What Causes the Illusion of Planets Moving Backwards in the Sky?

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Discussion Overview

The discussion revolves around the phenomenon of apparent retrograde motion of planets as observed from Earth. Participants explore how to identify when a planet appears to move backwards in the sky, the historical observations leading to this understanding, and potential methods for calculating these occurrences.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the methods for determining when a planet is moving backwards in its orbit, suggesting that plotting a graph may not be the only way.
  • Another participant explains that the apparent retrograde motion occurs due to the differing orbital speeds of Earth and other planets, leading to observable loops in their paths against the starfield.
  • A third participant introduces the concept of apparent retrograde motion and suggests plotting the position of a planet over time to identify retrograde motion, while also mentioning the possibility of calculating the geocentric ecliptic longitude of Mars to find when its motion rate is zero.
  • This participant notes that while precise calculations may be complex, a simplified model assuming circular orbits could provide rough estimates of retrograde periods, specifically mentioning Mars' retrograde motion repeating approximately every 2.1 years.
  • A later reply introduces an external link discussing the influence of minor planets Ceres and Vesta on this phenomenon, implying potential complications in the calculations or observations.

Areas of Agreement / Disagreement

Participants express various methods and understandings of apparent retrograde motion, but no consensus is reached on the best approach or the implications of external factors like Ceres and Vesta.

Contextual Notes

Some assumptions about orbital mechanics and the simplifications made in calculations are not fully explored, and the discussion includes references to external sources that may influence the understanding of the topic.

Philosophaie
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Backward "orbit" of the planets

How do you tell when a planet is going backwards in its "orbit" of the earth?

Do you have to plot a graph and pick out the points?

There must be an easier way!
 
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The planets were observed over thousands of years through the skies. Over time it was realized that they made odd little "loops" backwards through the sky against the background starfield. This occurred because the Earth is orbiting the Sun at a different rate than the other planets.

Now you can probably look it up online and find out when this will occur. I don't know if they have to calculate the orbits and all that or if it simply occurs on a repeating schedule over time.
 


The phenomenon is called Apparent Retrograde motion [1].

Conceptually, I think the easiest method would be to do as you propose and simply plot the position of, say, Mars in the sky of Earth as a function of time and note when the motion becomes retrograde.

However, from the orbital elements of Earth and Mars it should be theoretically possible calculate the apparent rate of the geocentric ecliptic longitude of Mars and (numerically) solve for times when this rate is zero. If you want to be very accurate, such calculations will probably be very long winded and be something you'd want a computer to do for you.

If you only want a rough estimate for when the rate is zero, I guess it should be possible to simplify the problem assuming coplanar circular orbits, maybe even so much that an analytic solution is easy. Also, in this simple model the time between when the rate is going positive (prograde motion) or negative (retrograde motion) repeats itself with the synodic period [2]. For instance, for Mars retrograde motion repeats itself after about 2.1 year.


[1] http://en.wikipedia.org/wiki/Apparent_retrograde_motion
[2] http://en.wikipedia.org/wiki/Orbital_period#Relation_between_the_sidereal_and_synodic_periods
 

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