Orbit of Mars

Orbit of Mars relative to the orbits of inner Solar system planets

Mars has an orbit with a semimajor axis of 1.524 astronomical units (228 million kilometers), and an eccentricity of 0.0934.[1][2] The planet orbits the Sun in 687 days[3] and travels 9.55 AU in doing so,[4] making the average orbital speed 24 km/s.

The eccentricity is greater than that of every other planet except Mercury, and this causes a large difference between the aphelion and perihelion distances—they are 1.6660 and 1.3814 AU.[5]

Changes in the orbit

Mars is in the midst of a long-term increase in eccentricity. It reached a minimum of 0.079 about 19 millennia ago, and will peak at about 0.105 after about 24 millennia from now (and with perihelion distances a mere 1.3621 astronomical units). The orbit is at times near circular: it was 0.002 1.35 million years ago, and will be about 0.01 a million years into the future. The maximum eccentricity between those two minima is 0.12.[6]

Oppositions

Mars reaches opposition when there is a 180° difference between the geocentric longitudes of it and the Sun. At a time near opposition (within 8½ days) the Earth-Mars distance is as small as it will get during that 780-day synodic period.[7] Every opposition has some significance because Mars is visible from Earth all night, high and fully lit, but the ones of special interest happen when Mars is near perihelion, because this is when Mars is also nearest to Earth. One perihelic opposition is followed by another either 15 or 17 years later. In fact every opposition is followed by a similar one 7 or 8 synodic periods later, and by a very similar one 37 synodic periods (79 years) later.[8]

Close approaches to Earth

Mars comes closer to Earth than any other planet save Venus at its nearest—56 versus 40 million km. The distances have been declining over the years, and in 2003 the minimum distance was 55.76 Gm, nearer than any such encounter in almost 60,000 years (57617 BC). This modern record will be beat in 2287, and the record before 3000 will be set in 2729 at 55.65. By 4000, the record will stand at 55.44. The distances will continue to decrease for about 24,000 years.[9][10]

Historical importance

A German astronomer, Johannes Kepler (1571-1630) formulated three laws of planetary motion. A key discovery was that the motion of Mars followed an elliptical path. His model with a circular orbit did not match the observations of Mars.[11] The planet's pronounced eccentricity was key in discovering the non-circularity of its orbit, and consequently of orbits in general.[12]

Accuracy/predictability

From the perspective of all but the most demanding, the path of Mars is simple. An equation in Astronomical Algorithms that assumes an unperturbed elliptical orbit predicts the perihelion and aphelion times with an error of "a few hours".[13] Using orbital elements to calculate those distances agrees to actual averages to at least five significant figures. Formulas for computing position straight from orbital elements typically do not provide or need corrections for the effects of other planets.[14]

For a higher level of accuracy the perturbations of planets are required.These are well known, and are believed to be modeled well enough to achieve high accuracy. These are all of the bodies that need to be considered for even many demanding problems. When Aldo Vitagliano calculated the date of close Martian approaches in the distant past or future, he tested the potential effect caused by the uncertainties of the asteroid belt models by running the simulations both with and without the biggest three asteroids, and found the effects were negligible.

Observations are much better now, and space age technology has replaced the older techniques. E. Myles Standish wrote: Classical ephemerides over the past centuries have been based entirely upon optical observations:almost exclusively, meridian circle transit timings. With the advent of planetary radar, spacecraft missions, VLBI, etc., the situation for the four inner planets has changed dramatically. (8.5.1 page 10) For DE405, created in 1995, optical observations were dropped and as he wrote initial conditions for the inner four planets were adjusted to ranging data primarily....[15] The error in DE 405 is known to be about 2 km and is now sub–kilometer.[16]

Although the perturbations on Mars by asteroids have caused problems, they have also been used to estimate the masses of certain asteroids.[17] But improving the model of the asteroid belt is of great concern to those requiring or attempting to provide the highest-accuracy ephemerides.[18]

Table of orbital parameters

No more than five significant figures are presented here, and to this level of precision the numbers match very well the VSOP87 elements and calculations derived from them, but also Standish's (of JPL) 250-year best fit, and calculations using the actual positions of Mars over time.

