# Ecliptic Plane

 If the sun's path is observed from the Earth's 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 Earth's spin axis is tilted with respect to the plane of the Earth's 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 Earth's 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 Earth's orbit . This has led to a number of theories about Pluto's origin. Mercury is the only other planet which moves significantly away from the ecliptic plane ( 7°) .

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# The Ecliptic

The apparent path of the Sun's 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 Earth's 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 Earth's axis with respect to the ecliptic is responsible for Earth's seasons.

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# Celestial Sphere

The stars can be imagined to be points of light on a sphere which rotates about the Earth. Projecting the Earth's 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.
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# Declination and Right Ascension

Right ascension and declination are like longitude and latitude on the surface of the Earth except that they are measured with respect to the celestial sphere with the vernal equinox as the origin.

Right ascension is a celestial longitude measured in the direction of the Earth's rotation. Since that rotation makes a complete circle in 24 hours, the notation adopted for right ascension was in terms of hours and minutes with 24 hours representing the full circle. Declination is expressed as an angle with respect to the celestial equator. For example, the celestial coordinates of the star Betelgeuse in the constellation Orion are right ascension = 5 hours 52 minutes and the declination is 7 degrees 24 minutes. A declination south of the celestial equator is given a negative sign.

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# 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.
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# Celestial Measurement

 Celestial measurement is taken to mean the kinds of measurement with respect to the celestial sphere which allow you to locate astronomical objects for observation. Measurements with respect to the celestial sphere are typically expressed as right ascension and declination, measurements analogous to latitude and longitude on the Earth's surface.

In order to know where to look in the sky for a given object, a precise description of the Earth's motion around the sun and precise measurement of time are necessary. It is often more convenient to describe the apparent motion of sun and stars with respect to the Earth as if it were fixed. In the Earth's frame of reference, the Sun's apparent path is called the ecliptic. The ecliptic plane is inclined at 23.5° with respect to the celestial equator because of the tilt of the Earth's rotation axis with respect to the plane of its orbit around the sun.

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# Synodic and Sidereal Periods

The period of a planet's 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 Earth's spin axis. That precession period of about 26,000 years brings the vernal equinox about 20 minutes earlier each year. 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.

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Reference
Chaisson & McMillan
Ch 1

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