How Satellites Stay in Orbit: Gravity and Geostationary Orbits

Orbits, Gravity and Satellites

Gravity pulls the Moon, the ISS and every satellite toward Earth, and each one stays up because it moves sideways so fast that it keeps falling around the planet instead of into it.

This lesson is mapped to objective SO 1.2 of the CSEC Integrated Science syllabus, how bodies stay in orbit; it is not endorsed by CXC or the Ministry of Education. Teachers: the Teacher Page for CSEC sets this lesson beside the other four objectives, with class sheets dated for Guyana. All times on this page are Guyana time (America/Guyana, UTC-4, no daylight saving). Georgetown numbers use 6.80° N, 58.16° W. Lethem numbers use 3.38° N, 59.80° W.

Gravity pulls everything toward everything

Every object with mass pulls on every other object. This pull is gravity. The more mass an object has, the harder it pulls. Earth is so massive that its pull holds you on the ground, keeps the air around the planet and holds the Moon in its path.

Gravity gets weaker with distance, but it never switches off. It follows an inverse-square law: twice as far from Earth's centre, the pull is a quarter as strong.

At the height of the International Space Station, about 420 km up, Earth's pull is still about 88% as strong as on the ground.
At the Moon's distance, 384,400 km away, it is about 3,600 times weaker than on the ground, and still strong enough to keep the Moon going round.

So astronauts on the ISS do not float because there is no gravity up there. They float because they and the station are falling together, all the time.

Astronauts float inside the ISS, about 420 km above the ground. Why?

There is no gravity in space
The station is too far away for Earth to pull it
The station and the astronauts are falling around Earth together (the right answer)
The air inside the station holds them up

Earth's pull at that height is still about 88% of what it is on the ground. The station and everyone in it fall together, so nothing presses them against the floor, and they float.

Falling around the Earth: Newton's cannon

Isaac Newton imagined a cannon on a mountain so tall that its top was above the air.

Fire a ball slowly and it curves down and lands nearby.
Fire it faster and it lands farther away.
Fire it fast enough and, as it falls, the curved Earth drops away beneath it just as fast. The ball keeps falling but never reaches the ground. It is in orbit.
Fire it faster still and it swings out into a stretched loop, an ellipse.
Fast enough, and it escapes Earth's pull and never comes back.

An orbit is falling around a planet without ever hitting it. Gravity provides the pull toward the centre, and the sideways speed carries the object past the planet.

With no air, the speeds from the ground would be about 7.9 km/s for a circle and 11.2 km/s to escape. That is about 28,000 km an hour for a circle.

Newton's cannon, worked out exactly: a ball fired level from a tower as tall as the ISS is high. Change the speed and watch it fall back, circle, stretch into an ellipse or escape.

The tower in the piece is 420 km tall, the height of the ISS. The speed that makes a circle from there is 7.66 km/s, which is the speed the ISS really travels at.

A ball is fired level from the top of a very tall tower, above the air. It is fired a little faster than the speed for a circular orbit, but slower than escape speed. What happens?

It falls back to the ground
It circles at the same height for ever
It goes round in an ellipse, swinging higher on the far side (the right answer)
It flies off into space

Faster than circular speed but slower than escape speed gives an ellipse. The tower top is the lowest point of the loop, and the far side swings out higher.

Natural satellites

A satellite is any object that orbits a larger one. A natural satellite is one nobody built.

The Moon is Earth's natural satellite. It is on average 384,400 km away and goes once round Earth in about 27.3 days, measured against the stars.
The planets orbit the Sun, held by the Sun's gravity in the same way.
Moons of other planets: Jupiter has dozens. Its four biggest, Io, Europa, Ganymede and Callisto, show in binoculars from Guyana as points of light lined up beside it. Watch them move night by night with Jupiter's Moons Tonight.

The farther a body is from what it orbits, the slower it moves and the longer it takes to go round. Mercury, closest to the Sun, takes 88 days. Earth takes a year. Saturn takes more than 29 years. This pattern is Kepler's third law.

The planets around the Sun today and over the next two years: the inner planets race round while the outer ones crawl.

Artificial satellites

An artificial satellite is one people built and launched. Thousands orbit Earth today. They give us weather pictures, television, phone calls, internet links and the position on your phone's map.

Kepler's third law works for them too: the higher the orbit, the slower the satellite and the longer one trip round.

| Satellite | Height above the ground | One orbit takes | Speed | |---|---|---|---| | International Space Station | about 420 km | about 93 minutes | 7.66 km/s | | Hubble Space Telescope | about 483 km | about 94 minutes | 7.63 km/s | | GPS navigation satellites | about 20,200 km | about 12 hours | 3.87 km/s | | Geostationary satellites | 35,786 km | one turn of Earth, 23 h 56 min | 3.07 km/s | | The Moon (natural) | about 384,000 km | about 27.3 days | 1.02 km/s |

The heights come from NASA (the ISS, Hubble) and the US government's GPS site; the periods and speeds are worked out from them with Kepler's third law. NASA puts the ISS between 370 and 460 km up, going round about 16 times a day; at 420 km it is a little under 16.

