Hello, my name's Dr.

George, and this lesson is called Orbital Motion of Artificial Satellites, relationship Between Radius and Speed.

It's part of the unit Gravity and Space.

Here's the outcome for this lesson.

I can describe changes to a satellite's speed and velocity and explain what happens to its orbital radius if its speed changes.

Here are the key words for the lesson.

I'll introduce these as we go along, but you can come back to this slide anytime if you want to remind yourself of the meanings.

The lesson has three parts.

They're called satellites, speed of orbit and different orbits.

Any object in orbit around a planet is a satellite of that planet.

There are natural satellites such as the moon, which is earth's only natural satellite.

It travels around earth in a circular path at a distance of about 38,000 kilometres from Earth.

And this orbit takes about 27 days to complete.

Earth also has many artificial satellites which have been launched into orbit on large rockets since 1957.

The picture shows a model of Sputnik One, which is the first artificial satellite.

The spherical part is about 60 centimetres across.

Currently, Earth has over 12,000 satellites in various orbits doing a range of different jobs.

These include communications, for example, enabling us to use mobile phones, television, weather monitoring and spying.

Now is a question for you.

Io is one of the large moons of the planet Jupiter.

Which of these statements describes Io? And when I ask you a question, I'll wait five seconds, but if you need longer, just press pause and press play when you have your answer ready.

And the correct answer is B, Io is a natural satellite of Jupiter.

It's not counted as a planet because it's not orbiting directly around the sun.

Many artificial satellites are launched into what's called low earth orbit.

These have orbits between 300 and 2,000 kilometres above the Earth's surface, which is relatively low for a satellite.

Because these satellites are relatively close to Earth's surface, microwave signals, which travel at the speed of light, can be sent to and from them very quickly.

And that's how we communicate with the satellites.

This type of satellite is often used in observation systems, observing what's happening on the Earth's surface and creating images.

And which of the following heights would a satellite be in a low Earth orbit? Since low earth orbits are between 300 and 2,000 kilometres, The answer is B and C.

Only a few satellites such as the International Space Station, ISS, have a crew, have people on them.

The ISS was launched in sections between 1998 and 2011, and it's been occupied since 2000.

The crew carry out a wide range of experiments and they test technology for future missions to the moon or to other planets.

The ISS orbits at a height of 400 kilometres above the Earth's surface and completes 15 orbits per day, is large enough to see from the ground with the naked eye.

At night, you can see it as a moving point of light.

Some satellites are in polar orbit.

They travel around Earth going over the north and south poles repeatedly.

These satellites orbit between 500 and 800 kilometres above the Earth's surface and they complete 10 to 15 orbits per day depending on their exact heights.

As the satellites travel, the earth rotates beneath them, so they pass directly above most parts of its surface each day.

Weather satellites are usually in this type of orbit as it allows them to take detailed pictures each day of much of the Earth's atmosphere.

The picture shows a hurricane photograph by a weather satellite.

Now, which of the following statements about satellites in a polar orbit are correct? The correct answers are C and D.

Some of them are weather satellites and they're outside earth atmosphere.

They're above it.

They don't travel directly above the equator, they're not going around the earth that way.

They're going between the two poles and they don't pass above exactly the same ground in every orbit.

'Cause as they swing between the north and south pole, the earth turns below them.

There's another kind of orbit called a geostationary orbit.

Satellites and geostationary orbit are in a ring 38,000 kilometres directly above the equator.

They travel at a speed that keeps them directly above a fixed point on the equator, and that means that they appear stationary in the sky to anyone looking up from Earth.

Television broadcast satellites are placed in geostationary orbit so that a satellite dish for picking up the TV signal doesn't have to move to receive the signal from the satellite.

It can just constantly point in the same direction, and that's where the satellite will always be.

Geostationary satellites orbit at the same rate that earth rotates.

So one complete orbit takes exactly 24 hours.

Here are some images showing Earth viewed from far above the North Pole and a geostationary satellite.

The key shows what each symbol means If this is a starting position, If we are at the point on the equator where the red triangle is and we look up, we'll see the satellite directly above six hours later is a quarter of a day, a quarter of 24 hours.

And so the earth has done a quarter of a turn and the satellite has moved a quarter of the way around its orbit.

Again, if we look up from where the red triangle is, we'll see the satellite directly overhead.

And 12 hours after the start, the earth has done a half turn.

The satellite has done half of its orbit, and it's still directly above from the point of view of the person At the red triangle.

How long does it take a geostationary satellite to complete one orbit of earth? And the answer of course is one day 24 hours.

