HOMEWORK #2 EARTH-MOON SCALE MODEL Introduction The solar system is big. Really big. But what does that statement really tell you? One of the goals of this course is to have each of you develop some feel for the size of the solar system and the objects in it. To do that requires more than just numbers. When I say tab the two objects are a mile apart, most of us can comprehend that in everyday terms. We know how long it would take us to walk or drive that distance. But what does it mean to us when I say that Jupiter is 7.78 x 108 kilometers away? Since we do not have everyday experience with such distances, the number becomes mostly meaningless. One way to start caps to comprehend such distances is to place them into a more familiar scale. This is similar to how road maps of Oklahoma or the US are scaled down so that 1 inch is equivalent to 50 miles (or something like that). Your first problem in this homework is to generate a scale nift for the Earth-Moon system. The Data For the first part of this exercise, we are going to simply use the length of your arm as the scale distance for our model. To do this, you can measure the length of your arm, or you can just assume that it's about 30 inches from your shoulder to the tip of your middle finger. Now, assume that the center of the Earth is at the very tip of your middle finger, and the center of the Moon is right at your shoulder. Using this scale, we will convert the various distances and sizes to positions along your arm (starting at your finergtip). For instance in our model, we know that the distance from the Earth to the Moon is equivalent to 30 inches or the length of your arm). However, the distance to a geosynchronous satellite orbit is 33,000 km, so in our scaled model, the distance to a geosynchronous satellite orbit would be 33,000 km x (30 inches), or 2.6 inches. 2.6 inches is about the length from the tip of my middle finger to my second knuckle, so in my scaled model, the Earth would be at the tip of my middle finger, the Moon would be at my shoulder, and a geosynchronous satellite would be located on my knuckle. Using this method and the data given below, fill out the table on the next page. Earth-Moon Data Earth-Moon Distance: 384,000 km Radius of the Earth: 6378 km Radius of the Moon: 1738 km Typical Space Shuttle Orbit: 400 km above Earth's surface Geosynchronous Satellite Orbit: 33,000 km Distance to Asteroid 2004 FH on 3/18/2004 50,000 km Distance to Asteroid Apophis on 4/13/20291 38,400 km Length of Oklahoma 747 km ASTR 1523 2- 1 ASTRONOMY1) One example explicitly showing how you transformed the size from the data to your scale. Show all of your math.) sh fn Approximate Scaled Size Position Relative to Your Fingertip Earth-Moon Distance Radius of the Earth Radius of the Moon Typical Space Shuttle Orbit Geosynchronous Satellite Orbit Distance to Asteroid 2004 FH Distance to Asteroid Apophis Length of Oklahoma ASTR 1523 2 - 2 ASTRONOMY