Satellites and their orbits

# Satellites and their orbits

## Introduction

All of the planets in the Solar System have natural satellites, bodies in orbit round them. The Earth has one natural satellite, which we call the Moon, and many Man-made, or artificial, satellites. Today most people other than astronomers usually refer to a planet's natural satellites as its moons and reserve the word satellite for artificial satellites in orbit round the Earth.

The rest of this Page is concerned only with the Earth's artificial satellites.

The orbit of a satellite may be elliptical or circular, at any height above the surface of the Earth, and at any angle to the Equator.

The Earth's atmosphere stretches thousands of kilometres into space, although of course it gets thinner as you go higher. All satellites are slowed down by air friction, and will eventually fall back to Earth - most burn up harmlessly as they do so. A satellite in a very high orbit will last much longer than one in a low orbit, but the higher the orbit the greater the energy, and so the bigger the rocket, needed to put it into orbit.

## Why does a satellite stay in orbit?

Everything in the Universe, from galaxies to atoms, obeys the same Rules. The Rules which explain the movement of galaxies, stars, planets and satellites were first put forward by Sir Isaac Newton (1642 - 1727).

Newton’s Theory of Gravity says that all bodies attract each other. The gravitational attraction between two bodies is given by

where F is the force between them, M and m their masses, r the distance between them, and G is the Universal Gravitational Constant.

The Universal Gravitational Constant is very small indeed, so the gravitational force between two bodies is also very small indeed unless one of them is very big, for example the Sun or the Earth, or they are very close to each other, for example the atoms and molecules in a solid. There is a gravitational attraction between you and me but neither of us notice it because I am not very large and you are not very close. (I expect you are as glad about this as I am!) But you do notice the gravitational attraction between yourself and the Earth: it is called your weight!

Newton’s First Law of Motion states that a body continues in its state of rest or of uniform motion in a straight line unless a force acts upon it. This means that if something is not moving we need a force to make it start moving, while if something is moving we need a force to make it stop or slow down or get faster or change its direction. If you have ever played any sort of ball game you will already know this for yourself.

Newton’s First Law of Motion means that we need a force to keep something moving in a circle (or any other curved path). You can feel this force for yourself by tieing something (something soft please) onto the end of a piece of string and spinning it round in a circle. The force in the string can be several times the weight of the object, depending upon how long the piece of string is (the radius of the circle) and how fast it is being spun round.

We often refer to this force as a g-force. A force on you of 1 g (for gravity) is your weight, so a force of 3 g means that the force acting on you is three times your weight. If you are not strapped into a car if it goes round a bend too fast you may get flung against the side of the car, or even out of it, by the g-force. Actually, you keep going in a straight line while the car goes round the bend, even if that is not what it feels like. There is no force trying to throw you out of the car, what you feel is the force trying to stop you from being thrown out, so that you move in a circle with the rest of the car rather than in a straight line.

A satellite stays in its orbit round the Earth because the gravitational force between the satellite and the Earth is exactly equal to the force needed to keep it moving in its curved path round the Earth rather than flying off into space or falling into the Earth. Newton’s Laws can be used to show that a satellite can move in a circular orbit with the Earth in the middle or in an elliptical orbit with the Earth at one focus.

There is more about circular orbits in the Page on The Tides and elliptical orbits in The Earth and its Orbit.

We show on the Page on the Tides that the orbit of an object depends only on its distance from the body it is orbiting and not its mass, for example the asteroid belt consists of millions of pieces of rock with diameters ranging from less than a metre to more that a hundred kilometres. But they are all the same distance from the Sun so are all moving at the same speed and in the same orbit. Similarly what is true of a satellite as a whole is true of everything inside it.

On the surface of the Earth the Earth's gravity is pulling us towards the Earth. When we stand on a pair of bathroom scales to weigh ourselves the only reason why we do not fall through the bathroom floor into the room below is because the floor is strong enough to support our weight. But inside a satellite you are in orbit round the Earth just as much as the satellite is: if there was a hole in the floor you would not fall through it, or if you let go of a spanner you were holding it would still stay travelling in the same orbit and would not drop onto the floor. So inside, or outside, a satellite everything including ourselves is weightless. Even the water in a bottle is weightless, so when we try to pour some out instead of going into the glass its surface tension pulls it into a spherical shape. This makes even the simplest tasks, like cleaning our teeth, very “interesting” (to use no stronger word), but also opens up lots of very exciting possibilities. Lots of experiments on weightlessness are being carried out in the International Space Station.

If you let go of a spanner while you are working inside the Space Station the spanner will of course still return to Earth when the rest of the Space Station does; when an astronaut really did let go of his Hasselblad camera while working outside the Space Shuttle it has stayed in its orbit long after the astronaut and the Space Shuttle returned to Earth.

It would be possible to build a large spacecraft and rotate it to produce an artificial gravity inside it, but so far no one outside Hollywood has actually built one.

## Satellites and radio waves

The ionosphere is a region of the Earth’s atmosphere stretching from about 80 km to 400 km above the Earth. It contains many charged particles so it reflects longer wave radio signals. This allows LW radio signals to be received over distances of hundreds or thousands of kilometres, but of course because they are reflected off the ionosphere they cannot pass through it. The shorter the wavelength the less they are reflected, so satellites and spacecraft must use very short wavelengths (SHF for super high frequency) to penetrate the ionosphere. But these very short waves cannot bend round objects, not even the Earth, so you can only send radio signals to or receive them from a satellite (or spacecraft of any sort) if it is in line of sight. This means that you cannot normally receive signals from a satellite unless you can see the sky. The GPS on your smartphone does not work indoors but it remembers your position from the last time you were out of doors.

There is more about this on the Electromagnetic Radiation Page.

## Circular Orbits

The higher the orbit of a satellite, that is, the further it is from the Earth, the longer it takes to orbit the Earth. The time it takes to orbit the Earth is called its period. A satellite in a circular orbit at a height of 800 km has a period of about a hundred minutes. (The Moon, at a height of about 400 000 km, has a period of about twenty nine days, about one moon-th, get it?)

A satellite at a height of about 36 000 km will have a period of twenty four hours. If we put a satellite into a circular orbit at a height of about 36 000 km above the Equator it will go round the Earth at exactly the same rate as the Earth is rotating on its axis so it will always be above the same point on the Equator. This orbit is called a geostationary orbit or a geosynchronous orbit (from the Greek for at the same rate as the Earth). A satellite in a geostationary orbit is however 36 000 km from the Earth and so you need a special very directional hi-gain aerial (usually a dish or a special aerial called a YAGI) to send signals to it or receive signals from it, but once you have aligned your dish or YAGI to point to the satellite you never have to align it again. Satellite tv comes from a satellite in a geostationary orbit, which is why you need a dish to receive it. “SatNav” satellites, and many other communications and other satellites are in much lower orbits so can use a much simpler aerial. SatNav and the Global positioning System are described on their own Page.

The footprint of a satellite depends upon its height. A satellite in a high orbit can see and send radio signals to a much larger part of the Earth’s surface than one in a lower orbit - a satellite which is out of line of sight is also out of radio contact.

A satellite in a geostationary orbit will see almost the whole of one hemisphere, but always the same hemisphere, whereas a satellite in any other orbit will pass over different parts of the Earth's surface. By turning these drawings through ninety degrees you can see that you cannot get satellite television at the North and South Poles. In fact you can show that you cannot get satellite tv at latitudes of more than about 75° North or South. But this area is little more than Antarctica and the Arctic Ocean.

A satellite in a polar orbit, that is, where the satellite always passes over both the North Pole and the South Pole every orbit, will in the course of a few orbits pass directly over every part of the Earth's surface.

The angle the orbit of a satellite makes with the equator is called its inclination. A satellite in a geostationary orbit has zero inclination, and one in a polar orbit has an inclination of 90°. The inclination of the orbit of a satellite depends upon what it is being used for: the International Space Station (ISS) is in an orbit at a height of about 400 km and has a period of about ninety minutes. It has an inclination of about 50°, which takes it over 85% of the Earth's surface and 95% of its population. There is more about the ISS in the Paragraph on Satellite Watching. The Hubble Space Telescope is in an orbit at a height of about 550 km with an inclination of about 29° - this gives it the best view of the centre of our galaxy.

Geostationary orbits are used for tv satellites, and some communications satellites, as once the satellite dish has been correctly aligned on the satellite it will remain aligned - of course if you want to receive signals from more than one satellite you must have more than one dish, or a motorised dish. They are also used for some weather satellites because you can take still pictures of a part of the surface of the Earth at regular intervals and transmit them back to Earth and store them, and then play them back at a higher speed to produce an animated sequence, as we see on the weather forecast on tv.

Satellites in geostationary orbit are 36 000 km from the Earth, so signals from them cannot be received without using a dish or YAGI, which rules them out for use with satnav and mobile phones etc. Satnav and communication satellites in lower orbit need much simpler aerials, but they have much shorter periods so several similar satellites in similar orbits are needed to ensure that you are always receiving a signal from at least some. A set of similar satellites in similar orbits is called a constellation. There are twenty four satellites in the GPS constellation.

A satellite in a low orbit will see a much smaller part of the Earth's surface but from much closer, and so photographs will show much more detail, but of course only a satellite in geostationary orbit takes all its pictures from the same point in the sky, so only pictures from a geostationary satellite can be animated. Satellites used for making maps or carrying out geological surveys are usually in low orbits.

## Solar Panels

All satellites get the energy they need to drive their cameras, on-board computers, transmitters and other electronic equipment from solar panels. Satellites in low orbits are often in the Earth's shadow (that is, the Earth is between them and the Sun) so need to have large rechargeable batteries on board; a satellite in a geostationary orbit is so far from the Earth that the only time it is in the Earth's shadow is for less than an hour a day for a few days near the time of the equinoxes (March 21st and September 21st), so it need only carry small rechargeable batteries.

However, at this time of year the Earth is between the satellite and the Sun at one point in its orbit but twelve hours later the satellite is between the Sun and the Earth, so your dish will be pointing not only straight at the satellite but also straight at the Sun, and you will be picking up a lot of solar interference.

Until the beginning of the Space Age, in the 1960s, solar panels were little more than a scientific curiosity; they have only become feasible for generating useful amounts of power because of the improvements in their performance brought about by the Space Race.

Solar panels can be used in satellites and spacecraft going to the Moon, Venus and Mercury and Mars, but not beyond Mars because they would be too far from the Sun to receive enough solar energy. Spacecraft going beyond Mars are powered by Radioactive Power Supplies, using the heat produced by the radioactive decay of plutonium-238 to generate electricity. Plutonium-238 is chosen because it is non-fissile, that is it cannot produce a nuclear explosion (unlike plutonium-239), so there is no danger if the spacecraft fails to launch properly and falls back to Earth, or eventually lands on another planet.

## Satellite watching

Satellites, like the Moon and the Planets, do not give out any light of their own: we see them only because they reflect the Sun’s light. Even the very largest satellites are too small to reflect enough light to be seen from the Earth without a telescope: it is only their huge solar panels which make it possible to see them without one. The solar cell arrays on the International Space Station (ISS) have a total area of about 1500 m² - this makes it very easy to see as it passes overhead, but of course you do need to know when it will be doing so. To find out all about the ISS and when you can see it you can visit the NASA ISS Site. You need to feed in your country and the nearest large town but once you have done this for the first time it is well worth bookmarking the Page and checking it every week. It goes over most countries at least once a day but of course you can only actually see it at night. It moves across the sky quite quickly and is seldom visible for more than four minutes. There are also other web sites giving the times of visibility of other satellites which can be seen with the naked eye. Heavens Above is one of these, and this also gives lots of other information about what you can see in the sky, but it is not quite as easy to use as the NASA site, and it carries advertising. Satellites in geostationary orbits are of course far too far away to be seen without a powerful telescope.

## The life and death of a satellite

A satellite in orbit round the Earth is subject to the Earth's gravity, which is the force keeping it in its orbit. But it is also subject to the gravity of the Sun and Moon, even the gravity of the asteroids and other planets, to atmospheric drag, and to impact from particles of dust and other space debris, and also to the solar wind. All of these tend to disturb its orbit or set it spinning, so that for example its solar panels no longer point at the Sun. On-board rockets are needed to correct for these disturbances. These rockets are controlled by either on-board computers or radio signals from an Earth station. The ISS is in quite a low orbit and is subject to a lot of atmospheric drag, so its orbit is gradually getting lower: it needs regular boosts to put it back into a higher orbit. A satellite in geostationary orbit is subject to very little atmospheric drag but at its altitude it is almost totally unprotected from the solar wind and it needs frequent control interventions to keep it in the correct orbit.

At some stage the satellite will come to the end of its life: it may be damaged by meteorite impacts so its solar panels or other equipment no longer work properly, its task may be taken over by another satellite, for example analogue tv satellites are replaced by digital ones, or it may just run out of fuel for its control rockets. Once it is no longer being controlled its orbit will begin to change, and almost all changes to its orbit will tend to make it more elliptical - elliptical orbits are discussed in the next section. An elliptical orbit will take it nearer the Earth for a part of each orbit, and the increased atmospheric drag will gradually slow it down, putting it into a lower and lower orbit, and eventually it will fall to Earth, usually burning up the Earth's atmosphere.

This is the fate of all satellites, even Space Stations, except that Space Stations are too big to burn up completely in the Earth's atmosphere. These are brought down in a controlled way, by firing special on-board rockets, so that the pieces fall into the sea or uninhabited parts of the Earth's surface.

The time taken for a satellite to fall to Earth depends upon its height. The Hubble Space Telescope, at a height of about 550 km, was put into orbit in 1990 and it is estimated it will eventually fall to Earth and burn up in the atmosphere some time after 2020. (The mirror will not burn up.) Satellites in geostationary orbits are so high up that they will not actually fall to Earth and burn up for at least a thousand years, although they will cease to be in geostationary orbits very soon after they stop being controlled. Then they become just so much space junk. There are currently more than three hundred satellites in geostationary orbit and the number is increasing every year.

Space junk, Man-made objects in orbit round the Earth, includes old satellites and the rockets used to put them into orbit, a Hasselblad camera dropped by an astronaut working outside the Space Shuttle, and a vast amount of other stuff. Some of it might be dangerous if it fell to Earth without burning up in the atmosphere; even a pea-sized piece would be dangerous if it hit a satellite or spacecraft travelling at 12 000 km/hr. NASA is currently tracking more than fifteen thousand pieces of space junk.

## Elliptical orbits

Most satellites are in circular or almost circular orbits, but a few very specialised satellites are put into very elliptical orbits. These come very much closer to the Earth at one point in their orbit. The closest point to the Earth is called perigee and the furthest point from the Earth is called apogee.

Elliptical orbits are often used for observation and reconnaissance (spy) satellites. These are designed to come very near the Earth at the point of interest, for example a place where there is a lot of military activity, to take photographs, monitor radiation levels, and record radio, even mobile phone, transmissions. These are stored on board the satellite and then transmitted back to its base as it flies over it. A satellite in a circular orbit at this height would be subject to so much atmospheric drag that it would have a very short life. To extend its life it is put into an elliptical orbit so that for most of its orbit it is much higher and so experiencing very much less drag.

© Barry Gray, revised May 2014