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Author Topic: why is earth's journey elliptical?  (Read 1705 times)

Offline annie123

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why is earth's journey elliptical?
« on: 23/09/2013 00:18:07 »
Why does the earth go round the sun in an elliptical path?  Is the moons' path also an ellipse?


 

Offline syhprum

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Re: why is earth's journey elliptical?
« Reply #1 on: 23/09/2013 10:40:09 »
A circle is the limiting case of an ellipse when the major and minor axis's are equal. the elliptical orbits of moons, planets etc are the consequence of the inverse squared/distance  attraction of gravity.
Bodies orbit around the centre of gravity of the system with this point being the minor focus point of the ellipse (in the Earth/Moon system this lies below the surface of the Earth).
The Earths orbit around the Sun is slightly modified by the large attraction between the Sun and Jupiter.   
 

Offline evan_au

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Re: why is earth's journey elliptical?
« Reply #2 on: 23/09/2013 11:13:26 »
The elliptical orbit of planets around the Sun was discovered by Kepler. This same rule also applies to the orbit of the moon and artificial satellites around the Earth, and the orbit of the Sun around the Galaxy.   

It was Newton who showed that the inverse square law of gravity was the only possible solution for this observation* - this "Universal Law of gravitation" applies to all massive objects (including you and me, if we should be so lucky as to visit the International Space Station).

The inverse square law of gravitation allows a perfect exchange between kinetic energy and gravitational potential energy, allowing repeating cyclic orbits of two objects which do not decay. In a solar system of many planets, kinetic and potential energy is also exchanged between the different planets in the system, resulting in slow changes in the radius, angle and eccentricity of the planetary orbits.

On a computer, you can model the orbit of a planet in an imaginary universe where the gravitational field differs slightly from a perfect inverse square law - and the planets collapse into their star, or go sailing off into interstellar darkness far more often than with an inverse square law.

*The inverse square law also allows orbits which are other conic sections, including circles, parabolas and hyperbolas. Parabolas and hyperbolas are seen with one-time comets, which never return to the vicinity of the Sun - they are in orbit around the galaxy, rather than orbiting around the Sun.
 

Offline Pmb

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Re: why is earth's journey elliptical?
« Reply #3 on: 24/09/2013 03:30:40 »
Why does the earth go round the sun in an elliptical path?  Is the moons' path also an ellipse?
"Why?" questions require a mathematical derivation to give a complete answer. If that's what you'd like I can create a webpage on my website to prove it. But its like explained above, it's a result of the gravitational force being a central force and following an inverse square law in magnitude.
 

Offline annie123

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Re: why is earth's journey elliptical?
« Reply #4 on: 27/09/2013 23:49:06 »
Thanks.
 

Offline David Cooper

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Re: why is earth's journey elliptical?
« Reply #5 on: 28/09/2013 18:53:09 »
If you dangle a weight on a string you can make it swing like a pendulum or go round in circles, while anything in between will make it move in an elipse, though it will be a distorted one as the weight will go up at the pointed ends of the elipse and down in altitude for the straighter parts. With this elipse the gravitational pull is not coming from either of the foci of the elipse [foci = plural of focus], and nor is it coming from the centre of the elipse, but thousands of miles down below the elipse, so it does not serve at all well as a model for an object orbiting another.

As a child, I wondered why planets/moons/etc. orbiting in elipses wouldn't also work with the heavier of the two objects being directly in the centre of the elipse and with nothing at either of the foci, but diagrams always put the heavier object at one of the foci and I couldn't work out why it should be so. It's only clear that it should be so when you work out the maths of it, and that's best seen by running a computer program to watch the maths of it at work, so I wrote a little program to test it: http://www.magicschoolbook.com/science/eliptical.html

The program repeatedly applies the appropriate amount of force to the orbiting object according to its current distance from the central object (which means more force is added the closer it is to that central object), and that gets added as vectors to the vectors for the orbiting object's current movement. The numbers that keep changing on the screen show you the current force the orbiting object is receiving from the object it's going round (the square root of this number can be divided into 1 to get the distance between the two objects), and the coordinates of the orbiting object every time it switches from getting closer to the other object to getting further away again, and the opposite such that they give you the points of closest approach and the furtherst out point of the orbit.

The orbiting object is steered purely by applying that same simple maths to it over and over again - it is not following a fixed pre-programmed path repeatedly like a bit of looping video, and you can see the errors building up over time as a result. I wrote a couple of other programs which simulate the movements of the planets going round the sun: http://www.magicschoolbook.com/science/inner-planets.html and http://www.magicschoolbook.com/science/sun2saturn.html, again with everything driven by the simulated force of gravity from the sun alone. You can see with Mercury that its orbit is highly eliptical, and Mars too.

[These programs run more smoothly in some browsers than others, so they will look good in some and awful in others depending on how good the browser is, though a bad operating system can also make them very stop-start if it's doing a lot of work in the background.]

(Edit: looks as if I've been misspelling ellipse for a long time!)
« Last Edit: 29/09/2013 17:11:16 by David Cooper »
 

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Re: why is earth's journey elliptical?
« Reply #5 on: 28/09/2013 18:53:09 »

 

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