In orbital mechanics there are a few main things we need to know, to calculate an orbit.
- Apoapsis
- Periapsis
- Inclination
- Eccentricity
- Semi-major axis
- longitude of the ascending node
Before I describe those things, I want to say what an orbit is. If you throw an object upwards, it will go up and then fall down again. If you shoot an arrow you will fly further. This happens because all objects fly on a trajectory.
Now if you launch a rocket. It will fly so fast that it its whole trajectory is above the surface of Earth. You could say it is falling since it is in Freefall. This is exactly what happens when you are in an orbit. You are going so fast that you will not fall down.
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Now when we are in an orbit there are a few things about the orbit we can define. The first 2 things I think will be easiest to understand is the apoapsis and periapsis. When you are in an orbit, there is a point when you are the furthest away from an object and then there is the point where you are the closest. The apoapsis is the furthest point from an object and the periapsis is the closest.
Now lets look at the Semi-major axis. The Semi-major axis is the distance between the center of the orbit to the side of the orbit. In the picture below there are 2 lines, A and B. A is just the distance between the apoapsis and the center which is know as the Semi-minor axis. The Semi-major axis is the line B.
Any orbit can have a different shape. Some are more round than others. In order to say how round an orbit is we use something called the Eccentricity. The Eccentricity represents the shape of the orbit and is defined as the ratio of the distance between the foci of the ellipse (where the central body is located) to the length of the major axis of the ellipse. An eccentricity of 0 represents a perfect circle, while values closer to 1 indicate highly elongated orbits. In the imagine below you can see different objects with different Eccentricity.
In all the pictures above, the orbits were on a 2D-plane. In reality they are in an 3D area. This means that they can have different angles which is called the Inclination. To measure the Inclination we have an imaginary 2D plane at the equator. Then we measure the angle of the plane between the orbital plane of the object and the imaginary 2D plane.
The final major thing about an orbit is the Longitude of the ascending node. We have to measure 2 angles in order to say which direction the object is flying the Latitude and Longitude. The Inclination describes the angle in the latitude direction and then there is the longitude of the ascending node. This is just the second angle
You wanted to know how to change the orbit of an object in order to reach another celestial body. In order to do so you have to change the speed of an object. The best position to do so is at the Periapsis. Since when you increase your speed at the periapsis, the distance between the apoapsis and the mass you are orbiting grows.
To go to another object in an orbit you have to make sure the trajectory of the other objects meets with the trajectory of your spacecraft. However, you cannot make the 2 trajectories just meet somewhere random since the 2 objects will arrive there at different times. This is why there is a transfer window. The transfer window is a time period where you should change the orbit of one object so that is can be at the connecting point of the 2 trajectories when the other object is there. This is known as the Hohmann transfer orbit.
For example if you fly to Mars, you change your speed at your periapsis so that your apoapsis meets the same position where Mars is.
To calculate the when you need to launch is a bit hard to do by hand, so usually most people use other programs like Mathcad to calculate it. A very important thing you need to consider is the delta V. Since in theory, you could always launch directly to another object, but normally we try to use a way to get there using almost no fuel. So one tries to keep the delta V required as low as possible.
Since this was a long answer, I will try to sum it up:
- Apoapsis: The farthest point in an orbit from the central object.
- Periapsis: The closest point in an orbit to the central object.
- Inclination: The angle between the orbital plane and a reference plane (usually the equator).
- Eccentricity: A measure of the orbit's shape, representing the ratio of the distance between the foci of the ellipse to the length of the major axis.
- Semi-major axis: Half of the longest diameter of the elliptical orbit, representing the average distance between the orbiting object and the central object.
- Longitude of the ascending node: The angle between the reference direction and the point where the orbit crosses the reference plane, measured in the direction of the orbit's motion.
By understanding these elements, we can accurately describe the shape, size, orientation, and position of an orbit. Additionally, to change the orbit of an object and reach another celestial body, altering the speed of the object at the periapsis is crucial. Calculating the optimal launch window and minimizing the delta-v (change in velocity) required for the transfer are important considerations in achieving efficient interplanetary travel.
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