Perihelion velocities--which of these are incorrect and why
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Perihelion velocities--which of these are incorrect and why

[From: ] [author: ] [Date: 11-12-11] [Hit: ]
Which of the following are incorrect, and why? (Velocities should be relative to the Sun,20, 30, and 50 km/s are incorrect and I had no idea how to approach this problem.......
This is another previous exam question that I've got marked down as incorrect, and I'm REALLY confused.

Four new comets whose perihelion distances = 1 AU have been discovered. However, each astronomer announces a different perihelion velocity as shown below. Which of the following are incorrect, and why? (Velocities should be relative to the Sun, NOT Earth's circular velocity of 30 km/s)
- 20 km/s
- 30 km/s
- 40 km/s
- 50 km/s

20, 30, and 50 km/s are incorrect and I had no idea how to approach this problem.

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50 km/s is beyond the solar system's escape velocity at 1 AU distance (which is 42.1 km/s). 20 km/s would make 1 AU the aphelion, not perihelion. 30 km/s would make the orbit nearly circular. No comet would survive very long in that orbit. In a nutshell, a comet's speed when reaching a perihelion of 1 AU would have to be significantly above 29.7 km/s, but below 42.1

Yes. An orbit will fall between two speeds at perigee: circular and escape velocity. Escape velocity is the square root of 2Gm/r. A circular orbital velocity is the square root of Gm/r. Or just take the escape velocity and divide by the square root of 2. G = gravitational constant (6.673 * 10^-11). m = mass. r = radius (from the sun). Make sure all units are in meters, kilograms, and seconds. The mass of the sun is 1.9891 * 10^30 kg. 1 AU is 1.496 * 10^11 meters.
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