5. Building the Model Before we go outside, we need to make some conversions. Fi

Question

5. Building the Model Before we go outside, we need to make some conversions. First, let’s scale it down so that one Astronomical Unit is equal to 2 feet, 6 inches or 76.2 centimeters. Multiply it all out. Just do either feet/inches or meters/centimeters depending on which kind of measuring sticks you’ll be using outdoors. When you’re done, take this outdoors and mark it out with the surveyor flags on the football field! The instructor will check your calculations with a tape measure which has all the markings for all the planets. You’ll be graded on how close you get to those markings.

Object _____ Average Distance in AU from the Sun ________Convert to feet and inches _______Convert to cm or meters

Mercury

Venus

Earth ________________ 2 feet, 6 inches ________________76.2 cm or 0.762 m

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Voyager 2

Sirius

How far away is Sirius in this model, and what is a landmark for that location?

Explanation / Answer

We know that one Astronomical unit is the distance between earth and sun. It is given that our scale is 1AU = 2 feet 6 inches = 2.5 feet. So what we need to do is find out the distance of each object from the sun in AU and multiply it by 2.5 to get the scaled distance in feet. Now, 1 feet is 12 inches. So multiply the decimal part by (1/12) to get it in inches.

It is also given that 1 AU = 76.2 cm so to convert the distance of the object from sun in AU to the scaled distance multiply it by 76.2. To convert cm to meters multiply by 102.

These are done in the table below, distance of each object from the sun in AU can be found out from any astronomical chart.

Sirius is 414431.226 meters away, that is 414.4 km away. It cannot be included in a football field.

Object Average distance in Au from sun Distance in feet and inches Distance in cm or meters Mercury 0.39 0.975 ft = 11.7 inches 29.718 cm = 0.297 m Venus 0.723 1 feet 9.69 inches 55.0926 cm = 0.55 m Earth 1 2 feet 6 inches 76.2 cm = 0.762 m Mars 1.524 3 feet 9.72 inches 116.1288 cm = 1.16 m Jupiter 5.203 13 feet 0.09 inches 396.4686 cm = 3.96 m Saturn 9.539 23 feet 11.79 inches 726.8718 cm = 7.268 m Uranus 19.18 47 feet 11.4 inches 1461.516 cm = 14.615 m Neptune 30.06 75 feet 1.8 inches 2290.572 cm = 22.9 m Pluto 39.53 98 feet 9.9 inches 3012.186 cm = 30.12 m Voyager 2 118.69 296 feet 8.7 inches 9044.178 cm = 90.44 m Sirius 543873 1359682 feet 6 inches 41443122.6 cm = 414431.226 m

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