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? b. Is the equant centered on the Earth? 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? b. Is the center of the deferent or equant in the same location relative to the Earth for each planet?

3. Run the animation. a. Does the sun orbit in a clockwise or counterclockwise direction around the Earth? b. What is the shape of the orbital path of the sun in the Ptolemaic system? c. Are the motions described in parts a and b consistent with observations of the sun? * Is the sun’s motion prograde? Does the sun move retrograde (westward) through the zodiac constellations? 4. Set the preset for Venus and run the animation. Does Venus exhibit retrograde motion? 5. Run the animation for different planets. Is this general motion of each planet in the Ptolemaic model simple or complicated? * Is the model more complicated than or simpler than the heliocentric Copernican model (explained below)? While the Ptolemaic model was able to resolve the issue of retrograde motion that challenged the accepted geocentric model, the complexity of the model made predictions inaccurate after only a short period and the model had to be applied slightly differently to each planet. Copernicus believed the sun to be a more divine object than the Earth and figured it was a more logical object for the universe to be centered on. His obsession with circles, like many at the time believing a circle to be a perfect shape, made him hate the Ptolemaic model since each equant was located in a different position relative to the Earth. He created the much simpler model that more accurately predicted the motion of planets, the heliocentric (sun-centered) model. Today, we understand that the heliocentric model is the correct model, even though some slight alterations need to be made to make the motion more accurate to observation. Superior Planets in the Heliocentric Model 6. Close the Ptolemaic System Simulator and open the Planetary Configurations Simulator . Select the Mars preset in the radius of target planet’s orbit . Run the simulation. a. Do the planets orbit in a clockwise or counterclockwise direction? b. Which planet is moving at a faster speed, Mars or Earth? c. What is the shape of the orbital path each planet follows around the sun? d. Is the orbital shape described in part c the correct orbital shape?

Inferior Planets in Heliocentric Model 9. Select the Venus preset in the radius of target planet’s orbit . Run the simulation. a. Do the planets orbit in a clockwise or counterclockwise direction? b. Which planet is moving at a faster speed, Venus or Earth? c. What is the shape of the orbital path each planet follows around the sun? d. Is the orbital shape described in part c the correct orbital shape? 10. Looking at the zodiac strip in the bottom-left corner you can observe how Venus and the sun move relative to the background stars that are close to the ecliptic. The motion of Venus relative to the background stars is generally prograde (eastward), but once in a while, Venus starts to move retrograde (westward). a. Watch the planets motions in the main simulation window while retrograde motion of Venus is occurring. What causes retrograde motion of Venus? b. Would this retrograde motion be observable from the surface of the Earth closer to nighttime or day time? *Look at the position of Venus relative to the sun from the Earth. Is Venus closer to the daytime side (the side facing the sun) or nighttime side of the Earth? * 11. Run the animation with the preset of Mercury (an inferior planet, like Venus). Is the cause of retrograde motion the same as it was for Venus?

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 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.