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2.1 The Ephemeris and Appearance Functions

Ephemeris returns all the common ephemeris data about a celestial object at the current time, date, and viewing location. It includes information such as the object's position and its rising and setting times.

Printing ephemeris information.

Ephemeris is typically applied to solar system objects such as Mars, Moon, and Io; stars such as Sirius and Alpha.Centaurus; constellations such as Leo and UrsaMajor; and special objects such as SouthCelestialPole and Zenith.

The ephemeris data for Mercury at 03:20 on 1993 November 17 shows that Mercury rises at about 05:19, or approximately 45 minutes before the Sun. At the given date and time, Mercury is below the horizon. When it does rise, Mercury has a magnitude of about 1.0 and is visible in the general direction of the zodiac constellation of Libra.

In[3]:=Ephemeris[Mercury, {1993,11,17,3,20,0}]


You will note that additional information is given in the ephemeris output, such as the object's azimuth and altitude. Azimuth is the compass direction around the horizon, and altitude is the angle above the horizon. Ascension and declination values are included as well.

Basic information about the planets, asteriods, and even Galilean moons can be accessed using the ? function.

?Mercury gives basic information about the fixed properties of the planet Mercury.


Ephemeris can also be applied to the Moon and other objects. The fourth to last line on the right shows that the Moon is in the evening sky, as opposed to the morning sky. Its phase is 10%, which is almost a new moon; as seen from Earth only 10% of its surface is illuminated by the Sun.

In[5]:=Ephemeris[Moon, {1993,11,17,3,20,0}]


Here is the ephemeris data for the constellation of Leo.

In[6]:=Ephemeris[Leo, {1993,11,17,3,20,0}]


In the case of the Moon, distance is given in Megameters (1 Mm = 1,000km). For most other objects, distance is expressed in astronomical units (1 AU = 149,597,900km). In some cases, such as for the constellations, distance does not have any meaning, and the entry in the Ephemeris output is simply left blank. For stars and other very distant objects, distance is measured in light years (1 LY = 63,240 AU).

As with other coordinate functions, the default for the option ViewPoint (i.e., the point from which you make the observation) is calculated as if you were at the center of the Earth, but with the correct longitude and latitude for the purposes of determining the local horizon. In other words, the default setting is calculated as if you live on the surface of a very small ball at the center of the Earth.

On some occasions, as when viewing the Moon or a low-orbit satellite, parallax comes into play, and it is important to use your correct location on the surface of the Earth, which is provided by the TopoCentric object. The option setting ViewPoint -> TopoCentric, available in Ephemeris and other functions, accurately computes angles for your specific site, rather than approximating them as from the center of the Earth.

The Appearance Function

A related function is Appearance, which returns rules related to the appearance of an object on a given date. For instance, the phase rule represents the amount of the object's disk illuminated by the Sun as seen from the current viewpoint. A phase of 1 represents full illumination, whereas 0 represents no illumination, due to the Sun's location being directly behind the object.

Computing appearance information.

The general appearance of the Moon on 1993 November 17 shows that the apparent diameter of the Moon is 0.533 degrees and its phase is 0.10, which means that only 10% of the Moon's surface, as seen from the Earth, is currently illuminated.

In[7]:=Appearance[Moon, {1993,11,17,3,20,0}]


This shows that Jupiter's phase is nearly 100% as is always the case when it is viewed from the Earth. Its apparent diameter is 0.0087 degrees, or about 31 arc-seconds, and its apparent magnitude is -1.7, which is slightly brighter than the brightest star at -1.5.

In[8]:=Appearance[Jupiter, {1993,11,17,3,20,0}]


Two important quantities returned by Appearance are the central longitude and latitude of an object. These are the local longitude and latitude of the spot at the very center of the object's disk as seen from the viewpoint on the given date. Section 9.6 discusses in detail the coordinate system used for the local longitude and latitude of various planets, the Moon, and the Sun.

The Moon always presents the same face toward the Earth, but due to an effect known as libration, the Moon rocks slightly from side to side about a mean state. The central longitude and latitude of the Moon are equivalent to the angles of libration if the viewpoint is the Earth.

A combination of libration and the viewing location on the surface of the Earth allows you to see 6.35 degrees around the western edge of the Moon; and 4.08 degrees above the northern edge of the Moon.

In[9]:=Appearance[Moon, {1993,11,17,3,20,0},


The place with lunar longitude equal to 149.1 degrees has the Sun directly overhead.

In[10]:=Appearance[Moon, {1993,11,17,3,20,0},


The place with Martian longitude equal to -64.5 degrees is facing the Earth on the given date and time. The central latitude is +8.15 degrees, so the north pole of Mars is tilted toward the Earth.

In[11]:=Appearance[Mars, {1993,11,17,3,20,0}]


The coordinate system on Europa and the other Galilean moons is such that the zero of longitude and latitude is the point facing Jupiter. As with the Earth's moon, there is a small libration rocking the Galilean moons.

In[12]:=Appearance[Europa, {1993,11,17,3,20,0},


The Appearance function can be applied to stars, star clusters, nebulae, and galaxies. In the case of a star, the apparent magnitude and spectral color is returned by Appearance.

Every star has a particular temperature, which depends on its mass, age, and internal composition. This temperature is directly related to the color that we see. Some stars, such as Antares in Scorpius, have a very definite red appearance. In general, hot stars are blue in color, and cooler ones are red. Stars of intermediate temperature can be white, yellow, or orange.

Scientific Astronomer uses the standard spectral type sequence to classify the color of stars. The sequence begins with "O" and "B" to designate the hottest stars; "A", "F", and "G" refer to intermediate temperature stars; and the coolest stars are classified as "K" and "M". Each spectral type is further subdivided into ten divisions numbered 0 through 9. In this classification our own Sun is rated as a G2 star. The table shows the relationship between spectral type, color, and temperature. A G2 star like our Sun, for instance, has a yellow-white appearance.

Spectral types.

Appearance is used to find the color of the star Betelgeuse. Spectral type M1 corresponds to a very red color.



The reddest star known is the 5th magnitude TX.Pisces. Another extremely red star is the Mira-type variable R.Lepus. John Hind in 1845 described this star as appearing "like a drop of blood on a black field". The magnitude of R.Lepus ranges between 5.5 and 10.5 over a period of 432 days. Some notable blue stars include the 2nd magnitude supergiant Zeta (zeta) Puppis and the 1st magnitude Spica.

Objects and DatesPlanetChart, EclipticChart

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