Here is the data:
MERCURY
Aphelion distance: 69,817,079 km 0.466 AU
Perihelion distance: 46,001,272 km 0.307 AU
Semi-major axis: 57,909,176 km 0.387 AU
Orbital period: 87.969 days (0.240 years)
Orbital circumference: 360,000,000 km (2.406 AU)
Avg. orbital speed: 47.36 km/s
Max. orbital speed: 58.98 km/s
Min. orbital speed: 38.86 km/s
VENUS
Aphelion distance: 108,941,849 km 0.728 AU
Perihelion distance: 107,476,002 km 0.718 AU
Semi-major axis: 108,208,926 km 0.723 AU
Orbital circumference: 680,000,000 km 4.545 AU
Orbital period: 224.700 days (0.615 years)
Avg. orbital speed: 35.020 km/s
Max. orbital speed: 35.259 km/s
Min. orbital speed: 34.784 km/s
EARTH
Aphelion distance: 152,097,701 km (1.016 AU)
Perihelion distance: 147,098,074 km (0.983 AU)
Semi-major axis: 149,597,887.5 km (1.000 AU)
Orbital circumference: 924,375,700 km (6.179 AU)
Orbital period: 1 year
Avg. orbital speed: 29.783 km/s (107,218 km/h)
Max. orbital speed: 30.287 km/s (109,033 km/h)
Min. orbital speed: 29.291 km/s (105,448 km/h)
MARS
Aphelion distance: 249,228,730 km 1.665 AU
Perihelion distance: 206,644,545 km 1.381 AU
Semi-major axis: 227,936,637 km 1.523 AU
Orbital circumference: 1,429,000,000 km 9.553 AU
Orbital period: 686.9600 days (1.8808 years)
Avg. orbital speed: 24.077 km/s (53,859 mi/h)
Max. orbital speed: 26.499 km/s (59,277 mi/h)
Min. orbital speed: 21.972 km/s (49,150 mi/h)
JUPITER
Aphelion distance: 816,081,455 km 5.455 AU
Perihelion distance: 740,742,598 km 4.951 AU
Semi-major axis: 778,412,027 km 5.203 AU
Orbital circumference: 4.888 Tm 32.675 AU
Orbital period: 4,333.2867 days (11.86 years)
Avg. orbital speed: 13.056 km/s
Max. orbital speed: 13.712 km/s
Min. orbital speed: 12.446 km/s
SATURN
Aphelion distance: 1,503,983,449 km 10.053 AU
Perihelion distance: 1,349,467,375 km 9.020 AU
Semi-major axis: 1,426,725,413 km 9.537 AU
Orbital circumference: 8.958 Tm 59.879 AU
Orbital period: 10,756.1995 days (29.45 years)
Avg. orbital speed: 9.639 km/s
Max. orbital speed: 10.183 km/s
Min. orbital speed: 9.137 km/s
URANUS
Aphelion distance: 3,006,389,405 km 20.096 AU
Perihelion distance: 2,735,555,035 km 18.286 AU
Semi-major axis: 2,870,972,220 km 19.191 AU
Orbital circumference: 18.029 Tm 120.515 AU
Orbital period: 30,707.4896 days (84.07 years)
Avg. orbital speed: 6.795 km/s
Max. orbital speed: 7.128 km/s
Min. orbital speed: 6.486 km/s
NEPTUNE
Aphelion distance: 4,536,874,325 km 30.327 AU
Perihelion distance: 4,459,631,496 km 29.810 AU
Semi-major axis: 4,498,252,900 km 30.068 AU
Orbital circumference: 28.263 Tm 188.925 AU
Orbital period: 60,223.3528 days (164.88 years)
Avg. orbital speed: 5.432 km/s
Max. orbital speed: 5.479 km/s
Min. orbital speed: 5.385 km/s
SPOT THE TRENDS
The bigger the orbit, the slower the orbital speed.
The bigger the orbit, the longer the planetary year, both because the orbital speed is slower and because the orbital circumference is greater (further to go and slower getting there).
2007-01-12 16:12:01
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answer #1
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answered by Anonymous
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Let S be the mass of the Sun,
P be the mass of the planet
G is Newton's gravitational constant
v is the velocity of the planet
r is the distance of the planet from the Sun
So the force of gravity on the planet is
-GSP/(r^2)
This is Newton's law of gravity. The force is negative because it is inwards.
The "centrifugal force" on the planet (in a circular orbit) is
P(v^2)/r
These two forces must balance, so they add to zero:
P(v^2)/r - GSP/(r^2) = 0
Solve for v:
v = sqrt(GS/r)
where sqrt(x) is the square root.
So the velocity varies inversely as the square root of r.
For example, an asteroid or planet 4 times as far from the Sun as the Earth would be moving half as fast as the Earth. And the size of its orbit is 4 times as big, so its orbital period is 8 times as long, or 8 years.
Note that this does not depend on the mass of the planet.
Note that if you know G, r, and v you can solve for S, the mass of the Sun.
2007-01-12 01:53:32
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answer #2
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answered by cosmo 7
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