Orbit
The effects of other gravitating bodies can be very large. For example, the orbit of the Moon cannot be in any way accurately described without allowing for the action of the Sun's gravity as well as the Earth's.
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Earth orbits
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Scaling in gravity
The gravitational constant G is measured to be:
- (6.6742 ± 0.001) × 10−11 N·m²/kg²
- (6.6742 ± 0.001) × 10−11 m³/(kg·s²)
- (6.6742 ± 0.001) × 10−11 (kg/m³)-1s-2.
Thus the constant has dimension density-1 time-2. This corresponds to the following properties.
Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the earth.
When all densities are multiplied by four, orbits are the same, but with orbital velocities doubled.
When all densities are multiplied by four, and all sizes are halved, orbits are similar, with the same orbital velocities.
These properties are illustrated in the formula
for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density σ, where T is the orbital period.
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Role in atomic theory
When atomic structure was first probed experimentally early in the twentieth century, an early picture of the atom portrayed it as a miniature solar system bound by the coulomb force rather than by gravity. This was inconsistent with electrodynamics and the model was progressively refined as quantum theory evolved, but there is a legacy of the picture in the term orbital for the wave function of an energetically bound electron state.
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See also
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References
- Abell, Morrison, and Wolff (1987). Exploration of the Universe, fifth edition, Saunders College Publishing.
- ^ Stern, David (3-24-05). (20) Newton's theory of "Universal Gravitation" (en). Retrieved on 2008-06-01.
- ^ Stern, David (3-21-05). Kepler's Three Laws of Planetary Motion: An Overview for Science teachers (en). Retrieved on 2008-06-01.
- ^ Jones, Andrew. Kepler's Laws of Planetary Motion (en). about.com. Retrieved on 2008-06-01.
- ^ Basics of Spaceflight a JPL primer used by its employees.
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External links
- Understand orbits using direct manipulation
- An on-line orbit plotter: http://www.bridgewater.edu/~rbowman/ISAW/PlanetOrbit.html
- Orbital Mechanics (Rocket and Space Technology)
- The NOAA page on Climate Forcing Data includes (calculated) data on Earth orbit variations over the last 50 million years and for the coming 20 million years
- The orbital simulations by Varadi, Ghil and Runnegar (2003) provide another, slightly different series for Earth orbit eccentricity, and also a series for orbital inclination. Orbits for the other planets were also calculated[1], but only the eccentricity data for Earth and Mercury are available online.
- Java simulation on orbital motion
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