Jason DavisJan 17, 2014

# How to get a satellite to geostationary orbit

I’ve been writing a lot about geostationary satellites lately. In December, SpaceX’s upgraded Falcon 9 rocket placed the SES-8 communications satellite into geostationary transfer orbit, and on Jan. 5, India’s Geosynchronous Satellite Launch Vehicle pulled off a similar feat with the GSAT-14 communications satellite

As I wrote about the GSLV-D5 mission, I was tempted to include this standard informational line, punched directly out of the press kit:

The satellite was placed into a geostationary transfer orbit with a perigee of about 180 kilometers, an apogee of about 36,000 kilometers and an inclination of 19.3 degrees.

But unless you’re familiar with basic orbital mechanics, that sentence doesn’t have much meaning. What’s a transfer orbit? Is there a difference between geostationary and geosynchronous? Why is there such a wide range between the perigee and apogee?

For help explaining all of this, I turned to Mike Loucks of The Astrogator’s Guild. The Astrogator’s Guild uses a software package called STK/Astrogator from Analytical Graphics Inc. that is used to help spacecraft mission managers plan the trajectories of a variety of space missions. The software has been used on numerous NASA missions, including WMAP, LRO, LCROSS, New Horizons, Messenger, LADEE and MAVEN.

The first concept I want to tackle is the difference between a geosynchronous and geostationary orbit. Although these terms are often used interchangeably, they are not the same thing:

A Geosynchonous Orbit (GEO) takes a satellite around the Earth at a rate of once per day, keeping it roughly in the same area over the ground.

A Geostationary Orbit (GSO) is a geosynchronous orbit with an inclination of zero, meaning, it lies on the equator.

All geostationary satellites are geosynchronous. Not all geosynchronous satellites are geostationary.

Think of it like this: the “synchronous” part of geosynchronous describes the rate of the satellite’s orbit but says nothing about its inclination—the orbit’s angle with respect to the equator. A geosynchronous satellite with a non-zero inclination will trace out a figure eight in the sky as it dips above and below the equator.

The “stationary” part of geostationary describes how a satellite in this orbit remains fixed with respect to an observer on the ground. This is an ideal orbit for communications satellites, since ground-based antennas can remain pointed at the same spot in the sky.

It’s also important to remember that even geostationary satellites drift over time as they are tugged on by the moon and sun’s gravity. For that matter, the Earth’s gravity isn’t uniform, either, so the satellite needs an onboard fuel supply to make slight corrections over time.

What, then, is a transfer orbit? Rockets sending payloads to geosynchronous and geostationary orbits drop off their payload in transfer orbits, halfway points en route to the satellite’s final position. From transfer orbit, a satellite conducts engine burns to circularize its orbit and change its inclination. Both SES-8 and GSAT-14 were bound for geostationary orbits, so we say that the Falcon and GSLV launched their payloads to geostationary transfer orbits.

What does a geostationary transfer orbit look like, and how does the satellite get from there into its final position? Of the two satellites I mentioned, GSAT-14 took the more common route, so we’ll use it as an example. (SES-8 used a supersynchrounous transfer orbit, where the orbital period is longer one day.)

Mike doesn’t have all the parameters required to make an exact GSAT-14 simulation, so he’s made a few assumptions and created a virtual cocktail napkin outline for us to follow.

Let’s revisit the line I struck from my GSLV article:

The satellite was placed into a geostationary transfer orbit with a perigee of about 180 kilometers, an apogee of about 36,000 kilometers and an inclination of 19.3 degrees.

GSAT-14 launched out of India’s Satish Dhawan Space Centre. The mission began in powered flight under the GSLV, which is represented by the red line:

When it hit the equator, the GSLV finished its share of the work and released GSAT-14. This point in the orbit is our descending node. Ascending and descending nodes are just fancy ways of saying you crossed the equator in either a southbound (descending) or northbound (ascending) direction. For a geostationary transfer orbit, the descending node is also at perigee, the orbit’s lowest point. Here, GSAT's altitude is 180 kilometers. For comparison, the International Space Station has a typical altitude of just over 400 kilometers.

GSAT-14 now coasts as it dips beneath the equator to a latitude of 19.3 degrees (our inclination), and starts heading back north. As we cross the equator again, we’re at the ascending node, and we’re also at apogee, the highest point of our orbit—36,000 kilometers above the Earth. For perspective, the Earth’s radius is 6,400 kilometers and the average distance to the moon is 384,000 kilometers. In other words, we’re five-and-a-half radii above the planet, and roughly one-tenth of the way to the moon.

Here’s what that looks like from two different angles:

Our orbit is still fairly elliptical at this point. That’s no good—we want to circularize the orbit and lower its inclination to zero. We can accomplish both of these tasks by conducting a series of engine burns at apogee. According to the Indian Space Research Organization, GSAT-14 used three Apogee Motor Firings (AMFs) to get into its final orbit. For simplicity’s sake, we’ll assume a burn happens each time the satellite hits apogee.

Why do three burns, instead of one long burn? Mike says that in some cases, single, long-duration burns can be less efficient, and there may also be limitations on a spacecraft’s engines that prevent them from firing for too long. We’ll also assume each of the three burns gets us a third of the way to our final orbit.

After the first burn, our orbit becomes the pink line:

After a second burn at apogee, our orbit becomes the teal line:

And after a third burn at apogee, our orbit becomes the green line:

And there we are! One geostationary satellite roughly 36,000 kilometers high, positioned at 74 degrees East, ready to provide communications services to the people of India. Here’s a video that puts it all together: