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Orbits and satellites - Physics narrative
Physics Narrative for 11-14
A Physics Narrative presents a storyline, showing a coherent path through a topic. The storyline developed here provides a series of coherent and rigorous explanations, while also providing insights into the teaching and learning challenges. It is aimed at teachers but at a level that could be used with students.
It is constructed from various kinds of nuggets: an introduction to the topic; sequenced expositions (comprehensive descriptions and explanations of an idea within this topic); and, sometimes optional extensions (those providing more information, and those taking you more deeply into the subject).
The ideas outlined within this subtopic include:
- Natural and unnatural motions
- Motion and centripetal force
- Satellites and their uses
Physics Narrative for 11-14
Over the last 50 years, satellites have become as commonplace as other tools of technology before them, such as clocks, telephones and computers. Satellites help us to communicate, navigate, monitor the environment and forecast the weather.
A satellite is any object that moves around another object. So the Moon and Meteosat (the weather probe) are satellites of the Earth, and the Earth is a satellite of the Sun.
Artificial satellites have many uses. The idea of using a satellite for telephone communications was first proposed by Arthur C Clarke, the famous science fiction writer, back in 1945 in the magazine Wireless World. At the time, many people thought that he was mad as they could not think of a way of putting satellites into orbit around the Earth. Yet in 1957, the Soviet Union succeeded in putting the first satellite, Sputnik I, into orbit (image © NASA). People often assume that satellites must be physically big in size. In fact, Sputnik I was about the size of a basketball, weighed only about 83 kilogram, and took about 98 minutes to orbit the Earth on its elliptical path.
The success of Sputnik I was an enormous shock to the Americans and they rapidly accelerated their own space program, launching the first communications satellite, Telstar, in 1962. This was followed by other satellites to explore Mars (the Mariner satellites) between 1962 and 1965, and then landing a man on the Moon in 1969.
But the first step is to explain the circular motion of satellites.
Explaining circular motion
To make anything move along a circular path it is essential to have a force that acts towards the centre of that path.
For example, to make a rubber bung travel around in a circular path on the end of a string, there must be a force acting towards the centre of the motion. The force acting towards the centre of the motion is called a centripetal force.
centripetal is a combination of two Latin words:
centrum meaning centre and
peto meaning to go in. The centripetal force goes in towards the centre.
It's necessary to have a centripetal force to maintain a circular motion because if there is no resultant force acting on an object (that is all forces acting on the object add to zero), then the object travels with uniform motion in a straight line, or stays at rest.
Newton's first law
This is an expression of Newton's first law of motion (see the SPT: Motion topic). If you want to change the motion of an object and make it follow a circular path, you must exert an inward centripetal force.
In the case of the rubber bung, the centripetal force is provided by the tension in the string. In other words the string provides a continuous force on the bung, tugging it along its circular path.
When the string is cut the centripetal force is removed and the bung leaves its circular orbit, continuing along a tangential path.
In the case of the Moon orbiting the Earth, or the Earth orbiting the Sun, it is not an invisible string which tugs each body along its circular path, but the force of gravity. For any Earth satellite it is the gravitational pull of the Earth on that satellite which keeps it moving in its orbit.
Newton challenged what counted as natural motion
Before Newton, people used to think that circular motion was
natural and needed no explanation. Newton's great insight was to realise that motion in a straight line is the natural form of unforced motion and that it is circular motion that requires an explanation.
This led Newton to ponder on the nature of the force that keeps the Moon in orbit around the Earth. The incident that is supposed to have suggested the answer to him was the apple falling on his head. If gravity can act between the Earth and the apple, why should it not also act between the Earth and the Moon? Newton's subsequent calculations led him to the idea that gravity is a universal force acting between all objects.
Acceleration to move in a circle
Physics Narrative for 11-14
The connection between circular motion and the motion of satellites
The centripetal force is interesting in that it acts at right angles to the direction of travel of the object moving along a circular path. As such, the centripetal force does not increase the speed of the object, but simply changes its direction of travel.
