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

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

synodic period

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

1/T = 1/TMars + 1/TMars

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:
mars opposition node
The opposition of
2005, Nov 07
occuring near the ascending node
(shape of "Z")


mars opposition loop 2005
mars opposition loop
The opposition of
2031, May 04

occuring near the descending node
(shape of "S")

mars opposition loop 2031
opposition
The opposition of
2010, Jan 29

occuring half way between the nodes


retrograde
The opposition of
2018, Jul 27

occuring half way between the nodes


retrograde

retrograde angular velocity


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


Mars Opposition 2003 Perigee

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.

opposition distance mars earth

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



4. The duration of retrograde motion

mars retrograde motion duration

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



5. The angle of retrograde motion

mars loop angle

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




6. The velocity of retrograde motion

retrograde angular velocity

retrograde





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

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