Celestial Motion Tutorial

Celestial Motion Introduction

This webpage provides an introduction to basic celestial motion. The purpose is to provide a basic introduction to how celestial objects move and give the necessary background information to understand telescope mounts and celestial tracking. 

Celestial Sphere

The celestial sphere is a large sphere, centered on the Earth and having the same center point and rotational axis (below diagram). Imagine that all celestial objects are located on the inside of the non-rotating celestial sphere. As the Earth rotates within the celestial sphere (W. to E.), an observer on the Earth will see celestial objects move across the sky on the inside of this sphere (E. to W.). Because the celestial sphere is tilted to the same axis of rotation as the Earth, celestial objects move across the sky in arcs, centered on the Earths polar axis. Note that the celestial sphere is imaginary and does not actually exist.

Coordinates can be placed on the celestial sphere that are similar to the Earth's longitude and latitude lines.  Right ascension (RA) lines run pole to pole on the celestial sphere, and are similar to longitude lines on Earth (below left diagram). Declination (Dec) lines run parallel to the celestial sphere's equator, and are similar to latitude lines on Earth (below right diagram). The Earth's equator can be projected outward to form a plane intersecting the celestial sphere and forming the celestial equator (below right diagram). The celestial equator
is directly overhead for an observer at the Earth's equator and located on the horizon for an observer at the Earth's pole. For locations between the equator and pole, the maximum altitude of the celestial equator equals 90 deg. - the observer's latitude.


How Stars Appear to Move

Stars appear to move across the sky from east to west, but actually its the Earth that moves. As the Earth rotates within the celestial sphere, the stars to appear to move. How the stars appear to move depends on your location on Earth. The below diagrams show how a star appears to move for an observer located at the equator, at the pole, and at a location between the equator and pole (left, center, and right diagrams, respectively). For the observer at the equator (left diagram), the Earth's rotational axis is on the horizon (dashed white line) and the celestial equator (dashed green line) is directly overhead. As the Earth rotates on its axis, stars will follow an arced path around the rotational axis or pole. This causes stars to rise in the east and follow a vertical path to the west (the solid pink line). For an observer located at the pole (center diagram), the Earth's rotational axis is directly overhead (dashed white line) and the celestial equator (dashed green line) is on the horizon. Stars will move in circles around the pole (the solid pink circle) and never set below the horizon; these are called circumpolar stars.  For an observer at a position between the equator and the pole (right diagram), the Earth's pole will be located at the same angle above the horizon as the observer's location (for example at 45 deg. N. latitude, the N. pole is located 45 deg. above the horizon). Stars will move in arcs around the polar axis that cross the sky at an angle relative to the horizon. Some stars will be close enough to the pole to be circumpolar at the observer's location (never set below the horizon), but starts farther away from the pole will rise and set.

The Constellations Change With the Seasons

The Earth's rotation is responsible for how the stars appear to move (rise, transit, set, etc.), but its the Earth's revolution around the sun that causes the constellations to change with the different seasons. The below left diagram shows how a circumpolar constellation changes with the four seasons (the N. pole is marked by the small cross). Circumpolar constellations are always visible, but their orientation and position in the sky changes from season to season. Other constellations (those that rise and set) are only visible during certain seasons. This is because as the Earth revolves around the sun, different parts of the celestial sphere are visible at night during the different seasons (below right diagram). The stars we can see at night are in the direction facing away from the sun.  In the winter we can see the constellation Orion because at night we can look in the direction of Orion (it is away from the sun). During the summer, we can only look in the direction of Orion during the daytime-when Orion is not visible due to the sun. If we try looking for Orion on a summer night, we are facing in the wrong direction (towards Sagittarius) and can't see Orion. We will need to wait 6 months for the Earth to revolve to a nighttime position that directly faces Orion.