It's a bit strange (at least at first) to recognise that an object moving around a circular path at steady speed is accelerating. The centripetal force is an unbalanced force and as such accelerates the object. This acceleration is manifested as a continuous change in direction rather than as an increase in speed.
This is an acceleration because acceleration is defined as the change in velocity in each unit of time.
Velocity depends on both speed and direction, so a change in direction is enough to give a change in velocity.
How do satellites stay in orbit?
Physics Narrative for 11-14
Getting into orbit
Perhaps the first question to think about is how they get into orbit in the first place. Let's try a thought experiment that was first suggested by Sir Isaac Newton himself.
Imagine a mountain on the Earth's surface that is so big that its summit sticks out above the Earth's atmosphere (it would need to be about ten times as high as Mount Everest). Supposing you climb to the top of this mountain and throw a cricket ball horizontally outwards. The ball is pulled by gravity so that it falls to the ground along a curved path.
Let's assume you now try a lot harder and the ball travels much farther outwards before it hits the ground.
You now summon up all of your strength and manage to throw the ball so fast that it flies outwards and as it falls, its path follows the curvature of the Earth. The ball follows this falling path right round the Earth. In fact, you need to duck as it comes by after completing one orbit! You have managed to throw the ball into orbit around the Earth so that it is now an Earth satellite.
Putting satellites into orbit
Putting satellites into orbit involves the same kinds of actions and ideas. First of all the satellite is placed on top of a huge rocket to carry it away from the Earth and up through the atmosphere. Once it is at the required height, sideways rocket thrusts of just the right strength are applied to send the satellite into orbit at the correct speed.
If the satellite is
thrown out too slowly it will fall to Earth because the centripetal pull of gravity is too great. If the satellite is thrown out too fast it will escape from the Earth's orbit because the gravitational pull is not sufficient to provide the required centripetal force. With the correct
launch speed the satellite continues in its falling orbit around the Earth.
It is just a matter of setting the horizontal speed of the satellite such that the gravitational pull of the Earth (at the given height) tugs it round on its orbital path.
When talking about satellites with pupils it is quite likely that someone will pose the (very good) question:
Cas: Miss, what keeps the satellite going?
The short answer to the question is:
Teacher: Nothing keeps it going, it keeps going itself.
As the satellite is launched from the carrier rocket, a rocket thrust acts to throw it out in the desired direction at the prescribed speed. The crucial point to understand here is that the satellite speeds up only for as long as the rocket thrust is acting. Once the rocket motor is switched off the satellite continues at the final speed achieved, neither speeding up nor slowing down, and the gravitational pull of the Earth continuously tugs the satellite in and along its orbital path. In this sense, the satellite
just keeps going itself.
If the satellite was moving through empty space it would stay in its orbit forever, there being no forces acting to speed it up or to slow it down. In reality low orbit Earth satellites are not travelling through empty space and so experience a resistive force or
drag due to the
thin atmosphere which they encounter. In such circumstances, occasional rocket thrusts are needed to maintain the motion of the satellite, otherwise it will fall to Earth.
Geostationary and polar orbits
Satellites can operate in several different types of Earth orbit. A geostationary orbit is one in which the satellite is always in the same position with respect to the rotating Earth. The satellite orbits at an elevation of approximately 35 831 km, because that produces an orbital period (time for one orbit) equal to the period of rotation of the Earth (23 hour, 56 minute, 4.09 second).
By orbiting at the same rate, in the same direction as the Earth (synchronous with respect to the rotation of the Earth), the satellite appears stationary from the Earth's surface. The big problem with geostationary satellites is that there is only one distance from the Earth where they can orbit while maintaining the same position above the Earth's surface. Given that there are now over 22 000 satellites in orbit around the Earth, this geostationary orbit is getting highly crowded and there is great competition for space.
