HW4
docx
keyboard_arrow_up
School
New York University *
*We aren’t endorsed by this school
Course
101
Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
3
Uploaded by PrivateValor12642
Hannah Davis-Jacobs
Homework 4:
2. The Ptolemaic system depicts the universe and the planetary movements using secondary
circles termed as epicycles. Every planet is linked to its respective epicycle, which in turn
revolves around the Earth on a primary circle called a deferent. The apparent backward motion,
or retrograde motion, of the planets can be explained by the movement of these planets on
their epicycles.
6. Kepler's First Law posits that the trajectory of planets around the Sun is elliptical, with the
Sun positioned at one of the two foci. Consequently, as planets traverse this ellipse, their
distance from the Sun varies since the Sun isn't centrally located. Kepler's Second Law asserts
that as planets move, they sweep out equal areas in equal time intervals. This implies that when
planets are nearer the Sun, they move more swiftly. Finally, Kepler’s Third Law indicates that the
farther a planet's orbit is from the Sun, the slower its average velocity will be. Formulated
mathematically, the cube of the average distance from the Sun is proportional to the square of
the orbital period.
8. The Moon undergoes eight main phases, determined by the proportion of its sunlit half
visible from Earth, a result of its orbit around our planet. Over approximately 28 days, it
transitions through these phases, initiating with the new moon where the illuminated part isn't
directed towards Earth. Since we consistently view one face of the Moon, what varies is its
illumination based on its position relative to the Sun. Eclipses don't happen at every new and
full moon due to the Moon's orbit not being perfectly aligned with Earth's orbital plane; it's
tilted by about 5 degrees. For a lunar eclipse, the requirements are a full moon, its orbit
crossing 5 degrees above or below Earth's orbital plane, and Earth being directly between the
Sun and the Moon. In the case of a solar eclipse, the Moon should be directly between the Sun
and Earth, casting its shadow on a specific area on Earth.
9. Eclipses transpire when the Sun, Moon, and Earth align in a specific order. In a lunar eclipse,
the Earth positions itself between the Sun and the Moon. Conversely, during a solar eclipse, the
Moon intercepts between the Sun and Earth.
2. How would you calculate the distance to Mars in astronomical units, given an orbital period
of 1.88 years?
If
T
Mars
=
1.88
, then according to Kepler’s third law (T^2=R^3). Simplifying, cube root of
3.5344=R in AU. This is equal to 1.524 AU.
3. Calculate the orbital period of the space shuttle in an orbit 500 km above Earth’s surface.
T = √(4pi^2)(r^3)/(GM1)
T = √(4pi^2)((500+6371)*10^3)^3)/(GM1) : 10^3 is to put km to m, 6371 km is radius of
Earth
T = √(4pi^2)((6871)*10^3)^3/(6.67*10^-11)(5.97*10^24) : substitute M1 + G
T = √(39.4784176044)(6,871,000)^3/3.98 * 10^14
T = √(1.2806179 *10^22)/(3.98 * 10^14)
T = √32176329.1457
T = 5672.42 seconds or 94.54 minutes or
1.58 hours
4.
Calculate the escape velocity for Mars if its mass = 0.12MEarth and the radius = 0.55REarth.
V escape = (2GM/R)^½
V escape = [(2G)(0.12MEarth)/(0.55REarth)^½
V escape = (0.436 G MEarth/REarth)^½
V escape = [(0.44)(6.67*10^-11)(6 *10^24 kg)/(6.4 *10^6)]^½
V escape = (27.29 *10^6 m^2/s^2)^½
V escape =
5223.6 m/s
5.
Using Newton’s Law, Equation 3.5, Calculate the force that the moon exerts on your body.
Given: Moon mass, (m1) = 7.35 × 1022 kg, your mass in kg (1 kg = 2.2 lbs.), and Moon radius
= 1.74 × 106 m. Does this exercise prove that celestial objects have very little effect on humans
on Earth? (Astrology is a pseudoscience, right?)
F = G(m1m2)/r^2
My mass in kg; 72.5748 kg
F = 6.67*10^-11N*m^2/kg^2(7.35 × 10^22 kg)(72.5748 kg)/(386212282 m)^2
F = 0.00238532115 Newtons or
2.38 *10^-3 N
Given that the force exerted by the moon on a human body (using the given parameters) is just
2.38 *10^-3 N
, it is indeed minuscule. This small force demonstrates that celestial objects like
the moon have a negligible gravitational effect on individual humans on Earth.
As for astrology, it's distinct from the science of astronomy. While astronomy is the scientific
study of celestial bodies and the universe, astrology is a belief system that suggests that the
positions and movements of celestial bodies can have a direct influence on human affairs and
natural phenomena. In the scientific community, astrology is generally regarded as a
pseudoscience because its principles and practices aren't based on empirical scientific evidence.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help