# Selected Topics in Contemporary Astronomy and Space Science

## CONTENTS OF CURRICULUM UNIT 98.06.10

## Astronomy and Your Place in the World

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## Relative Sizes and Math Exercises

Our Sun has a diameter near 870,000 miles (1,390,00 km), which is over 100 times larger than the Earth! The circumference of the Sun is more than 2,700,00 miles (4,370,000 km).

Our Solar System is about 5.5 billion miles across (near 9 billion km). If we scaled down the solar system to the size of our classrooms, about 10 meters across, the Earth is smaller than a speck of sand (about 0.000014 meters, or 0.014 millimeter!), and the Sun is about the size of a piece of sand (about 0.0015 meters, or 1.5 mm)... albeit, a large bright piece of sand.

If we consider the Solar System to be disk, looking down at a 90-degree angle from the average ecliptic, then it's a disk with a circumference of 17.3 billion miles (27.6 billion-km). When we discuss distances of this size we usually discuss them in AUs (Astronomical Units), with 1 AU = average distance between the Earth and the Sun, or 93,000,000 miles (150,000,000 km). Thus, our Solar System is 59 AU across. For greater distances, we start using light years, the distance light travels in one Earth years. With light traveling at approximately 186,300 miles per second, a light year is about 6 trillion miles! Our Solar System is 0.0009 light years across.

We are about 30, 000 light years (180,000,000,000,000,000 miles) from the center of our Milky Way galaxy. The diameter of the Milky Way (across the disk) is about 100,000 light years!

We're about 2.2 million light years from the nearest similar galaxy to ours, the Andromeda Galaxy.

>GROUP ACTIVITY - 1: On the following chart, we have provided equatorial diameters for various space bodies. In groups, calculate the approximate equatorial circumference of each body and how long it would take you to walk around that body, assuming a walking rate of 20 miles per day. Note: all measurements are in kilometers, abiding by National Education Standards for Mathematics and Science.

RELATIVE SIZES (for this exercise II = pi =3.14)

Space Body Equatorial Diameter Equatorial Circumference Walking Time (around)

(diameter = d) (c=2 II r or II d) (20 miles/day-32 km/day)

Earth 12,756 km 40,074 km 1,252 days

Moon 3,476 km km days

Sun 1,390,000 km km days

Mercury 4,850 km km days

Venus 12,033 km km days

Mars 6,754 km km days

Jupiter 141,974 km km days

Saturn 119,306 km km days

Uranus 50,506 km km days

Neptune 48,318 km km days

Pluto 2,982 km km days

>GROUP ACTIVITY - 2: Now, in groups, develop a scale picture comparing the sizes of the planets, the Sun, our Moon, and a Saturn V rocket like the type used to carry our Apollo missions to the Moon. Use the scale that one meter (1 m) = the diameter of the Sun. Complete the following table first, and then obtain a piece of butcher paper or drawing paper and draw out these scaled down images, starting with the Sun and working down.

Calculation: 1 m/1,390,00 km = x in meters/diameter x in meters = diameter / 1,390,00 km

SCALE DIAGRAM

Space Body Actual Equatorial Diameter Scale Diameter

Sun 1,390,000 km 1 m or 100 cm

Mercury 4,850 km m or cm

Venus 12,033 km m or cm

Earth 12,756 km m or cm

Moon 3,476 km m or cm

Mars 6,754 km m or cm

Jupiter 141,974 km m or cm

Saturn 119,306 km m or cm

Uranus 50,506 km m or cm

Neptune 48,318 km m or cm

Pluto 2,982 km m or cm

Saturn V Rocket 0.11 km (length) m or cm

The following table provides distances and travel times from Earth (not from the Sun) and has obvious uses in mathematics classes as well as science classes.

RELATIVE DISTANCES: Travel Distance & Time From Earth

Destination Distance Jet Rocket Light/Laser/Radio

Moon 250,000 miles 16.5 days 9.4 hours 1.2 seconds

Sun 93,000,000 miles 17.7 yrs 4 months 8.5 minutes

Mercury 57,000,000 miles 10.8 yrs 3 months 5 minutes

Venus 26,000,000 miles 5.4 yrs 1.5 months 2.5 minutes

Mars 49,000,000 miles 8.8 yrs 2.5 months 4 minutes

Jupiter 90,000,000 miles 74.25 yrs 1.75 yrs 35 minutes

Saturn 794,000,000 miles 150.4 yrs 3.6 yrs 1.2 hours

Uranus 1.7 billion miles 318.5 yrs 7.6 yrs 2.5 hours

Neptune 2.7 billion miles 513.2 yrs 12.25 yrs 4 hours

Pluto 3.6 billion miles 690.1 yrs 16.4 yrs 5.4 hours

Alpha Centauri 25.2 trillion miles 4.8 million yrs 114,155.2 yrs 4.2 yrs

(Nearest star after our Sun)

Sirius 50.4 trillion miles 9.6 million yrs 228,310.4 yrs 8.4 yrs