Other satellites are in polar orbits. On every circuit of the Earth, a polar satellite travels over both the North and South poles. Polar satellites do not remain above the same spot on the Earth's surface and the data they provide is usually only updated once per orbit as they pass across the ground control station on the Earth – approximately once every 90 minutes in most cases.
Why only one geostationary orbit?
Physics Narrative for 11-14
Why only at one height and over the Equator?
A satellite that stays above one place on the Earth's surface has to sit above the Equator. Then the centre of the circle around which it is orbiting is the centre of the Earth, and the plane of orbit coincides with the equatorial plane. So the gravitational force is pulling the satellite towards the centre of its orbit: there is a centripetal force. If the plane of orbit of the satellite is moved closer to either pole then the gravitational force will be pulling the satellite towards the centre of the Earth, out of its plane of orbit.
The satellite sits at one height due to a balance of two factors, one depending on the speed in orbit and one on the gravitational field. Both of these depend on the radius of orbit, but in different ways. You'll recognise these as the two factors that affect the path without gravity, and the distance fallen towards the Earth.
The time for an orbit is fixed at 24 hours, so the greater the radius of orbit, the greater the speed must be, because there is a greater distance to cover in the same time.
The gravitational field gets weaker as you go farther out, so the acceleration and the rate of fall towards the Earth also lessens.
Think about 1 second of motion of the satellite:
- The farther out you go, the longer the (imagined) gravity-free path, taking the satellite tangentially away from the Earth. (That is the path taken if the
string is cut.)
- The farther out you go, the smaller the drop, due to gravity, that brings the satellite back to the same distance from the Earth, at the start of this second.
At one distance, and one distance only, these two factors balance, allowing a satellite to stay at the same height without having to fire rockets.
Satellites and their uses
Covering the whole of the Earth with communications satellites requires a minimum of three satellites evenly distributed.
Exploration of the solar system
Spacecraft have been sent to explore the planets, and some of these have been placed in orbit around those planets, becoming artificial satellites.
Artificial satellites have even been placed around the outer planets: Galileo (around Jupiter); Cassini (around Saturn).
Venus has been orbited by Magellan, and Mars has had a number of orbital missions including those which were a part of the Viking mission and more recently the Mars Global Surveyor.
The Moon has been explored by the Lunar Orbiters and others, but Mercury has only had
fly-bys so far.
Global positioning system
The global positioning system (GPS) consists of a network of Earth-orbiting satellites that can be used to determine the position of any point on Earth with considerable accuracy.
The system works by using the synchronised signals from four GPS satellites to estimate the position in three dimensions and time. Using a hand-held commercial device, a GPS user can determine their position to within about 2 metre. For military applications it is accurate to less than 1 metre.
In North America, tractors have been linked to the GPS. An imaging satellite can detect where crops are nitrogen deficient. The information from the satellite is then used to vary the amount of fertiliser delivered to the crops at that point.
Data from weather satellites is continuously updated and fed into large computer models that calculate the possible developments of weather patterns. The models are reliant on timely and accurate data but even then, because of the large amount of data involved, their predictions are only reliable for the next 48 hours. Good images are available from the web sites of the Meteorological Office and the American NOAA satellite.
Studying the universe
Among the first images of planets captured extra-terrestially were the photographs obtained by the Voyager satellites, many of which can be found on the Internet. The Hubble Space Telescope has provided images of better resolution and detail than those provided by any terrestrial telescope.
However, astronomers have also built ultra-violet, X-ray and gamma-ray satellites to detect radiation produced by stars and other astronomical objects. Most of this radiation is not detectable on the surface of the Earth because the atmosphere is not transparent to these wavelengths.
The data obtained from these satellites has helped to transform our understanding of the universe. For instance, astronomers have predicted that streams of matter falling into black holes will be heated to such an extent that they will produce X-rays as they fall towards the black hole. The detection of such sources in the constellation of Cygnus has confirmed their view that black holes exist even though they cannot be directly observed.
Finally, perhaps the major satellite in orbit around the Earth is the International Space Station. This is the largest artificial satellite ever to orbit the Earth.