Retrogradation

First movement

The observation of the movement of planets is done starting from the Ground. The first apparent movement of planets and the stars is due to the Rotation of the Earth around itself. It is a diurnal Mouvement which is carried out of is in west, movement whose Sun is the first example.

Second movement

The second movement is about the Année or more, and is due to the planet and earthmovings around the Sun. To observe this movement, it is necessary to choose a fixed Référentiel. It will be the whole of the remote star S. This unit was called by the astronomers of antiquity until the 18th century, the sphere of fixed stars. It is thus compared to fixed stars that this apparent movement is measured. Observed starting from the Sun, the apparent movement of each planet would be circular quasi-uniform. However, the source of observation being the Earth, the earthmoving introduces a skew into the observation and the external planets then seem sometimes to move back in their movement. It is what is called the retrograde movement. He is explained by the relative differences of angular Velocity of each movement.

Explanation of the phenomenon

The drawing opposite schematizes the observation of the movement of a planet external by projection on the sphere of fixed stars. The Earth and the external planet are supposed to evolve/move on circles (actually of the ellipse S of weak eccentricity) whose center is the Sun S. the Earth moves twice more quickly (in angular Velocity) that the planet observed. The positions T1, T2,…, T5 correspond to the positions of the Earth and the positions P1, P2,…, P5 with the positions of planet. The apparent movements of planet correspond to projection on the sphere of fixed stars (brought closer considerably on the diagram), i.e. at the points A1, A2,…, A5. The planet then seems to move back in its way A2, A3, A4.

The existence of a retrograde movement has constrained the holding astronomers of the Géocentrisme to imagine complex movements of planets to explain this phenomenon, in particular the épicycle.

Example of the retrogradation of Mars

The real experimental data are the following ones:

Approximation

The eccentricities of two planets being weak (0,017 and 0,093) one can assimilate the two elliptic trajectories by circles (eccentricity equalizes to 0). The slope of Mars being small, one can assimilate at first approximation the two trajectories by coplanar circles whose center is the Sun.

To simplify still more, one will use round data, and will study the model simplified according to:

With this simplified model, the respective positions of the Earth and Mars (measured in astronomical half unit) compared to the Sun can be written according to time $t$ (measured in terrestrial year) like complex numbers ( $i^2 = -1$ ):

\ left \ {
\ begin {matrix} z_ {T/S} (T) \ = \ 2 \ \ mathrm {E} ^ {+2 \ pi I T}
\ \ z_ {m/s} (T) \ = \ 3 \ \ mathrm {E} ^ {+ \ pi I T}
\end{matrix}
\ right.

One from of deduced that the relative position of Mars compared to the Earth is given by:

The representation of this relative position in the plan gives the following trajectory:

See too

rotation retrogresses

External bond

Why Planets Retrogresses an animation on the retrogradation of planets.

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