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

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.

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)

Velocity 7.189×103 km/h220 km/s km/h km/s 6.52 km/h km/s 1,674.4 km/h km/s km/h km/s 45,300 km/h 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)

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

Obliquity (axis)

ORBITS AND TRAJECTORIES

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

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

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

(measured in 24 hour days) Uranus Neptune day year day year

Distances From Solar Center

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

For expressing the velocity relative to period: :Escape Velocity

Retrieved from: Kepler's Laws of Planetary Motion

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

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

Computer Model Aids and Sources

Universe Sandbox 3.0 for PC emulates programmable scenarios

Demonstration of Universe Sandbox 3.0 on personal computer

(Sources for images in order of appearance) Sizes Speed Speed chart Obliquity Kepler Equation Mercury Venus Earth and Mars Jupiter Saturn Urnaus Neptune

Equations Kepler’s laws Oort cloud Kuiper belt Computer Models Universe Sandbox (sources continued) “Music of the Spheres“ by Chase Nordquist sp2015