ISP 205, Section 3 Fall 1996 Hufnagel & Stein
Homework 4
Due: Tuesday 11 February 1997
Name: ________________________
Student Number: ______________
1. (5 Pts) Suppose you discover an alien planetary system in which a planet
circles a star once every two years at an average distance of 3 AU.
What is the mass of this star in units of the mass of the sun?
Remember that you can ignore the mass of the planet because it's so
much less than the mass of the star. [See the textbook section 5.5.]
M1[Mo] + M2[Mo] = A3[AUs] / P2[years]
M1 + (small: ignore) = A3 / P2
M1 = 33 / 22
M1 = 27 / 4
M1 = 6.8 solar masses (or use the symbol Mo)
If you use the period and average distance from the Sun in units of years
and AUs, the units of the resultant mass will automatically be in units of
solar masses.
2. (5 pts) Comet Hale-Bopp, now visible right before sunrise in the northeast
above the star Altair, has a period of 4200 years. Its eccentricity
is 0.995, meaning that its orbit is extremely non-circular. (A circle
has eccentricity of 0.000.) At its closest approach to the Sun, it
will be 0.9 AUs away from the Sun. What is its average distance
in AUs from the Sun during one complete orbit?
A3[AUs] = P2[years]
A = (P2)1/3
A = (42002)1/3
A = 260 AUs
The information about the eccentricity and the closest approach to the
Sun were not necessary, but were helpful to assure you that such a
large answer was reasonable.
3. (4 Pts) New comets are one object which amateur astronomers usually
discover before
professional astronomers are aware of them. List two pieces of observational
evidence that convince such observers (it could be you someday!)
that they have found a comet. Several websites where you can find this
information are URLs:
http://www.halebopp.com,
http://encke.jpl.nasa.gov/hale_bopp/discoverers.html
although there are many more websites on this comet, which may be the
brightest one you will ever see in your lifetime.
a. At first, it's a new object which looks like a star, but isn't on any of the starmaps.
b. As time passes, it starts to look more and more fuzzy.
OR It changes position against the background stars.
OR It gets systematically brighter as time passes.
OR As time passes, it grows a tail which points away from the Sun.
4. (3 Pts) If you were to travel to a planet which had the same mass
of the
Earth, but had half the radius of the Earth, you would find that the
force of gravity on the surface of this new planet, compared to that on
Earth, was
a) half as large.
b) twice as large.
c) four times larger.
d) one-quarter as large.
e) the same as Earth.
Since "force of gravity" is mentioned, this should bring to mind
the equation F=GMm/d2. Now, you are changing the original
force by halving the distance. So substitute the old distance "d" by
the new distance d/2. Notice that since d is squared, this means the force
changes by 2*2=4, NOT just 2. Simplify your new expression by multiplying
the top and bottom by 4, and compare this to the original expression.
F
start = GMm/d
2
F
new = GMm/(d/2)
2
F
new = GMm/(1/2)
2(d)
2
F
new = GMm/(1/4)(d)
2
F
new = 4 GMm/d
2 = 4 (F
start)
Updated: 1997.02.12 (Wednesday) 17:27:43 EST
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Visions of the Universe
Beth Hufnagel's home page, email:
hufnage4@pilot.msu.edu
Bob Stein's home page, email:
steinr@pilot.msu.edu