Mots clés :
mechanics, astrophysics, the retrodradation of Mars, movement of Mars, Mars, Earth, Moon

The retrograde motion of Mars

Gabrielle Bonnet

Philippe Saadé

Lycée La Martinière Monplaisir Lyon

Gabrielle Bonnet

17 - 11 - 2003


The goal of those three simulations is to explain the movement of Mars relatively to the Earth.

The goal of those three simulations is to explain the movement of Mars relatively to the Earth. Indeed, though the movement of Mars is relatively simple seen from the Sun, from the Earth, its movement can be surprising.

The retrograde motion of Mars

In the first simulation, we show the movements of Mars, the Earth and the Moon, seen in the heliocentric (centered on the Sun) frame. The Earth-Mars axis is materialized in red. The second and third simulations show the movement of Mars in the geocentric frame. In the second simulation, we mainly see the movement of the red Earth-Mars axis, the blue axis representing the axis of the Earth. The third simulation shows the movement of the Sun, the Moon, and Mars seen simultaneously in the geocentric frame and also visualizes the trajectory of Mars. The movement of the Earth on itself is too quick and thus is not represented.

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In the geocentric frame

For more information :

About that "retrogradation of Mars"... Why is it called that way?

In the heliocentric frame, Mars, as the Earth, has an elliptic trajectory (in the case of the Earth, that ellipse is almost a circle). In the geocentric frame, however, the trajectory of Mars looks a lot like a cardioïd (cf third simulation). Mars goes in one direction, goes backwards (thus the word "retrogradation "), then moves in its initial direction again.

Some history :

The movement of Mars has been observed since antiquity.

While the stars, seen in Earth's frame, seem to move all together in a circular motion (corresponding, in the heliocentric frame, to the movement of the Earth on itself), the planets move around the Earth relatively to the "celestial sphere" (i.e. : they are not fixed relatively to the stars). It's from that observational result that the word "planets" comes, it means "erratic celestial body". Mars, with its retrograde motion, was particularly intriguing.

The first attempts at explaining those observations were created inside a geocentric system (homocentric spheres of the Greek Eudoxe of Cnide , (406 BC to 355 BC). While in this system the stars have a simple rotational motion around the Earth, seen as the center of the Universe, it is necessary, to explain the apparent movement of Mars as compared to the stars, to attribute it a double movement : the planet would be rotating around a point which itself would be moving along a circle around the Earth. .

The first heliocentric system (and the first explanation of the movement of Mars inside this system) has been elaborated by the Greek Aristarque of Samos (310 BC to 230 BC). That system, however, has been rejected for a long time, sometimes even forgotten, and it won't be until Copernicus (1473 to 1543) that we will find the statement that the solar system is not centered on the Earth openly defended again. Despite Galileo 's condemnation (in 1633), Copernicus' ideas did not totally disappear in future years, but it has been necessary to wait the end of the 17th century, or even the 18th century, according to the countries, to see those ideas commonly accepted by scientists.

Datas :

Distances :

  • From Earth to Sun :

    • when Earth is at its apogee (i.e. when it is the closest to the Sun) : 1,47 × 1011 m
    • at its perigee (i.e. when it is the furthest from the Sun) : 1,52 × 1011 m
  • Mars-Sun distance :

    • at its apogee : 2,07 × 1011 m
    • at its perigee : 2,40 × 1011 m
  • Earth-Mars distance : varies between 5,6 × 1010 m and 3,9 × 1011 m
  • Earth-Moon distance (on the simulation, this distance is not represented at the same scale as the other distances) : 3,5 × 108 m

Periods :

A Martian year is : 687 Terrestrian days. In the geocentric frame, Mars' trajectory is not periodic, however, Mars is almost at the same point every 79 of Earth's years (which corresponds to 42 of Mars' years).

Period of the motion of the Moon around the Earth : 29 days 12 hours 44 minutes

Radius :

Radiuses in meters : on the simulations, those lengths are all represented at the same scale, except that of the Sun (the scale used for radiuses is different from the scale used to represent distances between the different celestial bodies) :

  • The Sun : 6,96 × 108 m
  • Mars : 3,40 × 106 m
  • The Earth : 6,38 × 106 m
  • The Moon : 1,74 × 106 m
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