Question on my lab?

Question

I am doing a labratory investigation in which we are comparing a heliocentric (sun-centered) and geocentric (earth-centered) model of the solar system. In order to do this we must plot a planet's position in each orbit over a 24 month period.
My question is would the planet be on the same path with each revolution, or could the path be somewhat different. When I did it, my path was not the same with each orbit. Thank you!

Answer 1

Nope....The earth is continuously falling into the sun, but the difference in the radius is only a few meters every year. So i dont think there would be any possible way to measure it.

Answer 2

I am not certain what you mean in your question.

The orbits do "wobble" to a certain (and predictable) extent. The planes of the orbits do not change but the point where the planet is closest to the Sun does change (in relation to "fixed" stars) in response to the small gravitational pull of all other planets.

For example:
Earth:
2005 perihelion Jan. 2 at 01h UT 147,099,100 km
2005 aphelion July 5 at 5h UT 152,102,400 km
2006 perihelion Jan. 4 at 15h UT 147,103,600 km
2006 aphelion July 3 at 23h UT 152,095,700 km
2007 perihelion Jan. 3 at 20h UT 147, 093, 602 km
2007 aphelion July 7 at 0h UT 152,097,053 km

Earth does not retrace the same orbit year after year. However, when you plot the orbits in relation to the Sun (heliocentric system) the difference is small when you compare the distance at the same date, year after year.
The same is true of other planets.

Of course, when you plot other planets in relation to Earth (geocentric system), then the difference is much bigger. The Earth "error" will be transferred to the other planet. In addition, the other planet will have a period that is NOT one year, therefore, when its "year" is over, it will not be in the same place in relation to the Sun.

Example:
Begin the cycle with Earth at perihelion (in January) and Venus in inferior conjunction (between us and the Sun). For now, let us assume that the orbit of Venus around the Sun is perfectly circular. Venus will return to inferior conjunction after 584 days (this is called the Synodic period -- the period in relation to Earth). This puts us in late July (or early August), much closer to the date of aphelion than perihelion. The Sun is much further this time than last time, therefore Venus is much further from us, by a whopping 5 million km.

In addition, the orbit of Venus is not circular. Its own difference (aphelion - perihelion) could add or subtract another million km to the difference.

So, at inferior conjuction, when Venus is closest to Earth, the difference from one orbit to the other could be as high as 6 million km.

The average distance (Venus-Earth) at inferior conjuction is "only" 41.5 million km.
6 million over 41.5 million is a difference of 14% which is quite noticeable.

If instead, you decide that the next orbit begins when Venus is in line with the same "fixed" star, the error will be a lot bigger, as Venus will not be in the same position relative to the Sun and Earth. (I do not know who to explain this one without making a drawing, so I won't -- I'll let you do the drawing).