Distances and eccentricity AU million km
semimajor axis 1.5237 227.9
perihelion 1.3814 206.7
aphelion 1.6660 249.2
average[19] 1.5303 228.9
circumference 9.553 1429
closest approach to Earth 0.3727 55.76
farthest distance from Earth 2.675 400.2
eccentricity
0.0934
angles °
inclination 1.850
times days years
orbital period 687.0 1.881
synodic period 779.9 2.135
speed km/s
average speed 24.1
maximum speed 26.5
minimum speed 22.0

References

  1. ↑ Simon, J.L.; Bretagnon, P.; Chapront, J.; Chapront-Touzé, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and planets". Astronomy and Astrophysics. 282 (2): 663–683. Bibcode:1994A&A...282..663S.
  2. ↑ Jean Meeus, Astronomical Formulæ for Calculators. (Richmond, VA: Willmann-Bell, 1988) 99. Elements by F. E. Ross
  3. ↑ In ephemeris days of 86,400 seconds. The sidereal and anomalistic years are 686.980 days and 686.996 days long, respectively. (About a 20 minute difference). The sidereal year is the time taken to revolve around the Sun relative to a fixed reference frame. More precisely, the sidereal year is one way to express the rate of change of the mean longitude at one instant, with respect to a fixed equinox. The calculation shows how long it would take for the longitude to change 360 degrees at the given rate. The anomalistic year is the time span between successive perihelion or aphelion passages. This may be calculated in the same manner as the sidereal year, but the mean anomaly is used.
  4. ↑ Jean Meeus, Astronomical Algorithms (Richmond, VA: Willmann-Bell, 1998) 238. The formula by Ramanujan is accurate enough.
  5. ↑ The averages between 1850 and 2150. The extreme values in that range are 1.66635 and 1.38097 AU
  6. ↑ Mars distance and eccentricity, using Solex. By its creator, Aldo Vitagliano
  7. ↑ The synodic period may be calculated as 1/(1/p-1/q), where p and q are the smaller and larger sidereal periods.
  8. ↑ The synodic period of Mars is 92.9 days longer than its sidereal period of 687.0 days. It has then moved forward 92.9/687.0 times 360, or 48.7 degrees. After seven oppositions it has moved forward 341 degrees, and after eight it has advanced 390 degrees; in the first case its longitude is different from one revolution by 19°, and by 30° in the second. So the situations will then be similar. Similar calculations show that the longitude changes only 2° after 37 oppositions.
  9. ↑ Mars page, Vitagliano
  10. ↑ Meeus, Jean (March 2003). "When Was Mars Last This Close?" (PDF). Planetarian: 13.
  11. ↑ "Mars." Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2014. Web. 31 Jul. 2014. http://www.britannica.com/EBchecked/topic/366330/Mars
  12. ↑ William Sheehan, The Planet Mars: A History of Observation and Discovery (Tucson,AZ: The University of Arizona Press, 1996) Chapter 1
  13. ↑ Meeus (1998) pp 269-270
  14. ↑ see, for example, Simon et al. (1994) p 681
  15. ↑ Standish & Williams (2012). "CHAPTER 8: Orbital Ephemerides of the Sun, Moon, and Planets" (PDF). 2012 version of the Explanatory Supplement
  16. ↑ As noted in a 2008 JPL Memorandum regarding DE 421, "The error in the Earth and Mars orbits in DE 405 is now known to be about 2 km, which was good accuracy in 1997 but much worse than the current sub-kilometer accuracy."Folkner; et al. (2008). "The Planetary and Lunar Ephemeris DE421" (PDF). JPL Interoffice Memorandum IOM 343.R-08-003. p. 1
  17. ↑ "asteroid." Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2014. Web. 19 Aug. 2014. http://www.britannica.com/EBchecked/topic/39730/asteroid
  18. ↑ "The uncertainty in the Mars orbit for a one-year prediction is about 300 m, as required for the Mars Science Laboratory mission, but grows rapidly for times before and after the spacecraft observation time span due to the influence of asteroids with orbits near that of Mars. The predicted orbit and uncertainty depend greatly on the asteroid model used. "Folkner; et al. (2010). "Uncertainties in the JPL Planetary Ephemeris" (PDF). Proceedings of the Journées. p. 43.
  19. ↑ Average distance over times. Constant term in VSOP87. It corresponds to the average taken of many short, equal time intervals.
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