1. The Orbits, Sizes, Rotations, Velocities, and Trajectories of our Local Planets and of our Star Chase Nordquist MUSIC OF THE SPHERES

2. The applications of Mathematics have allowed our contemporary scientists to calculate and organize the physical properties of our celestial neighbors with great precision. The following figures may have been unknown to our ancestors but the importance of the paths and positions of objects in the sky were useful for knowing when to sow and reap, or how they might influence character. Despite the shift, these entities have perennially engendered awe and wonder.

3. SIZE Diameter, Density, and mass Sun: Diameter (1.39 M km), Density (1.41 g/cm^3), Mass (1.989 E30 kg) Mercury: Diameter (4880 km), Density (5.43 g/cm^3), Mass (328.5 E21 kg) Venus: Diameter (12104 km), Density (5.24 g/cm^3), Mass (4.867 E24 kg) Earth: Diameter (12742 km), Density (5.51 g/cm^3), Mass (5.972 E24 kg) Mars: Diameter (6788 km), Density (3.92 g/cm^3), Mass (639 E21 kg) Jupiter: Diameter (139822), Density (1.33 g/cm^3), Mass (1.898 E27 kg) Saturn: Diameter (116464), Density (.69 g/cm^3), Mass (568.3 E24 kg) Uranus: Diameter (50724), Density (1.27 g/cm^3), Mass (86.81 E24 kg) Neptune: Diameter (49248), Density (1.64 g/cm^3), Mass (102.4 E24 kg)

4. Velocity 7.189×103 km/h220 km/s 10.892 km/h 47.362 km/s 6.52 km/h 35.02 km/s 1,674.4 km/h 29.78 km/s 868.22 km/h 24.077 km/s 45,300 km/h 13.07 km/s 35,500 km/h 9.69 km/s 9,320 km/h 6.80 km/s 9660 km/h 5.43 km/s Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Orbital Speed Equatorial Rotational Speed (relative to galactic center)

6. ROTATIONS Sun: 7.25 ˚ 25.6d Mercury: 2.04 ˚ 58.55d Venus: 177.3 ˚ 116.7d (retrograde spin) Earth: 23.5 ˚ 1d (24h) Mars: 25 ˚ 1d +40min Jupiter: 3.13 ˚ 9h +56min Saturn: 26.7 ˚ 10h +39min Uranus 97.77 ˚ 17h +14min Neptune: 28.32 ˚ 16h +16min Obliquity Period of Equatorial Rotation (in Earth days/time)(perpendicular to ecliptic)

7. Obliquity (axis)

8. ORBITS AND TRAJECTORIES

9. Mercury Venus 88 day year 225 day year (measured in 24 hour days)

10. Earth Mars 365.25 day year 687 day year (measured in 24 hour days)

11. Jupiter Saturn (measured in 24 hour days) 4368 day year10585 day year

12. (measured in 24 hour days) Uranus Neptune 30660 day year 60225 day year

13. Distances From Solar Center

14. Equations for calculation of periods of solar orbit Kepler's Equation for approximating planetary trajectories Contributing Equations

15. For expressing the velocity relative to period: :Escape Velocity

16. Retrieved from: http://astro.unl.edu/classaction/outlines/renaissance/slide1.html Kepler's Laws of Planetary Motion

17. Other local features of interest The Kuiper Belt encircles our inner solar system Pluto is now described as a Kuiper Belt object The Kuiper is mostly comprised of ice an rock particles Renegade moons and planetoids may also exist in the belt

18. The Oort Cloud encompasses our entire solar system beyond the Kuiper Belt It acts like a boundary of ice and debris Oort Cloud

19. Computer Model Aids and Sources

20. Universe Sandbox 3.0 for PC emulates programmable scenarios

21. Demonstration of Universe Sandbox 3.0 on personal computer

22. (Sources for images in order of appearance) Sizes http://exchange.smarttech.com/details?id=4b919913-ddb8-4297-bd37-f704782afce1 Speed http://physicslens.com/page/2/ Speed chart http://www.ritholtz.com/blog/2012/10/interactive-visualization-of-simultaneous-planet-orbits/orbit Obliquity http://www.astronoo.com/en/articles/axial-tilt-planets.html Kepler Equation http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion Mercury http://songshuhui.net/archives/category/major/astro/page/8 Venus http://astrobob.areavoices.com/2012/06/01/venus-speed-dates-mercury-en-route-to-transit/ Earth and Mars http://www.sinequanonthebook.com/Gravity4.html Jupiter http://www.berkeley.edu/news/media/releases/2001/08/15_dippr.html Saturn http://www.slate.com/blogs/bad_astronomy/2009/03/17/incredible_quadruple_transit_on_saturn.htm Urnaus http://wisp.physics.wisc.edu/astro104/lecture24/lec24_print.html Neptune http://spaces.imperial.edu/russell.lavery/Ast100/Lectures/Ast100Topic12.html

23. Equations http://www.slideshare.net/GregoryTewksbury/math-in-space-planetary-orbits Kepler’s laws http://astro.unl.edu/classaction/outlines/renaissance/slide1.html Oort cloud http://wagner.edu/hawktalk/goddards-testing-facilities-where-we-build-satellites-then-try-to-break-them/ Kuiper belt http://astronomie-handeloh.de/projekte/planeten/pluto.htm Computer Models http://www.codeincodeblock.com/2012/06/3d-solar-system-simulation-graphics.html Universe Sandbox http://www.jasonloch.net/2011/06/universe-sandbox/ (sources continued) “Music of the Spheres“ by Chase Nordquist sp2015