-To give general remarks on orbits, I will have to limit our subject area and only talk about orbits around the Earth. With this hypothesis in mind, we will also simplify the problem and say that, instead of considering the three-dimensional shape of orbits, we will start with a two-dimensional case. Meaning that as observers, we will place ourselves a few thousand kilometers away from the Earth and look at orbits from above so that they are included in a plane. Now that these assumptions have been made, here is what an orbit looks like. First surprise, it is not circular. Indeed, the general shape of an orbit is elliptic. An orbit is only circular when the major and minor axes have exactly the same size. Second surprise, the Earth is not at the center of this orbit. Indeed, the Earth is located on one of the two focal points of the orbit. The orbit shape depends on the eccentricity. The eccentricity can be calculated with this formula. This value varies between 0 and 1. When the value equals 0, we are in the case of a circle. We will then define two other concepts, the perigee and the apogee. The orbit's perigee corresponds to the moment when the satellite, represented by a green dot here, is the closest to the Earth. The apogee is the exact opposite. It is when the satellite is the farthest from Earth. The specificity of the path followed by the elliptic orbit here is that when we add up the x and y values represented here, which link the satellite's position to the two focal points, this sum is always a constant. Finally, we will end with the definition of the orbital period. It is the time the satellite needs to do a full revolution on the orbit. How do satellites fly? Let us start with some vocabulary. A satellite does not fly. In order to fly like a plane, air is needed to create an overpressure phenomenon on a wing. But in space there is no air. So how does it work? We will assume, as illustrated here, that the satellite revolves around the Earth on a circular orbit. Its motion will be characterized by two factors. First its altitude, second its revolution speed. This speed will be expressed in meters per second. We add a r factor, the satellite's altitude and the Earth's radius. So it is the distance from the satellite to Earth's center. In that case, we can find a formula linking speed and the r factor. This formula is illustrated on the left. Speed equals the square root of the product of two constants divided by the distance from the satellite to Earth's center. When the satellite's altitude and speed follow this equation, a balance is established between the Earth's attraction on the satellite and the satellite's will to escape thanks to its speed. It can be compared to an object attached to a rope and spinning. Consequently, if we reduce the satellite's altitude, in order to keep this balance, we have to increase the speed. Conversely, if we reduce the speed, we have to increase the altitude. In both cases, if this equation is not obeyed, the satellite will either escape its orbit towards space, or crash on Earth. With this, we answered another question: how do we place a satellite in orbit? By sending it at the right altitude with an adequate speed considering the required orbit's altitude. In practice, this calculation is not that simple. We assumed that the Earth was perfect and immobile, but it is obviously not true. But the general principle is correct. Until now, we worked in two dimensions. We now need to specify the references that allow us to define the three-dimensional positioning of an orbit around the Earth. To illustrate this, we will consider an elliptic orbit. The green arrow on the illustration specifies the satellite's direction of rotation. We need six factors to characterize an orbit around Earth. We already know the first two factors. The first is the half of the ellipse's major axis' length. The second factor is the ellipse's eccentricity. Let us now see the other factors. The third parameter is the angle between the orbital plane, the plane which contains the orbit, and the equatorial plane. This parameter is called the inclination. To define the fourth parameter, we need to add two notions. First the vernal point, and second the ascending and descending nodes. Let us start with the vernal point. By the way, do not hesitate to pause this video to have a good look at the illustrations. The vernal point is the junction between the equatorial plane and the Earth's orbital plane in relation to the sun. It is called the ecliptic. It can be simply considered as a straight line from the center of the Earth to a certain longitude reference. It has nothing to do with the Greenwich meridian. Once the vernal point is defined as illustrated here, we can talk about the ascending and descending nodes. They are located on a straight line which goes through the Earth's center and represents the places where the orbit crosses the equatorial plane by respectively going up and down. By measuring the angle between the vernal plane and the ascending node, we get our fourth parameter, the longitude of the ascending node. Thanks to this longitude and to the inclination, we fully define the orbital plane, but not the orbit yet. The ascending node will allow us to define the fifth parameter. It is the angle between the orbital plane, between the straight lines from the Earth's center, which go through the ascending node and the perigee. This parameter is called the argument of the perigee. Now that we have defined all these parameters, the position of the orbit is now fully defined. There are no more ambiguities. However, we still need to position the satellite on the orbit. Let us imagine we have a t0. We do not know where the satellite is at this t0 moment. It will be defined in relation to the moment it reaches the perigee. This moment must be defined in relation to a known reference date. Thanks to these six parameters, we can fully define the orbit's geometry and thus the satellite's trajectory. You will see that when we want to publish an orbital shape we will give TLEs, a set of parameters grouped on these two lines. In these parameters, these published TLEs, you will find most of these values with other data such as the satellite's name for example, etc.
