Astro Homework 1 (2)
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School
University of Michigan *
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Course
435
Subject
Astronomy
Date
Apr 3, 2024
Type
Pages
3
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1.a) What do we mean by a habitable world? (10 pts)
A world that possesses the elements and conditions required for life is referred to as a habitable
world. This location provides the ideal environmental conditions for the emergence and survival
of life. Usually, when looking for a habitable planet, scientists search for an environment that
might support microbes. It is not necessary for there to be actual life for this place to be a
habitable world; in other words, the presence of actual life does not determine whether or not it
is a habitable world. The current planetary science context has provided substantial evidence
that the majority of stars in the universe may potentially be home to planets that support life,
which is why the search for additional habitable worlds is ongoing.
b) Does a habitable world necessarily have life? (10 pts)
It's not necessary for a habitable world to support life as we know it. When looking for habitable
planets, scientists mainly concentrate on locating regions with a chance of having microbial life.
Larger, more complex life forms may exist, but they are not the main factor used to determine
whether an area is habitable. A stable climate, liquid water, and other characteristics that are
favorable for the existence of life in some form define a world as being habitable. However, life
is not necessary for a world to be regarded as habitable, particularly complex organisms like
plants and animals.
2.a) What is apparent retrograde motion and why was it so difficult to explain with the
geocentric model? (10pts)
Apparent retrograde motion is when planets, which usually move eastward relative to the
constellations, reverse course and go backward. This was so difficult to explain with the
geocentric model because in the geocentric model, it was believed that planets moved only in
perfect circles meaning this directly contradicted this notion as it meant that the planets actually
weren't moving in a perfectly circular orbit. In an attempt to explain this phenomenon, keeping
with the geocentric model, the astronomer Ptolemy created the Ptolemaic model which stated
that the planets moved in small circles around the Earth that turned around larger circles.
b) What is its real explanation? (10 pts)
The real explanation is that the geocentric model was untrue. The earth in truth rotated around
the sun as suggested by the Greek scientist Aristarchus around the year 260 B.C.. This new
sun-centered model provided a new explanation for apparent retrograde motion in that it was
just simply an illusion. This illusion can be attributed to the fact that planets orbit around the sun
at different rates. For example, it takes the earth one year to complete a full orbit around the sun
whereas it takes Mars about 2 years to complete an orbit. Because of this, if we trace the lines
of sight between Earth and Mars from various points in their orbits reveals that, while the line of
sight generally moves in the direction of the stars, it shifts to the west when Earth is passing
Mars. Actually, Mars never alters its course. From our vantage point on Earth, it only seems to
reverse course creating the illusion of retrograde motion.
3. What is the difference between a hypothesis and a theory in science? (20 pts)
A hypothesis is a provisional link between theories and facts. It is commonly referred to as an
educated guess. It is a starting point for further investigation. A proven hypothesis becomes a
theory and/or a law, whereas a disproven hypothesis can be proven and changed with a revised
experiment. A theory is a well-established and extensively tested model that makes consistent
predictions that have been confirmed by numerous experiments. A theory cannot exist unless it
is supported by a large and compelling body of evidence. Future observations may contradict a
theory's predictions, so it can never be proven true. Scientific theories, on the other hand, are
only discarded or replaced if superior explanations emerge that better align with the available
evidence.
4.a) How does quintupling the distance between two objects affect the gravitational force
between them? (6 pts)
The strength of gravity between two objects decreases with the square of the distance between
their centers, according to Newton's Universal Law of Gravitation. In this case, quintupling the
distance between two objects reduces the force of gravity between them by a factor of 5^2 or
25. The force of gravity weakens significantly as objects move further apart. The inverse square
law is used to demonstrate this relationship.
b) Suppose the Sun were somehow replaced by a star with three times as much mass.
What would happen to the gravitational force between Earth and the Sun? (7 pts)
The strength of the gravitational force attracting any two objects is directly proportional to the
product of their masses, according to Newton's Universal Law of Gravitation. In this case, if the
sun were to be replaced by a star three times larger in mass, the gravitational force between the
Earth and the new sun would increase by a factor of 3.
c) Suppose Earth were moved to one-fourth of its current distance from the Sun. What
would happen to the gravitational force between Earth and the Sun? (7 pts)
Holding everything else constant, Newton's Universal Law of Gravitation, specifically the inverse
square law, would increase the gravitational force between Earth and the Sun by a factor of 16.
5. Comet Encke orbits the Sun every 3.3 years.
a) Find its semi-major axis distance in kilometers. (6 pts)
Kepler’s 3rd law p^2 = a^3
(3.3)^2 = a^3
10.89 = a^3
(10.89)^⅓ = a
a = 2.2165 AU
1 AU = 1.5 × 10^8 km
Semi major axis is 331583680 km
b) Encke's perihelion distance is about 50 million kilometers from the Sun. What is its
aphelion distance? Answer in kilometers. (8 pts)
Semi-major axis = (aphelion + perihelion) / 2
(331583680) = (aphelion + 50000000)/2
2(331583680) = aphelion + 50000000
663167360 - 50000000 = aphelion
aphelion = 613167360 km
c) Does Encke spend most of its time near its perihelion distance, near is aphelion
distance, or halfway in between? Explain. (6 pts)
Encke spends the majority of its time close to its perihelion distance. According to Kepler's
second law of planetary motion, a planet or comet sweeps out equal areas in equal times. When
a celestial body is closer to the Sun (at perihelion), it moves faster in its orbit, covering more
ground in less time. As a result, it spends less time in its outermost orbit (aphelion). Encke's
orbit is quite elongated, so it moves quickly near perihelion and spends more time in that region,
making it the most frequently located point in its orbit.
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