Orbit

There are two main types of orbits: open and closed. Closed orbits are the easier to understand, as they can be either circular or elliptical (oval) in shape. A body on a closed orbit constantly travels around another, such as a planet orbiting the Sun or the Moon orbiting the Earth.
An open orbit follows a mathematical shape: either one known as a parabola or another called a hyperbola. Both are sweeping curves that never join up. So, objects on open orbits simply fly by other celestial objects. Some spacecraft and comets follow open orbits.

All four classes of orbit are known as ‘conic sections’ because slicing a cylindrical cone in a different way can make each of their shapes. Closed orbits are achieved by cutting a







cone from one side to another at different angles. Open orbits are  achieved by  slicing the cone from one side down through the base.


Spacecraft can be put into a number of different closed orbits around a planet. These are defined by a number of orbital characteristics, such as the height above the planet’s surface, the inclination to the planet’s equator and the direction in which the spacecraft orbits the planet.

Defined by orbital altitude, these are:
Low-Earth orbit – As the name implies, this is the lowest altitude a spacecraft must achieve to in order to orbit the Earth. This is around 520 km altitude and spacecraft in these orbits circle the Earth once every ninety minutes or so.

Geostationary (or geosynchronous) orbit – This is a much higher orbit and so takes a lot more energy to reach. However, once at the altitude of 36,000 km, it takes the spacecraft a full 24 hours to orbit the Earth. Thus, the spacecraft moves at the same speed with which the Earth rotates and therefore appears to ‘hover’ over the same spot on the ground

Understanding orbits
There are a few common ways of understanding orbits.

>As the object moves sideways, it falls toward the central body. However, it moves so quickly that the central body will curve away beneath it.
>A force, such as gravity, pulls the object into a curved path as it attempts to fly off in a straight line.
>As the object moves sideways (tangentially), it falls toward the central body. However, it has enough tangential velocity to miss the orbited object, and will continue falling indefinitely. This understanding is particularly useful for mathematical analysis, because the object's motion can be described as the sum of the three one-dimensional coordinates oscillating around a gravitational center.
>As an illustration of an orbit around a planet, the Newton's cannonball model may prove useful (see image below). Imagine a cannon sitting on top of a tall mountain, which fires a cannonball horizontally. The mountain needs to be very tall, so that the cannon will be above the Earth's atmosphere and we can ignore the effects of air friction on the cannonball.


 

If the cannon fires its ball with a low initial velocity, the trajectory of the ball curves downward and hits the ground (A). As the firing velocity is increased, the cannonball hits the ground farther (B) away from the cannon, because while the ball is still falling towards the ground, the ground is increasingly curving away from it (see first point, above). All these motions are actually "orbits" in a technical sense they are describing a portion of an elliptical path around the center of gravity but the orbits are of course interrupted by striking the Earth.

If the cannonball is fired with sufficient velocity, the ground curves away from the ball at least as much as the ball falls so the ball never strikes the ground. It is now in what could be called a non-interrupted, or circumnavigating, orbit. For any specific combination of height above the center of gravity, and mass of the planet, there is one specific firing velocity that produces a circular orbit, as shown in
(C).













As the firing velocity is increased beyond this, a range of elliptic orbits are produced; one is shown in
(D). If the initial firing is above the surface of the Earth as shown, there will also be elliptical orbits at slower velocities; these will come closest to the Earth at the point half an orbit beyond, and directly opposite, the firing point.

At a specific velocity called escape velocity, again dependent on the firing height and mass of the planet, an infinite orbit such as
(E) is produced a parabolic trajectory. At even faster velocities the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space".
ESA/Wikipedia

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