I have already mentioned in this blog, that I use an application named ‘Celestia‘, which basically anybody can download and ‘play with’. This is an Astronomy application, which displays to the user graphically, not only what the sky above the Earth would have looked like at some arbitrary point in time, but also what the sky – i.e. the star field – would look like, as seen from elsewhere in the near regions of space, such as anywhere from within our own solar system, or from the closest neighbors to our own sun.

In fact, I even uploaded a YouTube Video, which explains to anybody, the basic usage of this program.

This is another video which I uploaded at 1920×1080 resolution, but which the viewer may have to play with somewhat, even after he has made it full-screen, to switch its resolution to True HD.

(Edit 11/07/2017 :

When recording the above screen-cast, I nearly sidetracked the main subject – of how to navigate the program – with the question, of how to change the Field Of View, the ‘FOV’, indicated in the bottom-right-hand corner of the screen. I do know from experience, that when ‘in synchronous orbit around the Moon’, and looking back at the Earth, using the scroll-wheel of the mouse does not make the earth look any larger or smaller, because using the scroll-wheel will then only change the distance with which my camera-position is orbiting the Moon.

The way to adjust the FOV is finally, to hold down the <Shift> Key, and then to click-and-drag with the Left Mouse Button.

Also, the distinction is known to me, between how this program defines ‘a synchronous orbit’, and what a synchronous orbit would be, correct to Physics. A synchronous orbit needs to have one specific altitude, at which a stable, circular orbit has the same rotational period, as the body we’re orbiting. In the case of the moon, this may not even be achievable. Yet, the way ‘Celestia’ defines a synchronous orbit, is as my screen-cast shows. )

But if this program is to be used for anything aside from pure entertainment, the question should ultimately be asked, how accurate the model is, by which planets are animated, at whatever time-period the user is observing. Basically, a program would be possible, which simply extrapolates Kepler’s Laws about the movements of Planets, according to which their orbits are purely elliptical, and according to which the periods of each orbit stay perfectly the same, over the Eons.

The problem with Kepler’s Laws is, that they not only assume Newtonian Gravity, but *They also assume that each orbit is only affected by the gravitational interaction of two bodies*: A body assumed to be orbiting, and the body around which the first is assumed to be orbiting. The problem with this is the fact that in the real Universe, every body that causes gravitation, eventually exerts that gravitation on any other body – up to infinite distance. The fact that each and every person standing on the surface of the Earth, experiences the gravitation of the Earth, is a kind of proof of that. In theory, the gravitation of the Earth not only affects the orbit of the moon, but to a lesser extent, also the orbits of Mars and Venus – except for the fact that some people fail to know, that at the distance of Mars, for example, the gravitation of the Earth would be assumed negligible in strength. The effect of a car that passes the street in front of an Inhabitant of Earth, is in fact stronger, than the effect of the gravitation of Mars, on the same Inhabitant. And this is simply because, the strength of gravitation does decrease, as the reciprocal of distance squared.

But what this means is that over longer time-frames, the orbits of the planets become ‘perturbed.’ Mostly, this is due to the effects of the gravitation of Gas Giants, on the smaller planets of our solar system, but it really applies generally, wherever gravitation exists.

Well The programmers of Celestia took this into consideration, when they created that program. What they did, was to assume that Kepler’s laws generally apply, when they are fed a single parameter – time – and that they predict elliptical orbits, as a linear function of time. But, because real orbits are perturbed, it was at some point thought best, that time first be fed through a polynomial, to arrive at the parameters, which are then fed into Kepler’s Model, such as the one parameter that states, in what phase of its orbit a planet is, as orbiting our sun.

In reality, this method of applying a polynomial, does not reflect any physical realities, of ‘how the orbits work’. What it reflects is that Real Astronomers at some time in the past, used very powerful computers in order to compute gravitational interactions, and that the result of their simulation was a continuous sequence of planetary positions, which next needed to be stated somehow. The reader might think, that nothing but a series of numerical values would be needed, except that one problem with that idea would be, that effectively an infinite series of numerical values would be needed, because any time-interval can be magnified, and the motion of planets is supposed to remain continuous.

And so what Astronomers did, was to express the results of their simulation as a polynomial approximation, which consumers’ computers can next turn into real values, for what the position of a planet is supposed to be, at any precise point in time.

In other words, the use of a polynomial approximation served essentially, as a type of data-compression, and not as a physical model of gravity.

This approximation is also known as “vsop87“.

(Updated 11/08/2017 : )

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