I’m going to deal with very simple situations, as these make both understanding and the maths easier, and most real situations can be usefully approximated by these simple cases. The central body is vastly more massive than the orbiting body, so we can consider the central body to be fixed, and just work on the orbiting body.

The simplest orbit is perfectly circular. The orbiting body moves in a circle at just the right speed so that its centrifugal force is precisely balanced by the gravitational force between the bodies. We will call that speed V

_{C}.Now physics purists will tell us that centrifugal force is an illusion, so to satisfy them we’ll consider acceleration rather than force and describe the orbit as the path where centripetal acceleration is provided by the gravity of the central body. We’ll do the maths for this in the next post. For now, here’s the circular orbit as a diagram.

A variation of this orbit is the elliptical orbit. If at point A the orbiting body accelerates by a small amount, (less than 41% of V

_{C}), then as it proceeds around the central body its extra speed will cause it to climb away from the circular orbit path. As it climbs against the force of gravity from the central body, the orbiting body decelerates. It reaches its furthest point at B, directly opposite A, and begins to accelerate back towards the original point A once again.Point A, the closest to the central body, is called periapsis. Point B, the furthest from the central body, is called apoapsis.

When the orbiting body is at point B, it is travelling more slowly than the circular orbit speed, V

_{C}’, at that radius from the central body. Now if the orbiting body accelerates again at point B, to V_{C}’, it will follow a new circular orbit passing through B.This kind of manoeuvre, where an elliptical transfer orbit is used to change between orbits of different radii, is used frequently in space flight. Some satellites are put into geostationary orbits, where they orbit once in 24 hours and appear stationary over particular points on the equator as the Earth rotates. When a geostationary satellite is launched, it is inserted into a transfer orbit with apoapsis at the geostationary radius. Then a dedicated engine is fired at apoapsis to accelerate and achieve a circular geostationary orbit. A variation of this kind of transfer orbit was used by Apollo spacecraft to reach the Moon.

Finally, if the orbiting body accelerates by 41% of V

_{C}or more, then this speed causes it to climb away as before, but this time it is travelling fast enough that the gravity field from the central body reduces more quickly than the body decelerates, and the body continues climbing indefinitely. The body has exceeded the escape velocity, V_{E}, has escaped the gravity field and will not return.These are the basic principles to grasp for now. Next time we will look at some simple maths to describe these different cases.

How can it really be known what the earths periods of eccentricity, perihelion and obliquity are when the observational data only cover at most 3,000 years? What I mean is that these parameters involve cyclical change so we have no direct observational evidence that would give the turning points of these cycles or the lengths of them. Considering that they are supposed to be controlled by the tiny masses of the planets I wonder how they can possibly know. For example, the obliquity cycle is supposed to be 41,000 years but since we are in the middle of that...

ReplyDeleteI particularly wonder how they could vary from the periodicity of precession. How could the physics be such as to have the precessional wobble vary at a different rate than the obliquity?

ReplyDeleteI think that common sense would suggest that the periodicities would be the same.

ReplyDelete