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Sol (borrowed from the Latin word for sun) is a solar day on Mars; that is, a Mars-day. A sol is the apparent interval between two successive returns of the Sun to the same meridian (sundial time) as seen by an observer on Mars. It is one of several units for timekeeping on Mars. A sol is slightly longer than an Earth day.
When accounting solar days on Earth, astronomers often use Julian dates—a simple sequential count of days—for timekeeping purposes. An analogous system for Mars has been proposed "[f]or historical utility with respect to the Earth-based atmospheric, visual mapping, and polar-cap observations of Mars, ... a sequential count of sol-numbers".
The basic time periods from which the calendar is constructed are the Martian solar day (sometimes called a sol) and the Martian vernal equinox year.The sol is 39 minutes 35.244 seconds longer than the Terrestrial solar day, and the Martian vernal equinox year is 668.5907 sols in length (which corresponds to 686.9711 days on Earth).
If the second set of parameters is not included it will automatically calculate the days between a given date and today. It is based on the product of the count of Earth days past and the ratio of the length of Earth's solar day length (86400 seconds) with a Mars solar day (88775.24409 seconds), rounded to the nearest sol.
The calculation takes into account that a Mars Sol is a few dozen minutes longer than an Earth day. NASA and secondary sources provide Sol numbers, but do not always give a UTC time or any Earth time zone for the events on Mars. NASA provides photographs from the events with a timestamp in local Mars time that facilitates the calculation. See here.
Along with unprecedent accuracy, the Keplerian model also allows put the Solar System into scale. If a reliable measure between planetary bodies would be taken, the whole size of the system could be computed. By this time, the Solar System started to be conceived as something smaller than the rest of the universe.
the Solar longitude (L s) system: 360 degrees per Mars Year that represent the position of Mars in its orbit around the Sun, or; the Sol system: 668 sols per Mars Year. This system consists of uniform time units. However, Mars Year sols may be confused with rover mission times that are also expressed in sols.
A numerical model of the Solar System is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time. Attempts to create such a model established the more general field of celestial mechanics. The results of this simulation can be compared with past measurements to check for accuracy ...