Download Astronomy 10 Quiz 2 SOLUTIONS

Astronomy 10
Quiz 2
SOLUTIONS
Some useful equations:
P 2 ∝ a3
P2 =
F = ma
4π 2
3
G(M +m) a
F =
GM m
r2
1. (10 points) During which two phases of the lunar cycle are tides strongest (ie. high tides
are higher than usual and low tides are lower than usual)? Draw a diagram of one of these
lunar phases, labelling each object and the lunar phase you are drawing.
Tides are strongest when the Sun and the Moon lie in the same plane with respect
to the Earth so that they amplify each other. This occurs during full moon and
new moon, illustrated below.
Full Moon
Earth
Sun
M
New Moon
Earth
M
Sun
2. (10 points) Write down the formula for the acceleration due to gravity (g) you feel standing
on the surface of the Earth in terms of any of the following constants you think you need:
G, MEarth , Mme , MSun , MM oon , REarth , RM oon , REarth−to−Sun , REarth−to−M oon .
Start with the force of gravity you feel standing on the surface of the Earth:
GMEarth Mme
Fg =
2
REarth
We are looking for the acceleration due to gravity, so set this expression equal to
mass times acceleration (Newton’s second law). The mass in this part is simply
Mme since we are talking about you standing on the surface of the Earth, and the
acceleration you feel.
GMEarth Mme
Mme ag =
2
REarth
The Mme cancels on each side, leaving us with:
g = ag =
1
GMEarth
2
REarth
3. (10 points)Which of Kepler’s laws enables us to use observations of Charon to calculate
the mass of Pluto? Explain your answer: what properties of Charon’s orbit do you need to
observe? (Recall that the mass of Charon is much smaller than the mass of Pluto)
Newton’s version of Kepler’s third law:
P2 =
4π 2
a3
G(M + m)
We can use this equation to describe Charon’s orbit around Pluto. Since the
mass of Charon is much less than the mass of Pluto, MP l + MCh ≈ MP l , so
2
PCh
=
4π 2
4π 2 3
a3Ch ≈
a
G(MP l + MCh )
GMP l Ch
Therefore, if we observe the period (P) and semi-major axis (a) of Charon’s orbit,
we can calculate the mass of Pluto using the equation above.
4. (8 points) For each of the following, write down which planet is being described (each planet
will match ONE fact).
• This planet is occasionally obscured by global dust storms. Mars
• The tidal forces of this planet are responsible for the extreme volcanism on Io. Jupiter
• This planet’s rotation axis is extremely tilted with respect to its orbital axis. Uranus
• This planet’s thick atmosphere creates a runaway greenhouse effect. Venus
• This is the only planet with plate tectonics. Earth
• The density of this planet is low enough that it would float in water if you could find a
bathtub big enough! Saturn
• Due to the tidal forces of the Sun, this planet’s rotation period is exactly 2/3 of it’s
orbital period. Mercury
• Before this planet was observed, its presence was predicted by careful analysis of the
orbits of the other planets. Neptune
5. (2 points) Which two elements are the Jovian planets made up of (mostly)?
Hydrogen and Helium
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