Opposition of Mars Details

1. The period of oppositions 2. The shape of the opposition loops 3. The distance from the Earth 4. The duration of retrograde motion 5. The angle of retrograde motion 6. The velocity of retrograde motion

Oppositions in the winter are occuring at large altitudes:
Example (Berlin, 52.51° N):
2001, Jun 13 at 01:05 CEST: altitude 11°
2007, Dec 25 at 00:11 CEST: altitude 64°


1. The period of oppositions


The the mean orbital period (interval of time between subsequent perigee passages) is 687,00 days,
and varies by about +/- 5 hours.



The period of oppositions T is the synodic period of Mars and the Earth:

1/T = 1/T_Mars + 1/T_Mars

T=779.9 days


The interval of time between subsequent oppositions (mean: 781 days = 2 years, 1 month, 20 days),
the synodic period of Mars, varies by about +/- 1 month.




2. The shape of the opposition loops

Mars Oppositions (1950-2061)

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Horizontal: Right Ascension (degrees) increasing from right to left,  vertical: Declination (degrees).
The duration of retrograde motion is 74 +/-10 days (2 ¹/₂ months)
(loop images by my Planet Applet: menu "Write/Draw" > "Draw Opposition Loop")

The shape of the loops depends on the position of Mars with respect to the nodes of Mars' orbit:
	The opposition of 2005, Nov 07 occuring near the ascending node (shape of "Z")
	The opposition of 2031, May 04 occuring near the descending node (shape of "S")
	The opposition of 2010, Jan 29 occuring half way between the nodes
	The opposition of 2018, Jul 27 occuring half way between the nodes
	The first diagram is showing the angular distance (eta in degrees, vertical axis) of Mars from it's position at opposition as a function of time (days before and after opposition, horizontal axis). The second diagram is showing the angular velocity (∆eta/∆t in degrees per day, vertical axis) as a function of time (days before and after opposition, horizontal axis). The total duration of the oppostion loop is about 73 days, and the variation of eta is 0° +/- 8°
Both diagrams are computed from rP / rE = sin(η+ε)/sin(η+β), resolved to: η = arctan((sin ε - K*sin β)/(K*cos β - cos ε)), and K=rP/rE

3. The distance from Earth




The opposition of 2003, Aug 27 happened close to the perigee of Mars, at a distance of 0.373 AU from the Erath.
From one opposition to the next (2.14 years) the heliocentric longitude of Mars increases by about 50°.
Thus every 7 oppositions (7*2.14=15 years) the oppositions occurs near perigee.



The Mars-Earth distance at opposition is between 0.373 AU and 0.678 AU.



4. The duration of retrograde motion



The duration of retrograde motion is 74 days +/- 10 days (2 ¹/₂ months)



5. The angle of retrograde motion



The celestial angle of retrograde motion is between 10° and 19.5° (mean 16.5°)




6. The velocity of retrograde motion

The first diagram is showing the angular velocity (∆eta/∆t in degrees per day, vertical axis) as a function of time (days before and after opposition, horizontal axis). The total duration of the oppostion loop is about 73 days, and the variation of eta is 0° +/- 8° The first diagram is showing the angular distance (eta in degrees, vertical axis) of Mars from it's position at opposition as a function of time (days before and after opposition, horizontal axis).

Both diagrams are computed from rP / rE = sin(η+ε)/sin(η+β), resolved to: η = arctan((sin ε - K*sin β)/(K*cos β - cos ε)), and K=rP/rE

Updated: 2009, May 21