And now here's a couple of written questions for you.

Can you explain the difference between earth's natural satellite and an artificial satellite in low earth orbit? And can you also explain why a geostationary satellite appears to be stationary in the sky? Press pause when you write your answers and press play when you're finished and I'll show you some example answers.

So here are some example answers.

Earth's natural satellite is the moon.

It's a naturally occurring huge ball of rock, which is about 28,000 kilometres away from Earth, orbiting every 27 days.

An artificial low earth orbit satellite is launched from earth's surface by a rocket and placed in orbit somewhere between 300 kilometres and 2000 kilometres above the earth's surface.

It takes between one and three hours to orbit depending on its height.

A geostationary satellite is an orbit directly above the equator, and it completes one orbit in exactly one day.

This means that as it orbits, earth rotates beneath it at the same rate.

It's always above the same place on the ground.

Compare your answers and check whether you made some of the same points and well done if you did.

Now let's move on to the second part of this lesson.

Speed of orbit.

Most satellites travel around Earth in circular orbits.

These satellites are therefore in circular motion.

As they travel, their speed remains constant, but they change direction of travel all the time.

So their velocity is always changing, because velocity is a vector, it includes the direction as well as the size and the speed.

A change in velocity is an acceleration.

And for something to accelerate, there needs to be a resultant force acting on it.

That force is earth's gravitational pull on the satellite.

That's what makes it accelerate.

So at the four points shown here, the movement direction, the direction of the velocity is as shown by these arrows.

And the gravitational force is as shown by the solid arrows always towards the centre of the earth.

Satellites can travel at a constant speed in orbit because the gravitational force is the only force acting on them, and it acts towards the centre of earth.

So it's always at right angles to the direction of movement.

When the force is at right angles to the movement, then only the direction changes, not the speed.

There are no frictional forces in space as long as the satellite is above the atmosphere.

And so a satellite will not slow down.

It doesn't need a thrust force to keep it moving, just as the moon doesn't need a thrust force to keep it going around the earth, which force acts on a satellite in geostationary orbit? It's the gravitational force.

The forces acting on an object following a circular path like an orbit can be modelled by a simple experiment.

And you're going to do this after I've explained it.

A rubber bung has a strong thread attached to it, and that thread is passed through a thin plastic tube as shown here.

The other end of the thread has masses hanging from it.

You hold onto the tube and you can spin the bung by moving the tube and you can make it follow a circular horizontal path.

So this is a view from above.

And in this model, the bung represents an orbiting satellite.

The direction of its movement is constantly changing.

It's moving in a circle.

Here's its movement direction at these four places.

And the force towards the centre is provided by the tension in the thread, and that represents the gravitational force that acts on the satellite towards the centre.

The size of the tension in the string can be varied by altering the size of the mass hanging from it.

Increasing the mass increases the tension, and this simulates increasing the size of the gravitational force.

So now in which of the experiments here will the force acting on the rubber bung be greatest? And the answer is A, because it has the greatest mass hanging from it.

Well done if you picked that.

So now you're going to do the investigation.

You'll attach a rubber bung to a strong thread, thread that a thin plastic tube and attach a hanging mass from the other end.

Then you hold the plastic tube firmly in one hand and you spin the bung around until it follows a circular horizontal path or very nearly horizontal path.

Rotate the bung in larger and smaller circles and observe any changes in how long it takes to make one complete orbit.

And then if you can, describe how the size of the orbit affects how long it takes to make one complete orbit, press pause when you do this activity and press play when you finished.

I hope you were able to see the effects of changing the radius of the orbit.

Here's what you would expect to see.

The bung takes longer to complete an orbit when the radius of the orbit is larger and the smaller the orbital radius, the shorter the time for each orbit.

And this is also true for satellites as the orbit the earth.

When the radius of orbit is larger, the satellite takes longer to complete one orbit.

And now for the third part of this lesson, different orbits.

It turns out that the speed of travel of a satellite is orbital speed, depends on the radius of its orbit, and that orbital radius isn't the distance of the satellite from the surface of the planet.

It's distance from the centre of the planet, as shown in this diagram.

For example, the radius of earth is 6,370 kilometres.

And so to find the orbital radius of a satellite, you need to add the height of the orbit above the surface to the radius of the earth.

For example, here the satellite is 1,500 kilometres in height above the surface.

So the orbital radius is that plus the radius of the earth, which is 7,870 kilometres.

So you need to remember that when you're doing calculations on satellites.

