the translational motion of stars & planets

[mubashirmansoor]

Hello,<br />I wanted to know if the translational motion of stars and planets are according to a pollynomial formulla...<br />If not then how do the scientists predict the position of the position stars after a specific period of time?<br />Thankyou,

 

[bobw]

I think astronomers have to take many pictures of stars, a constellation for example, over a period of many years to find that their positions have changed. Once they have found a direction and speed for a star's proper motion they can calculate that in a million years it will move 10,000 times as far as it moved during the 100 years they have observed the motion. Here's some information about the future shape of the big dipper.<br /><br />http://www.fourmilab.ch/yoursky/help/proper.html<br /><br />I don't think there is any way to predict the future positions of a star if they haven't got any information about which way it is going yet.<br /><br />One of Space dot Com's feature articles today is about a stream of stars which were once a globular cluster; very interesting too. They found it by observation. Now that they know it exists they can predict where it will go but they never could predict that before they knew it was moving. I hope I haven't misunderstood your question.<br /><br />http://www.space.com/scienceastronomy/060613_star_stream.html <div class="Discussion_UserSignature"> </div>

 

[mubashirmansoor]

Thankyou, The main thing which made me ask this question was the research of mine in maths available in the following website, <br />http://www.mathhelpforum.com/math-help/showthread.php?t=3410<br />This technique enables you to get the nth term of a sequence (a polynomial sequence) by inserting number of consecutive terms. <br />I thought we might be able to use it in this field of science...

 

[doubletruncation]

The motion of planets are described approximately (ignoring interactions with each other) by an ellipse. But to actually get the position of the planet along the ellipse at any given time you have to numerically solve an integral that does not have a solution that can be written as a combination of simple functions. I imagine you could probably approximate the solution via some polynomial though. <br /><br />When including interactions between different planets you have to solve a system of coupled differential equations numerically, in the solar system you could treat these as slight perturbations to the keplerian orbit. For general N-body simulation the solutions are highly chaotic so the solutions are explored via numerical integration. <div class="Discussion_UserSignature"> </div>

 

[CalliArcale]

Of course, what makes it really complicated to predict the future position of stars is that they are not the only stars out there. If they pass somewhat near another star or other massive object (eg a previously undiscovered black hole), it will deflect their trajectory. There are equations for solving this, but they are not simple and they require calculus to be accurate. In fact, that's why calculus was originally invented -- algebra just wasn't working.<br /><br />Calculus wasn't just invented for celestial mechanics, though. It was invented primarily for its military use in the field of ballistics. To accurately aim your cannon, you need to be able to calculate the trajectory of the projectile, and this requires calculus. Strange though it sounds, celestial mechanics is nothing more than ballistics on a fantastically grand scale. <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>

 

[siarad]

Amazingly our brains when catching a ball while moving too, calculate the second differential of the hyperbolic tangent of the angle of gaze taking into account the seen position is way behind the actual position <img src="/images/icons/smile.gif" /> <br />Was Calculus or fluxions invented or discovered in our brains <img src="/images/icons/wink.gif" />