AST 309-TIME
Solar System Model


Assignment

Name_______________________________

This assignment is DUE on September 11. Late work will be penalized! Be sure to save your work for the Astrolabe Assignment.

Calculate and plot the positions of all the planets on the day of your birth. (Note: This is NOT an astrology exercise; but lets have some fun!) You can use the extra copy of the chart that is provided, or if you don't want to spoil it you can make a photocopy of the chart and turn in the photocopy.

Again, determine which planets were up at sunset, midnight, and sunrise on the day of your birth. At midnight, determine whether the planets were in the Eastern third of the sky, the third that was nearly overhead (near the meridian), or in the Western third.

Turn in your calculations and your chart along with your answers to the following questions:

1.What is the date of your birth?

2.Which planets were up at sunset on that date?

3.Which planets were up at midnight on that date? For each planet that was up at midnight, state whether it was in the Eastern third of the sky, the Western third, or the third that is nearest the meridian.

4.Which planets were up at sunrise on that date?

The following tables and diagrams can be used to determine the position of the visible planets in the Solar System for any date in history covered by the tables. The tables and diagrams are adapted from Walter Bartky's book, Highlights of Astronomy, University of Chicago Press, Phoenix Edition 1961. However, the tables and diagrams have been completely recalculated and redrawn from first principles and some errors corrected.

To determine a planet's location in the solar system on any date, first look up the century, decade, year, month and (for Mercury, Venus and Mars) the day in the month in question. You will have to interpolate in the table for Day in the Month. Just split the difference for the date in question amongst the adjacent dates listed. Jupiter and Saturn move very slowly and do not need this table.

Under the column for the planet in question, read across the appropriate rows and write down the two-digit decimal fraction you see there. Add them up and drop any whole number part, retaining only the decimal fraction. Use the result to plot the position of the planet on the orbit marked out for that planet on the appropriate chart (use the first chart for Mercury, Venus and Mars, and the second chart for Jupiter and Saturn). Also, plot the position of the Earth for the date in question. The names of the months are given on the charts; just eyeball the right position and mark it.

For example: What was Venus' position on January 18, 1996? Calculate:

    Century: 1900   0.00
     Decade:   90   0.29
       Year:    6   0.75
      Month:  Jan   0.59
        Day:   18   0.08
   ----------------------
        Sum:        1.71 --> 0.71 (dropping the whole number part)

This places Venus to the right of the Sun, just above the line marked "Vernal Equinox."

Repeat this process for the other four planets. You can now determine the position of the planets as seen in the sky at sunset on that date. Draw a straight line on the chart that passes through the Earth and the Sun and extends past each. This line represents the horizon at sunrise or sunset (the Sun is on the horizon then!) Orient the chart so that the line is horizontal and the Sun is to the right of the Earth. This chart is drawn as seen from the North facing South, so at sunset, the Sun will be on the horizon to your right, as you face south. Think of the line as the Earth beneath your feet, and the ends of the line as the Eastern and Western horizons. For the Venus position we have just plotted, you will find that Venus is above the horizon by some 20-30 degrees, so if you go out on that night and look in the West, you will see Venus fairly high in the sky above the horizon.

If you divide the section of the chart above the horizon into three equal pie-shaped wedges, then the planets in the left wedge are rising, those in the right wedge are setting, and those in the center wedge are near the meridian. Are any other planets up at Sunset on that day? Where is Mercury?

To determine rough sky positions of the planets as seen at sunrise, simply turn the chart upside-down so that the Sun is to the left of the Earth. Now the Sun is on the Eastern horizon, and the sky positions of any planets that are up at sunrise can be estimated as before.

Finally, to determine the rough positions of the planets at midnight, draw a line on the chart through the Earth at right angles to the first. Since at midnight the Sun is under our feet, hold the chart so that the new line is horizontal and the Sun is below the Earth. The planets above the line are above the horizon.

In-class exercise

Calculate the positions of all the planets for today, using the tables in the handout. Check the calculation for each planet with your neighbors. If there is disagreement, try to figure out where the error is. If disagreement persists and cannot be resolved, raise your hand.

Once agreement has been achieved, plot the position of each planet, including the Earth, on one of the charts you have been given (note that each chart has two sides). After plotting them, check the plots with your neighbors. Again, try to resolve any disagreements.

Finally, we will all (with the aid of the Instructors chart, which will be shown on the overhead projector) try to figure out which planets are up at various times of the night (for example, at sunset, sunrise, and midnight). We will try to figure out approximately where in the sky each planet can be observed at various times of night, dividing the sky into thirds.


Click here to get a chart of the inner solar system (can be printed separately)

Click here to get a chart of the outer solar system (can be printed separately)

Century Merc Venus Mars Jup Sat Decade Merc Venus Mars Jup Sat Year Merc Venus Mars Jup Sat
1400 0.99 0.25 0.17 0.85 0.03 0 0.00 0.00 0.00 0.00 0.00 0 0.00 0.00 0.00 0.00 0.00
1500 0.19 0.80 0.33 0.28 0.43 10 0.52 0.25 0.32 0.84 0.34 1 0.15 0.63 0.53 0.08 0.03
1600 0.40 0.35 0.50 0.71 0.82 20 0.04 0.51 0.63 0.69 0.68 2 0.30 0.25 0.06 0.17 0.07
1700 0.60 0.90 0.67 0.14 0.21 30 0.56 0.76 0.95 0.53 0.02 3 0.46 0.88 0.59 0.25 0.10
1800 0.80 0.45 0.83 0.57 0.61 40 0.08 0.02 0.27 0.37 0.36 4 0.61 0.50 0.13 0.34 0.14
1900 0.00 0.00 0.00 0.00 0.00 50 0.60 0.27 0.58 0.21 0.70 5 0.76 0.13 0.66 0.42 0.17
2000 0.20 0.55 0.17 0.43 0.39 60 0.12 0.53 0.90 0.06 0.04 6 0.91 0.75 0.19 0.51 0.20
2100 0.40 0.10 0.33 0.86 0.79 70 0.64 0.78 0.22 0.9 0.38 7 0.06 0.38 0.72 0.59 0.24
2200 0.60 0.65 0.50 0.29 0.18 80 0.16 0.04 0.53 0.74 0.71 8 0.22 0.00 0.25 0.67 0.27
2300 0.81 0.20 0.67 0.72 0.57 90 0.68 0.29 0.85 0.59 0.05 9 0.37 0.63 0.78 0.76 0.31
Month Merc Venus Mars Jup Sat Day Merc Venus Mars
Jan 0.28 0.59 0.89 0.63 0.49 1 0.01 0.00 0.00
Feb 0.64 0.73 0.93 0.63 0.49 5 0.06 0.02 0.01
Mar 0.95 0.85 0.97 0.64 0.49 10 0.11 0.04 0.01
Apr 0.31 0.99 0.02 0.65 0.50 15 0.17 0.07 0.02
May 0.65 0.12 0.06 0.65 0.50 20 0.23 0.09 0.03
Jun 0.00 0.26 0.11 0.66 0.50 25 0.28 0.11 0.04
Jul 0.34 0.40 0.15 0.67 0.50 30 0.34 0.13 0.04
Aug 0.69 0.53 0.20 0.67 0.51
Sep 0.05 0.67 0.24 0.68 0.51
Oct 0.39 0.81 0.28 0.69 0.51
Nov 0.74 0.94 0.33 0.70 0.52
Dec 0.08 0.08 0.37 0.70 0.52

Tables for Planetary Positions

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