Orbital Motions

Fig. 1: A demonstration of a circular orbit.

This diagram shows the Earth in two locations during its orbit around the Sun: \( E_1 \) and \( E_2 \). At location \(E_1\), the Earth has a velocity of \(v_1\). However, by the time it is at the point \(E_2\) in its orbit, its velocity has changed to become \(v_2\). This happens because velocity is a vector quantity, and the Earth is not travelling in a straight line: its velocity must change between the points \(E_1\) and \(E_2\). As was stated above, however, the speed of the Earth does remain constant: the magnitudes of the velocities \(v_1\) and \(v_2\) are the same.

So what gives? Well, a changing velocity means one thing is happening: acceleration. In this case of the Earth orbiting the Sun, the Earth is accelerating because it is under the influence of the Sun's gravitational pull. The attracting force due to gravity is labelled as \(F_1\) and \(F_2\) in the diagram above, and this Force causes the Earth to accelerate and thus change the direction of its velocity, following its (circular) orbital path.

Elliptical/non-circular orbits

An elliptical orbit is a type of non-circular orbit. Take a look at the GIF below to get a bit of an understanding of how an elliptical orbit works, and then we'll explain it in a bit more detail.

Fig. 2: Example elliptical orbit.

In the GIF above, you should be able to see that at the side of the orbit closest to the planet, the object moves faster, unlike at the end of the orbit farthest from the planet, where it moves slower. As we have said above, the planets actually orbit the Sun in an elliptical motion, however, the orbits are not as extreme as the one shown in this GIF. Because the orbits of the planet are close enough to be circles, we can treat the orbits as such in GCSE physics.

Examples of orbit motion

There are lots of different kinds of objects in the Solar System, and most of them orbit some other object. There is one main rule we need to keep in mind: a larger object cannot orbit a smaller object. Remember, the Sun doesn't orbit the Earth but the Earth orbits the Sun!

The main celestial objects we are going to continue looking at are planets, moons, and comets. Each of these objects has a slightly different form of orbital motion, with different orbit lengths and different speeds.

Orbits of planets

All planets have very similar orbital properties and therefore exhibit similar motions. Every planet has a slightly non-circular orbit around the Sun, however for the sake of calculating things, we consider their orbits to be circular. It's also important to note that all planets in the Solar System orbit the Sun in the same direction, as well as in roughly the same planes. In other words, if you looked towards the Solar System from its side, you would see all the planets orbiting across the equivalent of the Sun's equator.

There are some differences between the orbits of planets, though! They all have a different orbital radius, which means they are all at a different distance from the Sun. The closer a planet is to the Sun, the faster it travels and, therefore, the less time it takes to orbit.

Orbits of moons

Moons follow most of the same rules as planets orbiting the Sun, except they orbit planets. The main differences are that they generally don't orbit along the same plane and that some of them have very non-circular orbits. Again, in the case of circular orbits, the orbital radius determines how fast or slow the orbit of a moon will be, with closer orbits being shorter in time with a higher speed.

Orbits of comets

Some comets orbit a star, so we will talk about those comets. The orbit of such a comet is usually highly elliptical, in other words, the orbit is stretched out, and this has some very interesting effects on the motion of the comet. The stretched nature of a comet's orbit causes extremely large changes in speed as the comet's distance from the Sun changes. At its furthest point from the Sun, the comet will be the slowest, and at its closest point to the Sun, the comet will be the fastest. On top of this, not all comets orbit in the same plane or even the same direction, they're all over the place!

Fig. 3: An elliptical orbit of a comet.

Orbit motion of galaxies

As we've discussed, a lot of celestial objects have some form of orbital motion, as they interact with something else. This holds even in galaxies, massive groups of stars held together around some galactic centre that is generally something with an extremely large gravitational pull. Look at the picture of the milky way below, taken by the European Space Agency's Gaia satellite, and notice how the majority of the stars are clustered along the centre line of the image. This is known as the galactic plane, and as we can see, most stars orbit the galactic centre along this plane.

Fig. 4: A panorama of the Milky Way.

Stability of orbit motion

Consider a satellite in orbit around a planet. For it to remain in a steady circular orbit, the speed of the satellite needs to be a specific value. If the speed of the satellite is too low, then it will fall back towards the Earth, and if the speed of the satellite is too high, it will move off into space, away from the Earth's gravitational pull.

Calculating orbital speed

The speed of the orbit of a satellite can be calculated using a few steps. The first step is to calculate the distance travelled in one orbit. This is calculated using the equation

\[\begin{gather}d=2\pi r, \\(\text{distance}=2\pi\times\text{radius})\end{gather}\]

where \(d\) is the distance travelled by the object and \(r\) is the radius of the orbit. The second step is to calculate the average speed using the following equation:

\[v_\text{average}=\frac{d}{T}.\]

In this case, the time \(T\) is how long it takes the satellite to complete a single orbit.