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# How to get a satellite to geostationary orbit

Posted by Jason Davis

17-01-2014 9:24 CST

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.

NASA / University of Texas Center for Space Research

##### The Earth's gravity field
This animation, created with data from the GRACE spacecraft, shows the variances in Earth's gravity field.

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:

Mike Loucks / SEE

##### GSAT-14 powered flight and coast

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:

Mike Loucks / SEE

##### GSAT-14 approaching apogee

Mike Loucks / SEE

##### GSAT-14 first apogee

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:

Mike Loucks / SEE

##### GSAT-14 after first engine burn (polar view)

Mike Loucks / SEE

##### GSAT-14 after first engine burn (equatorial view)

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

Mike Loucks / SEE

##### GSAT-14 after second engine burn (polar view)

Mike Loucks / SEE

##### GSAT-14 after second engine burn (equatorial view)

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

Mike Loucks / SEE

##### GSAT-14 after final engine burn (polar view)

Mike Loucks / SEE

##### GSAT-14 after final engine burn (equatorial view)

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:

### Other related posts:

Gene Van Buren: 01/17/2014 10:59 CST

Nice explanations, Jason (& Mike)! An additional complication then is timing this all so that the final burn ends with the satellite at the desired longitude. Perhaps that's achieved by waiting out a few of the un-syncrhonous orbits until the the longitude is right?

Stephen Williams: 01/17/2014 03:26 CST

Wait a minute. You're not just circularizing the orbit, you are also changing the inclination. As I understand it, the orbit will always include the point of the last burn, so there has to be at least one burn on the ascending or descending node of the orbit. Something is missing in this explanation.

Stephen Williams: 01/17/2014 03:27 CST

Oh, wait, the apogee IS the ascending node. Got it!

Joey Joe Joe: 01/17/2014 05:24 CST

What an informative article! Thank you so much!

markogts: 01/18/2014 04:57 CST

Hi, well written, but I am not sure about a detail: AFAIK, orbital plane changes are cheaper if the speed is low. For the same delta v you get more velocity angle change if the speed is small. So I suspect that the first burn is mainly devoted to orbital plane alignment and the following ones to circularization.

Jason Davis: 01/20/2014 03:45 CST

Gene, I wondered about that too. The “final” orbit may still require a little tweaking. From Mike: "In order to get into the right spot (longitude) at GEO, a spacecraft will usually transfer up to an intermediate orbit slightly above or below GEO altitude. At this altitude, the spacecraft will drift slightly with respect to the Earth (rather than remain fixed, as it would if it were at exactly GEO altitude). The spacecraft will then drift into the right spot, and then do small circularization burns at exactly the right spot to stop the drift and then "lock" into the final GEO location. (I say "lock" because GEO spacecraft still require maneuvers to keep them from drifting out of their assigned slots over time due to the non-spherically symmetric nature of the Earth's gravity).”

Sridhar Narayanan: 01/20/2014 08:42 CST

Gene and Jason, The third firing of the liquid apogee motor on January 9 placed the satellite in a circular near-geostationary orbit with an inclination of 0.25 degrees. The satellite was then allowed to slowly drift towards its orbital slot of 74 degrees east. It reached there on January 18, when a final short burn of the apogee motor placed it in the intended geostationary orbit. See this series of press releases from ISRO to see the sequence of activities to move the GSAT-14 from the geostationary transfer orbit it was placed on at launch to its final orbital slot. http://isro.org/gslv-d5/d5-post-updates.aspx

Bob Ware: 01/29/2014 12:52 CST

If I recall correctly, the burns are done 180 degrees from the needed point of effect. EX: burn on perigee to affect apogee.

Mudasir: 03/29/2015 05:00 CDT

It is really nice information shared ever, i have a question from the date of launch till final destination (Clarks belt), how the communication remains intact with satellite when it goes off the line-of light ...?

demoya: 05/06/2015 01:57 CDT

Through a global network of ground stations. This network is used also to relay data to the non-synchronous and non-stationary satellites.

PRajaram: 08/29/2015 09:09 CDT

Jason, This is a wonderful, very easy to understand explanation. Thank you! Can you also please explain the supersynchronous route taken by SES? This is the first time I'm hearing of the supersynchronous route to get to GStO.

John Martin: 02/02/2016 10:37 CST

The earth moves through space at 30-35km/s. How does the maths include the location of the earth in space, whilst the earth moves with such variable velocities around the sun in space? Also how does the satellite trajectory account for the earths motion towards and away from the sun of about 3 million miles caused by the elliptical orbit around the sun? thanks John M

Good question from John Martin. But this question was posted on 2nd February, and I wonder if there is anybody who can answer? This is important. All motions need to be taken into account. I would like to add my own questions: If the satellite is 36,000 km out, what speed is it rotating at to remain geosynchronous? Must be a fair clip. As the earth is orbiting the sun, the satellite must also be orbiting the sun but at a much faster pace. Does anyone know what that might be? Many thanks and if anyone has any answers I would be most appreciative, grateful and interested. Cheers ;)

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