PROBLEM SET #4
DUE THURSDAY APRIL 17
As you know Hale-Bopp is putting on a very good show. On April
Fool's day it made its closest approach to the sun at a distance of .913
AU (137 million km) moving at a speed of 158,000 km/hr or 44 km/sec. On
March 22 it approached closest to the earth at a distance of 1.3 AU (197
million km). On May 6 it will cross the ecliptic, where the sun will be on
June 4. On June 6 it will be about a degree north of Betelgeuse.
During the first weeks of April it should be at its brightest (-.5
magnitudes) outshining Capella in Auriga. During early may it will pass
through Perseus, reaching within 1-2 degrees of Algol, the Demon Star, on
approximately April 9-11. Its tail, which may be 20-30 degrees long, will
brush across that "dangerous" star, the awful eye of Medusa. Algol will
have two eclipses on April 5 and April 8. On April 10, there will be a
spectacular sight with the slender crescent moon will be just below
Aldebaran and the comet will lie off to the right, near Algol.
When recently measured at Lowell Observatory Hale-Bopp was
releasing 400 metric tons of dust per second and 27,000 gallons of
water/sec. The water lost by the comet was equal to a chunk of ice 13 feet
on a side per second! Its icy nucleus appears to be 30 km across, making
it 2-3 times larger than Halley. It is producing 200 times more dust than
Halley. Its nucleus is tumbling with a period of approximately 12 hours.
Excellent photos of the comet have been recently taken by Keith
Gleason at Sommers Bausch Observatory and posted on the Observatory's web
Using his two photos of February 18 and March 28, sketch the comet
on the SC001 Constellation Chart on those two days. Pay particular
attention to the lengths of its two tails on March 28.
Carefully sketch the path of the comet between February 18 and
June 6 and keep it for future reference.
- HOW MANY DEGREES HAS IT MOVED BETWEEN FEB 18 AND MARCH 28?
- WHAT WAS THE AVERAGE ANGULAR SPEED OF THE COMET (DEGREES/DAY)
DURING THAT PERIOD?
- CONVERT DEGREES TO DISTANCE USING THE SLENDER TRIANGLE APPROXIMATION
AND ESTIMATE ITS SPEED IN KM/DAY. (You may assume the comet is moving in
the plane of the sky)
- BY MEASURING YOUR DRAWING OF THE COMET ON MARCH 28, ESTIMATE THE
LENGTH OF THE ION TAIL IN KM. (Again you may assume the tail is in the
plane of the sky)
- WHY IS ITS DUST TAIL SHORTER THAN ITS ION TAIL?
(HINT: CONSIDER INERTIAL MASS)
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