# THE GEOMETRY OF THE SOLAR SYSTEM

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```					THE GEOMETRY OF THE SOLAR SYSTEM

Objective: To model the relative sizes and relative positions of the planets
within our solar system on any chosen date.

A. THE OBJECTS IN OUR SOLAR SYSTEM? 1.) Name the nine planets in our solar system. ________ ________ ________ ________ ________ ________ ________ ________ ________ 2.) Our solar neighborhood is a heliocentric (i.e. sun-centered) system. On polar coordinate graph paper, place each of the planets as you think they will be positioned on a chosen date. Note the angle and distance relative to the Sun and the Earth for each planet.

B. HOW LARGE ARE THE OBJECTS IN OUR SOLAR SYSTEM? 1.) What information in table 1 represents the actual size of the planets, our moon and the Sun? ______________________ 2.) List the planets, our moon, and the Sun in order of size, largest to smallest, in st the 1 column of a spreadsheet we will be creating for this project. 3.) Calculate the equatorial diameters in miles and place in the 2 column of the spreadsheet. 4.) Using this information calculate the size of each planet relative to the Sun. Place this information in the 3rd column of the spreadsheet. (Let the Sun = 1, our base of reference.) nd [Note: The 2 column in table 1 states the diameter of each planet relative to the Earth.)
nd

5.) What if the Sun was the size of a basketball (diameter = 9 ½ inches)? Using the relative sizes of the objects in our solar system located in the 3rd column of the spreadsheet calculate the size of the nine planets and our moon relative to the Sun as a basketball. Place your calculations in the 4th column of the spreadsheet. What is the scale? 1: ___________. (Hint: If 9 ½ inches represents 863,040 miles, then 1 inch = _______inches.) 6.) What if the Sun was the size of a golf ball (diameter = 1 5/8 inches)? Using the relative sizes of the objects in our solar system calculate the size of the= nine planets and our moon relative to the Sun as a golf ball. Place your calculations in the 5th column of the spreadsheet. What is the scale? 1: ____________. (Hint: If 1 5/8 inches represents 863,040 miles, then 1 inch = _______inches.)

D. HOW FAR AWAY ARE THE OBJECTS IN OUR SOLAR SYSTEM? 1.) Calculate the mean solar distance (in millions of miles for each planet and th place in the 6 column of the spreadsheet.

2.) With a basketball as the Sun, calculate the mean distance (in feet) to Pluto? Use the scale that you determined in C-4.

4.) With a golf ball as the Sun, calculate the mean distance (in feet) to Pluto? Use the scale that you determined in C-5..

E.

CREATING A MODEL OF OUR SOLAR SYSTEM Now let’s plan a realistic model of our solar system as it will appear on the date chosen. 1.) Using the formulae and data in table 2, calculate the angular position in degrees (L) of each planet and the distance (R)(in miles) to each planet from the Sun with the sun as the center of our solar system model. You may choose to write a program for each formulae using either a graphing calculator or computer. Mercury: L = R= Jupiter: L = R=

Venus: L = R=

Saturn: L = R=

Earth: L = R=

Uranus: L = R=

Mars: L = R=

Neptune: L = R=

Pluto: L = R=

3.) What scale should we use to place our model on Bryant Field (dimensions: 450’ x 550’)? Will the Sun be represented as a basketball or a golf ball? Therefore the numerical scale will be 1 foot = ___________miles.

TABLE 1 Body Equatorial Diameter (km) 4,880 12,100 12.756 6,794 143,200 120,536 51,800 49,528 2,330 3,476 1,392,000 Diameter with reference To Earth 0.38 0.95 1.00 0.53 11.23 9.45 4.06 3.88 0.18 0.27 109.13 Mean solar distance (M km) 57,9 108.2 149.6 227.9 778.3 1,427 2,871 4,497 5,914 0.38* * from Earth Mean solar distance (A.U.) 0.39 0.72 1.0 1.52 5.2 9.55 19.22 31.11 39.44 -

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Moon Sun

TABLE 2 p (period x (longitude y (longitude e (eccentricity a (semi-major

tropical years) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto 0.241 0.615 1.000 1.881 11.863 29.471 84.039 164.792 246.770

at epoch degrees) 60.751 88.456 99.403 240.739 90.638 287.690 271.063 282.350 221.413

of the perihelion degrees) 77.300 131.430 102.768 335.875 14.171 92.861 172.885 48.100 224.133

of the orbit) 0.206 0.007 0.017 0.093 0.048 0.056 0.046 0.009 0.246

axis of the orbit A.U.) 0.387 0.723 1.000 1.524 5.203 9.555 19.218 30.110 39.341

FORMULAE

d = the number of days since January 0, 1990 N = [(360)(d)] / [(365.42)(p)] M =N=x-y L = N + (360/)(e)(sin M) + x V =L-x R = [(a)(1-e^2)] / [(1 + (e)(cos V)]

credit: Peter Duffet-Smith Practical Astronomy Using A Caculator

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