 

The Zodiac and Ecliptic

The Earth and planets revolve around the sun in a plane called the ecliptic plane (below left diagram). The intersection of the ecliptic plane and the celestial sphere is called the ecliptic, and this is path the planets and sun follow across the celestial sphere. The 12 constellations forming a band around the ecliptic are called the zodiac (below center diagram). The zodiac is the constellations that the sun and planets appear to move through as viewed from the Earth. If the Earth's axis were perpendicular to the ecliptic plane, then the sun and planets would follow a path around the celestial equator-but this is not the case. The Earth's axis is tilted approximately 23 deg. with respect to the ecliptic plane. This tilt causes the planets and sun to follow a path (the ecliptic) that crosses the celestial equator at two points (equinoctial points). There are two equinoctial points, where the sun crosses the celestial equator during the March and September equinoxes (below right diagram).


Planetary Motion

Most of the planets revolve around the sun in elliptical orbits that are nearly circular; Venus and Neptune have very circular orbits, while Mercury and Pluto (no longer considered a planet) move in more elliptical orbits. Generally the planets move eastward through the stars, but sometimes they appear to move backwards (westward) for a period of time, and then continue eastward. This strange forward-backward-forward motion is called retrograde motion. The below top diagram illustrates retrograde motion. The planet (red sphere) moves eastward from Taurus into Gemini (position A). It continues eastward into Cancer (positions B and C), but then moves westward back to Taurus (position D) before it resumes eastward movement into Leo (position E). The planets exhibit retrograde motion to different extents: Mars's retrograde motion may span 20 deg. of the sky and last up to 81 days, Jupiter's retrograde motion is about half as much as Mars, and the effect is progressively less for Saturn, Neptune, Uranus, and Pluto. Because Mercury and Venus are located close to the sun, their retrograde motions are more difficult to observe.

Planetary retrograde motion is caused by the Earth passing a planet in its orbit.
This effect is something that can be observed while driving a car on a long, straight road. As you catch up and pass another car, it appears to move backwards. After the passed car is some distance behind, it appears to once again travel forward. The top diagram illustrates retrograde motion of Mars (red sphere) and the yellow letters correspond to the geometries in the bottom 5 diagrams (A-E). In diagrams A and B, the Earth (green) is approaching Mars (Red) and Mars appears to travel eastward (from Gemini into Cancer). In diagram C, the Earth catches up to Mars and in diagram D the Earth has passed Mars, causing Mars to appear to travel backwards into Gemini. In diagram E, both planets continue forward in their orbits and Mars again appears to travel eastward into Leo. Note that the below diagrams are not drawn to correct scale.






The Ptolemaic Model

Retrograde motion puzzled ancient astronomers, who believed that the planets and sun revolved around the Earth. The most successful (but still incorrect) model was developed by Claudius Ptolemy (90 AD-168 AD). The incorrect Ptolemaic model was accepted until the 16th century, when Nicolaus Copernicus proposed a sun centered or heliocentric model. It is interesting to note that Copernicus is popularly credited with inventing the sun centered solar system model, but this was first proposed by Aristarcus of Samos in the 3rd century BC.

The Ptolemaic model (below diagram) explained the apparent motion of the planets by attaching them to small circles called epicycles. Each epicycle was attached to a larger circle called a deferent. The Earth was located in the center of the deferents and the stars were attached to a celestial sphere that surrounded the epicycles and deferents. The epicycles rotated around their attachment point on their deferent and the deferents rotated around the Earth. This complicated model moved the epicycles and planets through the zodiac (as the deferents rotated) and the rotating epicycles caused forward and backward (retrograde) planetary motion.



The below diagrams illustrate how the rotating epicycles simulate retrograde motion. Note that for clarity I have only included rotation of the deferent in the last diagram (diagram E), which moves the epicycles around the zodiac. The top diagram illustrates retrograde motion of a planet (red sphere) and the yellow letters correspond to the geometries in the bottom 5 diagrams (A-E). Diagrams A-D illustrate how rotation of the planet around the epicycles simulates retrograde motion: the planet first appears to move eastward from Gemini to Cancer, then backwards to Taurus and finally forward into Leo.  The planet is in the same position on the epicycle in diagrams B and E, but in diagram E the deferent has also rotated. The rotation of the deferent drags the planet and epicycle eastward and the retrograde motion then repeats. Note that both the epicycle and deferent continually rotate, I have only shown the deferent rotation in a single figure for clarity. Remember that the Ptolemaic model is incorrect, it is only presented here for historical purposes.