You can see artificial satellites from Guyana with your own eyes. After sunset and before dawn, the ISS and many smaller satellites still catch sunlight high above you and glide across the dark sky as steady points of light. The ISS Pass Predictor lists the coming passes for your town, and Why the ISS vanishes shows why a pass can fade out halfway across the sky.

The ISS orbits about 420 km up and GPS satellites about 20,200 km up. Which goes round faster?

The ISS: lower orbits are faster and take less time (the right answer)
GPS: higher orbits are faster
They move at the same speed
Neither moves: satellites hang still

Lower orbits are faster. The ISS goes round in about 93 minutes at 7.66 km/s; a GPS satellite takes about 12 hours at 3.87 km/s.

Geostationary orbit: a satellite that stays put

Go high enough and one trip round takes exactly as long as one turn of Earth: 23 hours 56 minutes. That height is 35,786 km above the equator. A satellite there that moves east, the way Earth turns, stays above the same spot on the equator. From the ground it seems to hang still in the sky. This is a geostationary orbit.

Satellite television dishes and some weather and phone satellites use it, because a dish can be bolted in place and never has to follow the satellite.

Every geostationary satellite sits above the equator, so they form a line across the sky called the geostationary belt, or Clarke belt. Where that line sits depends on your latitude.

From Georgetown, a satellite on the same longitude (above 58.2° W) stands 82° up, due south: almost overhead.
From Lethem, closer to the equator, the same kind of satellite stands 86° up.
From London, at 51.5° N, it is only 31° up in the south.

So a dish in Guyana aimed at a satellite near our own longitude points steeply up, tipped a little toward the south. A satellite far to the east or west of Guyana sits lower, toward the east or west.

The geostationary belt across the sky from Georgetown, Lethem and London: slide a satellite east or west and see where a dish must point.

Where must a geostationary satellite be?

Above the North Pole, so it can see the whole Earth
Anywhere, as long as it is 35,786 km up
Above the equator, 35,786 km up, moving east once each time Earth turns (the right answer)
Just above the air, moving very slowly

Only above the equator, at 35,786 km, moving east once each time Earth turns, does a satellite keep pace with the ground below it.

Guyana's neighbour in space

Europe's Spaceport, the Guiana Space Centre at Kourou in French Guiana, is about 620 km east-south-east of Georgetown, at 5° N. Launching close to the equator gives a rocket a free push from Earth's spin of about 460 m/s, and puts it close to the plane of geostationary orbit. That is one reason Europe launches from South America's north coast.

Try it: gravity on a string

Safety: use a soft ball, swing it low, and keep everyone well clear.

Tie a soft ball to a strong string about 1 m long.
In an open space, swing it in a flat circle beside you. The string is gravity: it pulls the ball toward the centre.
Swing it faster. Feel how the string has to pull harder.
Let go at one point of the circle while a partner watches. The ball flies off in a straight line along the edge of the circle, not straight out. With no pull toward the centre, nothing bends its path.
Draw what you saw: the circle, the point where you let go and the path the ball took.

Spot a satellite. Open the ISS Pass Predictor for your town and pick a pass marked worth going out. Go out a few minutes early, face where it appears, and time how long it takes to cross the sky. Then look up for other, fainter satellites gliding steadily on a dark evening in the first hour or two after sunset.

Find your dish's direction. If there is a satellite dish nearby, look at which way it points. In Guyana most point steeply up, and the piece above shows why.

Common mix-ups

"There is no gravity in space." There is. At the ISS's height Earth's pull is about 88% as strong as on the ground. Astronauts float because they are falling around Earth with their station.

"Satellites need their engines to keep going round." No. Once a satellite is moving fast enough, it keeps falling around Earth with no engine. Low satellites like the ISS do brush the very thin top of the air, so they fire their engines now and then to climb back up.

"A geostationary satellite can hover over any town." No. It can only stay over a point on the equator. That is why, from Guyana, those satellites sit in the southern half of the sky, and from far north they sit low in the south.

Quick check

A satellite sits 35,786 km above the equator at 58° W, the same longitude as Georgetown. Which way does a dish in Georgetown point to receive it?

Low in the north, just above the horizon
Steeply up, about 82° above the horizon, toward the south (the right answer)
Straight down, through the Earth
It must turn all day to follow the satellite

Steeply up and a little to the south: the satellite is over the equator, just south of Georgetown's latitude, and it keeps pace with Earth's turning, so the dish never has to move.

Where next

Continue with ASTRO-109: Exploring Space, on the space station, the space telescopes and the missions to Mars and Jupiter.