In this lesson, we’re going to look at the reasons why our solar system actually is a solar system. Why do the planets orbit the Sun? And why do moons and satellites orbit the planets? Why don’t satellites collide with each other? The answer is gravity.
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Added on: 29th Sep 2018
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In this presentation, we’re going to look at the reasons why our solar system actually is a solar system. Why do the planets orbit the Sun? And why do moons and satellites orbit the planets? Why don’t satellites collide with each other? The answer is gravity.
We’ll begin our presentation with an introduction to the solar system. We’ll discuss the objects that form part of the solar system. Because everything in our solar system revolves around one or more other bodies, everything in our solar system is acted on by a type of force called centripetal force. We’ll find out just what centripetal force is and how it acts. Next, we’ll discuss the effects of gravity on our solar system, and just how it holds the solar system together. We’ll finish off by looking at bodies that orbit the Earth. These can be both natural (our Moon) and artificial satellites that we have launched into space.
So, what do we mean when we talk about our solar system? At the centre of our solar system is the star we call the Sun. It is orbited (or travelled around) by all of the other bodies. These include eight planets, a few planetoids (or planet want-to-bes like Pluto that don’t quite fulfil all the requirements for being a planet), asteroids, and moons that orbit each of the planets. The eight planets, in order, moving out from the Sun are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. In old books, you’ll find Pluto mentioned as the 9th planet. It was demoted to a planetoid or dwarf planet in 2006, partly because of the wonky way it travels around the Sun. Scientists have also discovered a number of objects of similar size to Pluto that orbit the Sun, but don’t quite make the cut for being a planet. They also believe that there might be another planet in our Solar System out past Pluto, but this hasn’t been confirmed yet. It will be interesting to see what happens. Everything in the solar system: the Sun, the planets and planetoids, the moons and the asteroids are never still. Everything, even the Sun, is spinning and revolving around something else.
So, if everything in the Solar System is moving, why don’t the bodies in our solar system run into each other? In fact, everything in our solar system stays in the same order, and roughly the same distance apart. We say that the bodies in our solar system maintain the same orientation and position with respect to each other. Every pair of objects with mass in our universe attract each other with a force called gravity. Gravity is the main reason why our solar system keeps its arrangement, and why the bodies in our solar system don’t collide with each other.
We said something about orbits a little earlier in this presentation. Let’s talk about them in more detail. The path that a planet takes around the Sun is called an orbit. It is the regular, repeating path that one object takes around the other. Scientists call the object that moves around (or orbits) the other object a satellite. So, our Earth is a satellite of the Sun, and our moon is a satellite of the Earth. The path that the Earth takes around the Sun is called its orbit, and the path that the moon takes around the Earth is its orbit. Some satellites are natural like the Earth, and our moon, but there are artificial satellites as well. You’ve probably used artificial satellites, for example, when you watch a live game from overseas, or your parents use the GPS in the car.
Now orbits are generally curved paths. Just what makes them curved? The answer is centripetal force. Without centripetal force, objects would not be able to follow a curved path. Centripetal force is a force that acts on any body moving along a curved path. If the path is circular, centripetal force is directed towards the centre of the circle. Our planets follow a path that’s a bit like squashed circle, or ellipse. Because of this, the direction that the centripetal force is a bit more complicated. Physicists say that it acts “towards the fixed point of the instantaneous centre of curvature of the path”. That’s a bit daunting, and a bit of mouthful. Just think of a centripetal force as a “centre seeking force”. It acts at right angles to the curved path, and towards its centre. The slide slows a formula for calculating the size of a centripetal force: F_c = mv^2/r. It depends on the mass m and speed v of the body, and the radius r of its path.