Celestial Coordinates

A star's position on the celestial sphere is specified by assigning two coordinates (right ascension and  declination), which specify positions on the celestial sphere in a similar manner as  longitude and latitude define a location on Earth.  Right ascension (RA) specifies how far the position is around the celestial equator, similar to how longitude specifies the distance around the equator from the Prime Meridian (longitude=zero). The starting point for right ascension is the location where the sun crosses the celestial equator during the March equinox (the First Point of Aries). A star lying anywhere on the right ascension line through the First Point of Aries has a right ascension (RA) = zero. The below left diagram shows two stars with different right ascensions (lying on different RA lines). Right ascension is measured in hours, minutes, and seconds of arc (notation hh:mm:ss), where a complete rotation around the celestial sphere is defined as 24 hrs. of arc. One hour of arc is 1/24 th of a 360 degree circle = 15 degrees; this is how far a star's position will move across the sky in one hours time.

Declination (Dec) specifies how far the position is above or below the celestial equator, similar to how latitude specifies the distance north or south of the Earth's equator (latitude=0). Declination is measured in degrees, minutes, and seconds (notation dd:mm:ss) and ranges from -90 deg. to +90 deg. at the S. and N. celestial poles, respectively.  The below right diagram shows 5 stars with equal declinations (equal distances from the dashed green celestial equator).

 

The below left diagram shows a yellow star rising on the horizon. The star is on the declination line (pink line) located 20 degrees above the celestial equator (dashed green line) and on the right ascension line (yellow RA line) through the First Point of Aries (the star has coordinates Dec=+20 deg, RA=00 hr.).  The yellow star rising on the horizon at Dec=+20 and RA=00 hrs. (left diagram) will take a quarter rotation of the Earth (6 hrs.) before it is overhead on the right ascension line running through the zenith (below right diagram). Once overhead on the right ascension line through the zenith, this star is still 20 deg. above the celestial equator and still on the RA=00 hr. line, so its celestial coordinates are unchanged. What has changed is that the Earth has rotated a quarter turn inside the celestial sphere. This moves all the right ascension lines a quarter Earth turn to the west. The right ascension line on the horizon 6 hrs. before (yellow) is now the right ascension line running through the zenith and a star with a RA=6 hrs. (blue star, blue RA line) is now rising on the horizon. 

     


Right ascension and declination specify a star's exact location on the celestial sphere, but right ascension is also a measure of time. Knowing the current right ascension on the horizon allows calculation of when a celestial object will rise or set; this can be determined from a planetarium program or by locating a known star on the horizon and looking up its right ascension. Knowing the difference in right ascension between two objects tells the time difference between when they rise, set, or transit past a fixed location (such as the right ascension line through the zenith, etc.).

Precession

The above discussion has assumed that right ascension and declination coordinates are constant with time. Actually these coordinates are not constant and change very slowly. This is because the Earth wobbles on its rotational axis, much like a spinning top. This wobble is called precession and causes the Earth's poles to slowly change position over the course of a 26,000 year cycle. The below diagram shows that Polaris is presently the pole star, but the Earth's polar axis is rotating toward Vega, which will be the new pole star in the year 14000 AD. Since precession shifts the orientation of the Earth within the celestial sphere, the positions of  stars relative to the celestial equator and the First Point of Aries slowly change (thus changing their celestial coordinates).


Tracking Celestial Objects

The preceding sections described how objects move across the sky and introduced the celestial coordinate systems. This information was presented as background material to understand why telescope mounts are constructed as they are and how they track objects.  Astronomical tracking is essential for astrophotography, scientific measurements, and it also simplifies viewing by holding objects centered in the telescope.  Examples of the most common telescope mounts and illustrations of how they function and track objects can be found on the Telescope Mounts Tutorial webpage.                                                                   


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