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PtolemyChartJupiterSystemPlot

5.7 The SolarSystemPlot Function

SolarSystemPlot is useful for displaying a plot of the solar system on a given date.

Plotting a representation of the solar system.

Earth is the blue dot at the center, and the Sun is the bigger yellow dot. Planets that happen to be near the yellow line can only be seen from the Earth at dusk or dawn. Examples are Venus and Mercury, which are always close to the yellow line. Planets near the red line are high in the sky when the Sun sets, and hence they are visible only in the evening sky for a certain length of time, until they set in the west. Similarly, planets near the blue line are high in the sky when the Sun rises, and hence they are visible only in the morning sky for a period of time after they rise in the east. Planets nearly 180 degrees away from the yellow line are visible all night long.

Here is a plot of the solar system on 1993 November 17. Most of the planets are in the direction of the Sun, represented by the yellow line, and hence not easily visible from the Earth. However, Saturn is a good distance away from the yellow line and close to the red line, so it is visible in the evening sky for about half the night after sunset.

In[22]:=SolarSystemPlot[{1993,11,17}];

The option Distance is used to show the plot just out to the orbit of Mars. The direction of the Moon is shown on the outer rim, in this case near the 18h mark.

In[23]:=SolarSystemPlot[{1993,11,17}, Distance->3*AU];

To zoom into a smaller region showing, for instance, as far out as the orbit of Mars, you can use the option Distance.

By default the Earth is placed at the center, but you can use ViewPoint -> Sun to put the Sun at the center. In this case the "Morning" and "Evening" lines will not be shown. To stop the lines being drawn in the case of Earth at the center, use ViewPoint -> GeoCentric.

The AspectChart Function

Scientific Astronomer includes functions that astrologers can use. AspectChart uses ancient astrological symbols to represent the aspects, or relative positions, of the planets. The chart is, in effect, the same as SolarSystemPlot, but is represented in a more symbolic and less graphical manner.

Generating an astrological aspect chart.

Although AspectChart returns a seemingly incomprehensible array of mystical symbols, it is in some contexts a useful representation of the relative positions of the Sun, Moon, and planets.

This is the astrological aspect chart for the given date, with the specified geographic location and time zone.

In[24]:=AspectChart[{1993,11,17,3,20,0},
     GeoLongitude -> 145.0*Degree,
GeoLatitude -> -37.8*Degree,
TimeZone -> 11];

Astrological symbols on the diagonal denote the ascendant , Sun , Moon , Mercury , Venus , Mars , Jupiter , and Saturn . The ascendant is the name of the point on the zodiac that is rising (or ascending) near the eastern horizon. Note that the symbols for Venus and Mars are also the symbols for female and male.

The off-diagonal entries show the aspect, or relative position, of pairs of objects on the diagonal. There are five main aspects. The first is conjunction , which occurs when two objects lie approximately in the same direction (i.e., as if they were conjoined); the second aspect is sextile , which occurs when two objects are approximately 60 degrees apart (or a sixth of a full circle; note that the sextile symbol has six points); the third aspect is quadrature , which indicates when the objects are approximately 90 degrees apart (or a quarter of a full circle); the next aspect is trine , which indicates a 120 degree separation (or a third of a full circle); and the final aspect is opposition , which indicates when two objects are 180 degrees apart (or opposite to each other in the sky).

The five main aspects cover most possibilities; two additional minor aspects are semisextile , for objects approximately 30 degrees apart (which is half of a sixth of a full circle); and quincunx , for objects approximately 150 degrees apart (which is five twelfths of a full circle).

The entries in the chart are arranged so that the object in the same row as an aspect rises before the object in the same column. Thus, when any aspect symbol is in the first row (the ascendant row), the corresponding object on the diagonal will be above the horizon.

This instance of AspectChart is for the default location at 07:00 on 1997 January 1. To read the chart, first consider the case of the Moon , the third object on the diagonal. You can find all the aspects of the Moon by looking in the same column and row as the Moon. There is only one aspect symbol in the same row as the Moon; an opposition to Saturn . All other objects listed on the diagonal rise later than the Moon. For instance, the aspect with the ascendant is trine , and so the Moon is 120 degrees higher than the point on the eastern horizon. Hence the Moon has been above the horizon for 8 hours. The next aspect of the Moon is quadrature with the Sun , which indicates the Moon is at quarter phase. Looking further down the column, you see the Moon is in conjunction with Mars . For Venus , there are only three major aspects. Venus is in quadrature with the Moon and Mars , and so rises 6 hours later than these objects. Venus is also in quadrature with Saturn , but rises 6 hours earlier because the aspect is in Venus' column. Note that at sunrise the Sun must be in conjunction with the ascendant , as in this example. Similary, at sunset the Sun must be at opposition to the ascendant .

In[25]:=AspectChart[{1997,1,1,7,0,0}];

The information returned by AspectChart is also contained in SolarSystemPlot. In this graphic you see all the aspects between the planets, Sun, and Moon. For instance, the conjunction of the Moon and Mars and the opposition of the Moon and Saturn are visible. Remember that the Earth is in the center of this graphic.

In[26]:=SolarSystemPlot[{1997,1,1,7,0,0}];

Some key points to be aware of are that the rising of any planet occurs when the planet is in conjunction with the ascendant. Similarly, a planet sets when it is in opposition to the ascendant. A full moon is in opposition to the Sun, and a new moon is in conjunction with the Sun. Venus is at its brightest when it is not in conjunction with the Sun. Any object in quadrature with the ascendant is at its highest point in the sky. These rules apply to other combinations of planets and aspects as well. Remember that the object in the same row as an aspect rises before the object in the same column as the aspect.

When there are many alignments between the planets, AspectChart will indicate this with many conjunction symbols.

At sunrise on 2000 May 4, the Sun, the Moon, and all the bright planets will rise as one above the eastern horizon. Although this type of cosmic alignment is relatively rare, it has happened before during the previous millenia (a similar event occurred at sunrise on 748 November 1). Here is an aspect chart clearly showing the alignment, with almost all objects in conjunction with the others. Mars is slightly out of the alignment, rising an hour too early.

In[27]:=AspectChart[SunRise[{2000,5,4}]];

The BirthChart Function

BirthChart produces a chart containing essentially the same information as SolarSystemPlot, except that it uses astrological symbols to represent the planets and the zodiac constellations. The horizontal line in the chart demarcates the regions above and below the horizon of an observer at the center of the chart. Thus, any planet symbol above this line corresponds to a planet above the observer's horizon.

Generating a birth chart.

The chart shows a circle containing the 12 zodiac signs with the position of the Sun, Moon, and main planets indicated relative to those signs. At the center of the chart is the Earth , and on the eastern and western horizons are the ascendant and descendant . Astrologers use the zodiac constellation nearest the Sun , at the time of birth, as the astrological sign of a person. The position of each zodiac constellation is taken as it appeared in the year 500 B.C., however. Precession, as of the year 2000 A.D., has moved the position of all the zodiac constellations more than one zodiac sign away, but this is not normally taken into account by astrologers. In BirthChart you can use the option Epoch -> Automatic to get the true position of the zodiac constellations at the time of birth. The default is Epoch -> -500.0, which corresponds to the position of the zodiac constellations in the year 500 B.C.

This is the birth chart for the given date, with the specified geographic location and time zone. All the main planets are below the horizon.

In[28]:=BirthChart[{1993,11,17,3,20,0},
     GeoLongitude -> 145.0*Degree,
GeoLatitude -> -37.8*Degree,
TimeZone -> 11];

Astrological symbols used for the zodiac constellations are Aries , Taurus , Gemini , Cancer , Leo , Virgo , Libra , Scorpius , Sagittarius , Capricornus , Aquarius , and Pisces .

The arrow in the chart corresponds to the direction of the meridian. For northern hemisphere observers the meridian is due south, and for southern hemisphere observers it is due north. The meridian arrow is always near the vertical in the chart, but it can vary up to 23 degrees on either side of the vertical due to the tilt of the Earth's axis.

This BirthChart is for the default location at 07:00 on 1997 January 1. It shows the Sun , Jupiter , and Mercury rising (or ascending) above the eastern horizon. This chart is for the southern hemisphere, so the ascendant is on the right, which is the opposite of its location on a northern hemisphere chart. Venus is higher in the sky near the zodiac sign of Sagittarius . The Moon and Mars are in conjunction near Virgo .

In[29]:=BirthChart[{1997,1,1,7,0,0}];

This is the birth chart for Charles Dickens, born at midnight on 1812 February 7. It shows all the planets below the horizon, with the exception of Jupiter . The position of the Sun is in Aquarius .

In[30]:=BirthChart[{1812,2,7,0,0,0},
GeoLongitude -> 0*Degree,
GeoLatitude -> 51*Degree,
TimeZone -> 0];

PtolemyChartJupiterSystemPlot



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