Solar system

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Slide 13

Satellites can orbit planets as well as the Sun. Moons are natural satellites that orbit planets. The Earth has one moon, some planets have no moons at all, and others have dozens of them. Mercury and Venus have no moons. Mars has two moons. Jupiter and Saturn have 53 moons. Uranus has at least 23 moons, while Neptune has 13. Just as the planets are satellites orbiting the Sun, these moons will not fall down into the planets they are orbiting because they are moving too quickly in a horizontal direction. The moons of planets with more than one moon do not collide because each has its own unique orbital speed, and hence its own unique orbital radius. No two moons of the same planet share an orbit.

Slide 14

The Earth also has many artificial satellites. These are scientifically manufactured objects that continuously orbit the Earth. We use them for telecommunications, navigation, weather forecasting, and surveillance, among other things. We obviously want to avoid two things happening with artificial satellites: we want to avoid them falling into the Earth, and we want to avoid them colliding. So, we need to keep track of the orbital speeds of our satellites. First, to stop them from falling into the Earth, we need to design satellites so that their horizontal speed exceeds a certain threshold value that depends on the orbital height. For example, to maintain an orbit of 242 km above the Earth, a satellite has to have a speed of approximately 27,359 km/h. To make sure that satellites don’t collide, we need to make sure that we never reuse the same orbital height, or equivalently, the same orbital velocity. Aerospace engineers need to choose a unique orbital radius for their satellite, and design it to have the corresponding orbital speed.

 
Slide 15

The formula that Aerospace engineers need to use to determine the required orbital speed of their satellites is found by equating the gravitational and centripetal force formulas, just like we did for the Sun. This gives us R = GM/v^2 or v equals the square root of GM/R. In this case, G is the gravitational constant, and M is the mass of the Earth. Both of these are constant, so the radius of the orbit is inversely proportional to the square of the orbiting velocity. When the velocity increases, the radius decreases and vice versa.

Slide 16

Satellites that are used for weather forecasting and telecommunications are often what we call geostationary satellites. These are satellites that appear to hover over a fixed point on the Equator. They aren’t really stationary. Instead, they hold what is known as a geosynchronous orbit, which means that they travel at the same rate as the Earth rotates about its axis. This gives them a velocity of zero, when measured from the Earth, so they appear to be stationary from the Earth. As the Earth is moving with respect to the stars, the satellite is also moving with respect to the stars. Just like the Earth, the geostationary satellite returns to the same position in the sky after each sidereal day. A sidereal day measures the time taken for the Earth to rotate on its axis relative to the stars. It is approximately four minutes shorter than the usual day we measure on Earth with respect to the Sun.

Slide 17

Let’s work out exactly where geostationary satellites live. Geostationary orbits lie directly above the equator, and have a radius of about 42,164 km measured from the centre of the Earth. This means that they are about 35,786 km above the average sea level. If we plug this radius into our formula for the velocity of a satellite, it turns out that the velocity of a geostationary satellite is approximately 3,000 metres per second. Now, I’m sure you’re wondering why geostationary satellites don’t collide. This is because, although they have the same height, they are all travelling at the SAME speed, so there’s no chance of them colliding, unless of course, we try to launch a second satellite to the same coordinates as one that’s already there. That’s something we have to be careful about!

Slide 18

Did you know that gravity is present throughout the universe? There is a force of gravity between any two bodies with mass, regardless of how far apart they are. Our solar system is part of a huge galaxy, called the milky way, and it contains over 100 billion stars. Our Sun moves with respect to many different stars, experiencing a gravitational attraction to billions of stars. The galaxy itself is constantly rotating. The milky way is part of a galaxy cluster, a group of 54 galaxies that are bound together by gravity. Clusters of galaxies combine to form super clusters. Super clusters typically contain dozens of clusters of galaxies again, linked by gravity. Progressively larger groups of stars exert progressively larger gravitational forces. So, the stars are not spread uniformly throughout the universe. Most are packed together into galaxies, groups, clusters and superclusters by the force of gravity.

Slide 19

Let’s pause for a while and do a thought experiment. Suppose there was a switch somewhere that someone could turn off and get rid of gravity. What would happen? Earlier, we talked about putting a tennis ball in a stocking and swinging it around your head. What would happen if you let go of the stocking? The ball would fly off in a straight line. Eventually it would stop and fall to the ground because of the actions of gravity and friction, and because its horizontal speed isn’t large enough to overcome the force of gravity. If there was no gravity, satellites would no longer orbit the Sun or the planets. Newton’s Law of Inertia tells us that they would fly off into outer space in a straight line at a constant speed equal to their orbital speed. The planets and stars would no longer be attracted to each other, and they would scatter. It is possible that they would collide with each other. There would be no solar system, and we wouldn’t be able to live on the Earth. We’d have no air to breathe, and we’d go floating off into space. Thankfully, there is no gravity switch, and the Physicists tell us that it’s impossible to get rid of gravity.

Slide 20

Let’s summarise the things we’ve talked about in this presentation. Gravity is an extremely important force, and one without which we could not survive. Gravity is the reason why the planets orbit the Sun. It generates a centripetal force, which allows planets to maintain their curved orbits. Gravity also helps the moon and artificial satellites to orbit the Earth. Finally, gravity is a basic force of nature that can never be switched off. This is fortunate, since without gravity, our Earth would not maintain its orbit around the Sun, the stars and planets would fly off in straight lines, and possibly collide, the Earth’s atmosphere would not be held around the Earth, so we could not breathe, and we would be unable to stay on the Earth. Gravity is crucial for our continued survival in the universe.