, potentially causing software issues or long term damage to electronics.

Geostationary Orbit

A very special and very important orbital trajectory is the geostationary orbit.

As you know, Earth rotates around once every 24 hours. But at the lowest altitudes, spacecraft orbit the planet in only around 90 minutes, resulting in many sunrises and sunsets for the space station before anyone on the ground sees a single day pass.

But circular orbits take longer to complete the further away from the planet they get. So you can imagine, as you increase the radius of an orbit, there will eventually be a point where a circular orbit takes exactly the same amount of time to complete one revolution as Earth does. These orbits are called Geostationary Orbits, and they only occur at the equator (zero degrees inclination). A satellite in a perfect geostationary orbit will forever hang over a single spot on the globe. With no atmospheric drag, a satellite can remain in geostationary orbit effectively indefinitely.

GIF of a Geostationary Trajectory, showing that the orbit takes the same amount of time as a day on Earth does.
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Geostationary orbits (or GEO) occur around 35,000 kilometers from the surface of the planet - many times higher up than the International Space Station. There are hundreds of massive, car-sized satellites up there as I type this, mostly for communications. Direct TV is an example of a company that uses GEO satellites (in this case they are used to deliver television channels to the ground). Satellite internet providers also use GEO satellites to provide high-latency internet access to certain areas of the planet.

Geostationary objects are well outside the protected region created by Earth's magnetic field, and as such can be subject to radiation issues when things like solar storms arise. Getting to GEO in the first place also requires passing through both Van Allen radiation belts, which can cause more radiation issues for missions without proper protections in place.

Sun-Synchronous Orbit

The last special type of orbit I'd like to discuss is the sun-synchronous trajectory, or SSO.

There are numerous effects that can slightly change a spacecraft's trajectory, including atmospheric drag, pressure from the sun's light, and gravitational forces from other objects like the Moon. One fairly significant effect is known as J2, and results from the fact that Earth is not a sphere. The planet is actually an ellipsoid, and has a "bulge" around the equator, making Earth very slightly wider than it is tall. J2 causes any given orbit to precess, with constant changes in some of the orbital elements.

Without getting too far into the details, J2 causes any orbit to change in a predictable way that is constant (rate-wise) with time.

We can take advantage of J2 to create orbits that always pass over certain places on Earth at the same local time. For example, say my mission is to take pictures of Los Angeles at 5PM every day. I can do this by putting my satellite into a sun-synchronous orbit. The J2 effect slowly changes the satellite's orbit over time, but it does so in a way that constantly changes the orbit so that whenever the satellite ends up over Los Angeles, it's 5PM.

Sun-synchronous orbit example.
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SSOs can also be used to, for example, keep a spacecraft constantly in sunlight for long periods of time (essentially a satellite would never have a nighttime). This could have many benefits, including never ending solar power, or the constant ability to take pictures.

Conclusion

The four special orbits sampled here are just a fraction of the possible trajectories used. Every mission has a different orbit, often tailored for the specific mission objectives. However, low-Earth (polar and otherwise) and Geostationary orbits make up the vast majority of spacecraft destinations, so it is a good idea to be familiar with these trajectories if you are interested in space exploration.

I hope you were able to learn something new here. Let me know if you have any questions, comments, or corrections. I'll do my best to answer any questions you may have.

Thanks for reading!

Additional Reading:
Celestrak: Basics of the Geostationary Orbit
Wikipedia Entry on Sun-Synch Orbits