Precession of orbital axes in the plane of the ecliptic is a common occurrence and easily described using tidal effects of other planets of massive bodies in the ecliptic.
This laboratory is an activity for you to evaluate possible sources for the vertical precession of a planetary orbit.
A vertical precession describes precession of orbital axes out of and back across the ecliptic. These are not so easily explained by the presence of other massive bodies in the plane of the ecliptic.
While it is part of the astronomy course principles of radiation astronomy, it is also independent.
Some suggested entities to consider for calculating and evaluating vertical precession of a planet of your choice are electric fields, tidal effects, mass, time, Euclidean space, Non-Euclidean space, or spacetime.
More importantly, there are your entities.
You may choose to define your entities or use those already defined.
Usually, research follows someone else's ideas of how to do something. But, in this laboratory you can create these too.
Yes, this laboratory is structured.
I will provide an example of phenomena to describe and produce a vertical precession of Mercury's orbit. The rest is up to you.
Questions, if any, are best placed on the discussion page.
You are free to create your own notation or use that already defined.
For creating a vertical precession force system, what would make an acceptable control group? Think about a control group to compare your vertical precession forces or your process of creating vertical precession to.
Def. the angle of intersection of a reference plane is called an inclination.
"The orbital inclination [(i) of Mercury] varies between 5° and 10° with a 106 yr period with smaller amplitude variations with a period of about 105 yr."
"Inclination of [Mercury's] orbit to [the] ecliptic [is] 5.15° [on or about July 20, 2010.]"
"Mercury Mean Orbital Elements (J2000) [...] Orbital inclination (deg) 7.00487 [...] Reference Date : 12:00 UT 1 Jan 2000 (JD 2451545.0) [...] Last Updated: 01 July 2013, DRW [David R. Williams]."
"The next largest [orbital inclination as of September 13, 2006,] is Mercury which orbits 7° from Earth."
"Mercury [...] Inclination [is] 7.00559432 degrees [as of March 20, 2014]."
The graphs at the top show the initial planetary orbital elements for the planet Mercury taken from the Development Ephemeris of JPL, DE245 (cf. Standish 1990) in the left portion marked (e) and the final integration results on the right (m).
The projected time spans from the integrations suggest that conditions within the solar system for the recorded data set are very stable.
The vertical precession of the orbit of Mercury
Using the available ephemeris for the orbital elements of the planet Mercury, computer calculations appear to have demonstrated that whatever forces are at work in the solar system are producing a reasonably stable system. Data is only available for the orbit of Mercury from several hundred years of observations.
Some of the forces present in the solar system during the course of data collection include gravity, electron influx from the interstellar medium, and outflux of neutrals and charged particles from the Sun (the solar wind).
A system such as the solar system may become "unstable when a close encounter occurs somewhere in the system, starting from a certain initial configuration. A system is defined as experiencing a close encounter when two bodies approach one another within an area of the larger Hill radius."
The experiment has consisted of locating data on the vertical precession of Mercury's orbit with respect to the ecliptic. In the choice of planet, at least one computer study has been performed using data available to provide integrations over time to test the overall planetary system for unstable conditions.
These very long-term numerical integrations suggest that the present planetary configuration and interaction appear stable.
The computer integrations for available data on the planet Mercury are limited to an apparently very stable period in the recorded history of the solar system. Significant changes in charge particle influx or outflux apparently have not occurred. Nor have any significant interstellar bodies of large size entered or passed through the solar system. The same may be said for large clouds of any kind. Supernovae have been observed at distances that have precipitated little or no effect on the solar system.
Although forces persist within the solar system that may under certain circumstance produce one or more close encounters, none apparently have occurred at least within the last several hundred years. The combination of forces within the solar system appear to be sufficiently balanced to allow the vertical precession of Mercury's orbit without specific delineation of their effects on this precession.
To assess your vertical precession force system, including your justification, analysis and discussion, I will provide such an assessment of my examples for comparison.
A specific interaction of forces within the present solar system has not been performed to test any hypothesis. Letting the apparent stability of the solar system be described by a computer integration may be little more than sticking one's head into the sand like an ostrich.
- The vertical precession of Mercury's orbit cannot be accounted for by relativity theory.
- Peale, S. J. (June 1974). "Possible histories of the obliquity of Mercury". Astronomical Journal 79 (6): 722-44. doi:10.1086/111604.
- A. Odman (July 20, 2010). Inner Planets part A Mercury and the Moon. Portland, Oregon USA: Portland Community College. Retrieved 2014-03-31.
- David R. Williams (January 1, 2000). Mercury Fact Sheet. Greenbelt, MD 20771 USA: NASA Goddard Space Flight Center. Retrieved 2014-03-31.
- Stu Burro (September 13, 2006). Asteroids. Cleveland, Ohio USA: Case Western Reserve University. Retrieved 2014-03-31.
- Larry McNish (March 20, 2014). RASC Calgary Centre - Planetary Orbits. Calgary, Alberta, Canada: The Royal Astronomical Society of Canada. Retrieved 2014-03-31.
- Takashi Ito and Kiyotaka Tanikawa (October 2002). "Long-term integrations and stability of planetary orbits in our Solar system". Monthly Notice of the Royal Astronomical Society 336 (2): 483-500. doi:10.1046/j.1365-8711.2002.05765.x. http://adsabs.harvard.edu/abs/2002MNRAS.336..483I. Retrieved 2014-03-31.
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