Geodetic AstronomyOrbits & Ecliptic• History• Orbit in physics• Celestial Sphere• The Ecliptic• Ecliptic Plane• Equinoxes and Solstices• Synodic and Sidereal PeriodsAhmed Eldehdeh
History Historically, the apparent motions of the planets were first understood geometrically (and without regard to gravity) in terms of epicycles, which are the sums of numerous circular motions. Theories of this kind predicted paths of the planets moderately well, until Johannes Kepler was able to show that the motions of planets were in fact (at least approximately) elliptical motions. In the geocentric model of the solar system, the celestial spheres model was originally used to explain the apparent motion of the planets in the sky in terms of perfect spheres or rings, but after the planets motions were more accurately measured, theoretical mechanisms such as deferent and epicycles were added. Although it was capable of accurately predicting the planets position in the sky, more and more epicycles were required over time, and the model became more and more unwieldy. The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarized in his three laws of planetary motion.
History First, he found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclical), as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planets distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship.
Orbit in physics In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System. Orbits of planets are typically elliptical Current understanding of the mechanics of orbital motion is based on Albert Einsteins general theory of relativity, which accounts for gravity as due to curvature of space-time, with orbits following geodesics. For ease of calculation, relativity is commonly approximated by the force- based theory of universal gravitation based on Keplers laws of planetary motion.
Celestial Sphere The stars can be imagined to be points of light on a sphere which rotates about the Earth. Projecting the Earths poles and equator out onto this imaginary sphere provides a framework for celestial measurement. Formal measurements of viewing direction from the Earth are usually expressed in terms of right ascension and declination, the analogs to longitude and latitude on the surface of the Earth
The Ecliptic The apparent path of the Suns motion on the celestial sphere as seen from Earth is called the ecliptic. The ecliptic plane is tilted 23.5° with respect to the plane of the celestial equator since the Earths spin axis is tilted 23.5° with respect to its orbit around the sun. The ecliptic plane intersects the celestial equatorial plane along the line between the equinoxes. The tilt of the Earths axis with respect to the ecliptic is responsible for Earths seasons.
Ecliptic Plane If the suns path is observed from the Earths reference frame, it appears to move around the Earth in a path which is tilted with respect to the spin axis at 23.5°. This path is called the ecliptic. It tells us that the Earths spin axis is tilted with respect to the plane of the Earths solar orbit by 23.5°. Observations show that the other planets, with the exception of Pluto, also orbit the sun in essentially the same plane. The ecliptic plane then contains most of the objects which are orbiting the sun. This suggests that the formation process of the solar system resulted in a disk of material out of which formed the sun and the planets. The 23.5° tilt of the Earths spin axis gives the seasonal variations in the amount of sunlight received at the surface. Pluto s orbit is exceptional in that its orbit makes an angle of 17° with the Earths orbit . This has led to a number of theories about Plutos origin. Mercury is the only other planet which moves significantly away from the ecliptic plane (7°).
Ecliptic Plane Still, we can think of the solar system as being quite flat. If we were to view the planets’ orbits from a vantage point in the ecliptic plane about 50 A.U. from the Sun, only Pluto’s orbit would be noticeably tilted.
Equinoxes and Solstices The points where the ecliptic crosses the equatorial plane of the celestial sphere are called equinoxes. On those dates there are 12 hours each of daylight and dark. The most northern excursion of the sun is called the summer solstice and will have the longest amount of daylight. The winter solstice opposite it is the shortest period of daylight.
Synodic and Sidereal Periods The period of a planets orbital period around the Sun with respect to the distant stars is called its sidereal period. The sidereal period of the Earth is about 365 1/4 days. Another type of period is useful for viewing the other planets - the period between the times their positions both lie on the same radial line from the sun, called the synodic period. When planets are on the same radial line from the sun, they are said to be "in opposition". For planets closer to the sun than the Earth, the synodic period of the Earth is longer than the sidereal period, and for outer planets it is shorter if seen by an observer on those planets. The sidereal period of Mars is 1.88 years, whereas the synodic period is 2.135 years as seen from the Earth. The time of opposition of Mars is associated with its apparent retrograde motion for an Earth observer. The period which brings the back to the same angular position with respect to the Sun is called the tropical year and is 365.242 mean solar days. Formally this period is defined as the interval of time from one vernal equinox to the next. The sidereal period (period with respect to the distant stars) of 365.256 mean solar days is about 20 minutes longer because of the precession of the Earths spin axis. That precession period of about 26,000 years brings the vernal equinox about 20 minutes earlier each year.
Synodic and Sidereal Periods The fact that the year is not exactly 365 days has led to the inclusion of the leap year days and other adjustments to the calendar. The sidereal day, which brings a "fixed" star back to the same position on the next night, is 23 hours 56 minutes and 4 seconds. The practical observable effect is that stars rise about 4 minutes earlier each night, about 2 hours earlier in a month, and appear as a parade that progresses westward across the night sky.
References: Blatt, Frank J.,Modern Physics, McGraw-Hill, (1992) Boynton, W. V., et al., "Distribution of Hydrogen in the Near Surface of Mars: Evidence for Subsurface Ice Deposits", Science 297, 81, 5 July 2002 Krauskopf, K and Beiser, A, The Physical Universe, 7th Ed, McGraw-Hill, 1993. Encyclopedia Britannica, 1968, vol. 2, p. 645