solar system models

Solar System Models A short video describing different solar system models - https://www.youtube.com/watch? v=qDHnWptz5Jo According to Aristotelian motion, the explanation for motion that was accepted by the church and scientists for thousands of years, there was no such force that existed that could move the Earth, so it must be stationary. It was believed that the Earth was the center of the universe and all ‘heavenly’ bodies moved around the Earth on perfect spheres. A solar system (or universe) model that places the Earth at the center is called geocentric . An observer can easily observe the stars, moon, sun and during most times the planets, and easily conclude that they could be orbiting the Earth, seeing as all objects rise in the east and set in the west. The sun, moon, and planets’ positions would change relative to the stars and, in general, moved in a prograde (eastward) sense relative to the background stars as one would expect for objects that were orbiting the Earth on different sized spheres. Careful observation of the planets however shows that they move in a retrograde (westward) path relative to the stars from time to time, which was not congruent with the simple model of objects orbiting the Earth on spheres. When Ptolemy created his version of the geocentric (Earth-centered) solar system, the only known planets were Mercury, Venus, Mars, Jupiter, and Saturn. The Ptolemaic model offered a complex model that accounted for this motion, though the model’s prediction capabilities were only accurate for short- term planetary motion. Ptolemaic Model Open the Ptolemaic System Simulator in the Solar System Models section of the NAAP labs application. The current planet shown orbiting the Earth is Mars in the simulation. In the Ptolemaic model, each planet moved along an epicycle , the smaller circular paths in this simulation. 1. The epicycle’s center moved along a deferent , the larger circular path in this simulation. The center of the planet’s uniform motion is called the equant , the green cross in the simulation. *The center of the deferent is the tiny purple circle in the simulation, the equant is the green cross* a. Is the deferent centered on the Earth? - No b. Is the equant centered on the Earth? - No 2. Click through the presets for Venus, Mars, Jupiter, and Saturn. a. Is the center of the deferent or the equant ever located at the EXACT center of the Earth for any of the planets? For venus yes 1

b. Is the center of the deferent or equant in the same location relative to the Earth for each planet? - For jupiter they are 2

- counter clockwise b. Which planet is moving at a faster speed, Mars or Earth? - earth is moving at a faster speed c. What is the shape of the orbital path each planet follows around the sun? - a circle d. Is the orbital shape described in part c the correct orbital shape? - No, because the planet moves retrograde so its not a complete circle 4

7. Looking at the zodiac strip in the bottom-left corner, you can observe how Mars and the sun move relative to the background stars that are close to the ecliptic. The motion of Mars relative to the background stars is generally prograde (eastward), but once in a while, Mars starts to move retrograde (westward). a. Watch the planets motions in the main simulation window while retrograde motion of Mars is occurring. What causes the retrograde motion of Mars? - Everytime the earth passes the planet, it slowly moves backwards b. Would this retrograde motion be observable from the surface of the Earth closer to nighttime or day time? - Yes it would, they are in a position for a period of time where it is visible *Look at the position of Mars relative to the sun from the Earth. Is Mars closer to the daytime side (the side facing the sun) or nighttime side of the Earth? * 8. Run the animation with the preset of Jupiter or Saturn (superior planets, like Mars). Is the cause of retrograde motion the same as it was for Mars? Yes, the same situation is happening, Jupiter is moving slower than Mars was, but when earth passes Jupiter, it moves in retrograde *Activity is continued on next page 5

Scaling the Solar System Now that we have explored solar system models, let’s take a moment to think about astronomical scales within our solar system. At the following link, you can see a scale model of the solar system on a map at any location you choose (you just need to know the latitude and longitude). The presets are set for the normal starting spot at EMU’s campus; we head eastward down the sidewalk toward Pierce Hall. https://thinkzone.wlonk.com/SS/SolarSystemModel.php?obj=Sun&dia=14cm&lat=42.246695 &lon=-83.624958&table=y&map=y At the following link, you can see a huge (7-mile diameter) scale solar system model created by some people in a dry lakebed in Nevada. https://www.youtube.com/watch?v=zR3Igc3Rhfg&t=24s When we meet on campus at EMU, we usually do a scale model walk of the solar system using a sun with a diameter of 14 cm. This is the approximate length of 7.5 penny diameters or the height of 140 stacked pennies. This is about 10,000,000,000 (10 billion!) times smaller than the actual sun diameter (1.39 x 10 9 m, 1.39 billion meters). 12. The actual diameter of each planet in the table below is given in billions of meters. With this tiny sun, what are the scaled sizes of each planet in our solar system? If a penny is about 1 mm thick (0.1 cm), how many pennies would we need to stack so the height of our stack matches the scaled diameter in our scaled solar system? Planet Actual Diameter (10 9 m) Scale Diameter (cm) Pennies Needed to Match Scale Diameter Mercury 0.00488 0.0488 ~0.5 Venus 0.0121 0.121 ~1.21 Earth 0.0127 0.127 ~1.27 Mars 0.00679 0.0679 ~0.7 Jupiter 0.142 1.42 ~14 7

Saturn 0.120 1.20 ~12 Uranus 0.0511 0.511 ~5.1 Neptune 0.0495 0.495 ~5.0 13. Now we will figure out the scaled distances in meters from our scaled down sun to each scaled down planet in meters and average step sizes. An average step size for most people is approximately 0.75 meters, so every meter is like taking a large step. Remember as you are calculating these values that the actual number of large steps you would need to take to get to each object from the sun is 10 billion times larger! Planet Actual Distance (10 9 m) Scale Distance (m) Steps from Last Object Total Steps From Sun Mercury 58 5.8 5.8 5.8 Venus 108 10.8 5.0 10.8 Earth 150 15 4.2 15 Mars 228 22.8 7.8 22.8 Jupiter 778 77.8 55 77.8 Saturn 1430 143 65.2 143 Uranus 2870 287 144 287 Neptune 4500 450 163 450 Remember each of the sizes and distances we calculated are actually 10 billion times larger! The scale of the solar system is HUGE compared to our daily Earth scales. 14. If you’re still not impressed, let’s take a quick look at how many large steps we might have to take to get to our closest neighboring star, Proxima Centauri (a dim red dwarf not visible to the naked eye), a short 4.243 lightyears away. This is a distance of 40,141,900 x 10 9 m (That’s over 40 million-billion meters away!). In our scaled solar system, how many large steps would you need to take to get to Proxima Centauri? *This would be like walking in the straightest line possible from Los Angeles, CA to Manchester, CT, see map at end of activity)! 4,014,190,000,000,000 (4 quadrillion) large steps! 8