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.
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.
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.