The motion of satellites is a form of projectile motion. The only force that acts on a satellite is gravity. Objects that are launched with an initial horizontal velocity follow curved paths. On the Earth, the curved path looks more like a parabola, a symmetric curve that has a peak, than an ellipse. We call this motion projectile motion because it’s the motion that is followed by a projectile. If we forget about air resistance, the only force that acts on the projectile is gravity. In space, there’s no air resistance to worry about, so the only force acting on the satellite is gravity. In an ideal world, that is, one with no air resistance, there’s nothing pushing against the motion of the projectile, so it doesn’t lose its horizontal speed. In space, there’s nothing dragging on the motion of the satellite, so it doesn’t lose its horizontal speed. However, the vertical speed of the projectile, and of a satellite is changing at every instant because of the vertical action of the gravitational force.
As we’ve discussed, gravity is the only vertical force that acts on satellites, and it’s the force responsible for the curved path, or orbit, that they take around the Sun, or around the Earth, or around another planet. Gravity generates the centripetal force that is required for the satellite to follow a curved path. It is always acting towards the body that is being orbited, so the satellite is always accelerating towards that body. However, it never crashes into the central body.
Have you ever tried placing a tennis ball inside a stocking, holding the open end, and swinging the stocking around your head? The ball keeps pinning around at the same speed at the same distance from you, only dropping towards you when your arm gets tired and drops down. The situation is similar with satellites, except that there’s no arm to get tired. Satellites follow a curved path, just like projectiles. The only force acting on them is gravity, and it pulls the satellite towards the Earth, but the horizontal speed of the satellite compensates for this. Newton’s Law of Inertia tells us that our satellite will keep moving in a straight line at the same velocity unless acted upon by an unbalanced force. Gravity provides the unbalanced force that pulls the path of the satellite into a curved orbit around the larger body. It never collides with the central body because it is moving quickly enough in a horizontal direction to avoid this. So, it keeps following its orbit at a constant speed.
Why don’t satellites stop? Because of inertia (the resistance of a body to change) and their initial horizontal speed. We’ve said that the motion of satellites is a form of projectile motion, yet we know that projectiles launched on Earth eventually come to a stop: they reach a maximum height, turn around, and then come back to the ground. Satellites do not fall into the Sun, or any other body that they might be orbiting for a number of reasons. First, they are orbiting a long way away from the Sun, so there’d be a long way to fall. Most importantly, their horizontal speed is so high that it overcomes the tendency of gravity to pull them into the Sun. Finally, they don’t lose any of this horizontal speed because there is no horizontal force (like friction) in space, impeding their motion. Because of Newton’s Law of Inertia, they tend to want to move in a straight line at their constant, high horizontal velocity. So, their horizontal motion never stops. Their straight-line path is pulled into the curved path that forms their orbit by gravity, but this force isn’t strong enough to pull them into the Sun. Satellites do not spiral into the Sun, crash and burn. They just keep going around and around.
Did you know that every satellite has its own orbit? Each satellite orbits the Sun, the Earth or another heavenly body in an orbit of a different radius. No two satellites have orbits around the Sun with the same radius, so no two satellites can collide. We can work out what this radius is by comparing the forces acting on the satellite. The only force acting on the satellite is gravity, and this generates the centripetal force acting on the satellite. This means that the gravitational force and centripetal force acting on a satellite are equal. We have formulas for the size of each of these forces. If we set them equal for a given satellite moving around the Sun, we can work out the radius of the orbit that it follows. R = GM/v^2. Here R is the radius of the orbit, G is the gravitational constant, M is the mass of the Sun and v is the speed of the satellite.
On the previous slide, we found the formula R = GM/v^2 for the radius of the orbit of a satellite. Here, R is the radius of the orbit, G is the gravitational constant and M is the mass of the Sun.
The mass of the Sun is a constant, and, funnily enough, so is the gravitational constant. This means that the radius of the orbit is determined solely by the speed (or velocity) of the satellite. Now, let’s think about the planets in our Solar system. They are all different distances away from the Sun, so their orbits all have different radii. Because the radius of the orbit only depends on the velocity of the satellite, this means that the planets must all have different speeds at which they orbit the Sun. The radius of the orbit gets bigger as the orbiting speed gets smaller, and vice versa. So, the satellites that are closer to the Sun must be the satellites that are moving most quickly. The satellites farther away from the Sun have slower orbiting speeds.