What is The orbital radius of the satellite shown here? The answer is D, 8,370 kilometres because it's the radius of the planet of the earth plus the 2000 kilometres in height above the earth's surface, the length of a circular orbital path, so the distance that the satellite travels in a single orbit can be found from the radius of the orbit.

We use the geometry of a circle here.

The circumference of a circle is two times Pi times the radius.

So therefore the length of an orbital path is two times Pi times the orbital radius.

For example, here is a satellite with orbital radius 7,000 kilometres.

So the orbital path length is two times Pi times 7,000 kilometres, and to three significant figures, that's 44,000 kilometres.

What is the orbital path length of this satellite? The correct answer is C, 52,600 kilometres.

Here's how we work that out.

Two times pi times the orbital radius, well done if you got that right.

The speed of a satellite can be calculated from the orbital path length and the period of the orbit.

That's the time taken for a single orbit using speed as distant, divided by time.

Here's an example, here's a satellite with orbital path length, 44,000 kilometres and period 1.

9 hours.

So if speed is distance over time, we get to two significant figures, 23,000 kilometres per hour because we used a distance in kilometres and a time in hours to do this calculation.

And it makes sense to write the answer to two significant figures because we had the time to two significant figures.

Here's a worked example.

A geostationary satellite orbits at a height of 36,000 kilometres above the surface of the earth, which has a radius of 6,400 kilometres.

Calculate the orbital speed of the satellite.

So step one is find the orbital radius is the orbital height plus the earth's radius, and we get 42,400 kilometres.

And then the orbital path length, the distance travelled in one circle around the earth, two times Pi times the orbital radius.

We get 266,000 kilometres to three significant figures.

And finally, the speed is that orbital path length divided by the orbital period, the time taken to go around once and we get 11,100 kilometres per hour to three significant figures.

It turns out that the orbital speed of a satellite only depends on its orbital radius.

The mass of the satellite doesn't make any difference.

So all satellites that orbit are the same height above earth surface will have the same speed.

And that means if you want to launch a satellite, you can't choose both the orbital radius and the speed you want it to have.

If you choose one of those, the other one is fixed.

The greater the orbital radius, the slower the satellite moves as you may have seen in the rubber bung investigation.

And the relationship looks like this.

For a stable orbit, an orbit whose radius isn't changing over time, a satellite needs to travel at a specific speed.

Closer to earth, it needs to travel faster and slower if it's further away from the earth.

If a satellite moves closer to earth, it will need to speed up so that it stays in orbit.

And as a satellite gets further from earth, its speed will need to decrease or else it will escape from its orbit and drift off into space.

This diagram shows four satellites orbiting Earth, which of the statements are correct? and the correct ones are A and C.

Satellite W has the lowest speed as we've seen.

The further from earth the satellite is, the slower it moves and satellites X and Z have the same speed because they have the same orbital radius.

It's not true that all four of them have the same speed.

Different radius will mean a different speed.

And now a couple of longer questions for you.

Press pause when you write your answers and press play when you're ready to check them.

And here are the answers.

An orbital radius of less than 6,400 kilometres wouldn't be possible.

That's only slightly more than the radius of the earth.

And so the satellite would either be within the Earth's atmosphere and air would slow it down and it would not be able to complete a full orbit or it would be inside the earth itself.

Next, you were asked to calculate the orbital speed of a satellite in a polar orbit, you were given its height above the surface of the earth, 800 kilometres, and the period of the orbit, 1.

70 hours, and also the radius of the earth.

So we start by finding the orbital radius.

We can use that to find the distance it travels in one complete orbit.

The orbital radius is the orbital height plus radius of earth.

It's 7,170 kilometres for the satellite.

The orbital path length is the circumference of the circle that the satellite travels in, which is two times pi times the orbital radius.

We get 45,050 kilometres and speed is distance over time.

So we can find the speed from the orbital path length divided by the orbital period, and to three significant figures, we get 26,500 kilometres per hour.

Well done if you got that too.

And now we've reached the end of the lesson, so I'll finish with a summary.

Satellites are objects in orbit around a planet.

They can be natural or artificial.

Some artificial satellites are in low earth orbits and can take detailed images of the earth.

Those in polar orbits can travel over all of Earth's surface every day as the earth rotates beneath them.

Communication satellites are in geostationary orbits above the equator.

They orbit once each day so that they remain above the same point on the ground as the earth rotates.

Gravitational forces cause a satellite to follow a circular orbital path around a planet, the greater the orbital radius of a satellite, the lower speed.

Well done for working through this lesson on satellites.

I hope you enjoyed it, and I hope to see you again in a future lesson.

Bye for now.