Homework # 2 1. For each of the following, make a sketch showing positions of the Sun, Earth & Moon. Name the lunar phase seen in College Park. & give the approx. time the Moon sets. [9 pts.]
a) The Moon rises at noon. Midway between New (rises--sunrise) & full (rises--sunset)
E S First Quarter Sets at midnight
b) On this day a solar eclipse occurs for people living in Peking, China.
Phase of the moon is the same everywhere on Earth since over 24 hours the moon moves just a little bit. A new moon is required for a solar eclipse.
E M S New Moon Moon sets at 6 PM with sun.
c) You see the Moon rising in the eastern sky on your way to your 3 PM class.
This means it is rising near 3 PM. Full moon rises at 6 PM so this would be the phase just before.
Waxing gibbous Moon sets at 3 AM.
d) You see the Moon with bright earthshine in the eastern sky.
In order for earthshine, you need a crescent moon, which is near the Sun. If the moon is in the east rising, the sun must be almost ready to rise, so it is 3-5 AM. It sets 12 hours later.
M Waning crescent Moon sets between 3-5 PM.
e) You see the Moon with bright earthshine in the western sky.
In order for earthshine, you need a crescent moon, which is near the Sun. If it is in the west, the Sun just set and the moon will set soon between 7-9 PM.
Waxing crescent Moon sets between 7- 9 PM
f) Approximately two days have passed after a full moon occurred.
Waning gibbous follows full moon.
E S Moon sets at 7:40 AM since full moon sets at 6 AM and it sets 50 min. later each day.
M SO 2 x 50 min = 100 min.= 1 hour 40 min. added to 6 AM
2. Page 53 #16. Copernican Players. Using a bulleted list format, make a one-page "executive summary" of the major roles that Copernicus, Tycho, Kepler, Galileo, and Newton played in overturning the ancient belief in an Earth-centered universe.
Nicholas Copernicus (1473-1543)
Based his work off of the heliocentric (sun-centered) ideas of Aristarchus (c. 260 BC)
Was able to order planets around the Sun and easily explain the perplexing retrograde motion of some planets
Held fast to circular orbits and included nearly as many epicycles as the Ptolemaic model
Didn't convince many people because his model was no more accurate than the Ptolemaic model
Tycho Brahe (1546-1601)
Observed a supernova in 1572 and showed it was a "new star" that had changed the "perfect" sky
Observed a comet in 1577 and proved by parallax measurements that it was not a feature of Earth's atmosphere
Founded a (pre-telescopic) observatory where he spent ~30 years measuring the positions of planets to 1 arcminute accuracy
Johannes Kepler (1571-1630)
Hired by Tycho to analyze the large data set he had collected
Worked diligently on a model with circular orbits, but was never able to match it perfectly to Tycho's accurate data
Finally threw out the canonical circular orbits and ended up developing a much more accurate system using elliptical orbits
Kepler's model is described by his three laws which place the planets in different sized elliptical orbits with the sun at a focus
Galileo Galilei (1564-1642)
Used the newly-developed telescope to overcome three important and long-held beliefs that would have made a heliocentric model impossible
Belief 1: If Earth were moving, objects in the air would be left behind.
Galileo used experiments to show how objects in motion will stay in motion (an early form of Newton's first law), so objects in Earth's atmosphere could conceivably continue to move with the planet
Belief 2: The heavens must be perfect and unchanging.
With his telescope, Galileo observed the Sun and moon. He found sunspots (imperfections!) on the Sun and observed mountains (more imperfections!) on the moon.
Belief 3: If Earth orbits the Sun, then we should see stellar parallax.
Galileo was able to resolve the band of the Milky Way into individual stars in his telescope, giving evidence that the stars were far more distant than most people had believed.
Additionally, Galileo observed several moons around Jupiter, showing it was very possible for objects to orbit something other than the Earth.
Galileo's most conclusive observations were that Venus goes through phases similar to those of the moon. It also changes size considerably during its phase cycle, something which can only be explained by a heliocentric solar system. Being contrary to the geocentric model, these observations falsified the theory of Aristotle and Ptolemy.
Isaac Newton (1642-1727)
Created calculus to allow for the mathematical description of many physical processes
Developed a universal law of gravitation which governs the motions of all bodies with mass
Newton's work demonstrated why the planets of the solar system acted as Kepler had described
3. Page 74 #16. Two Kinds of Planets. In words a friend would understand, explain why the jovian planets differ from the terrestrial planets in each of the following aspects: composition, size, density, distance from the Sun, and number of moons.
The nebular theory of the formation of the solar system provides all the important clues about the differences between the two types of planets.
The early solar system was formed by the collapse of the large solar nebula, which contained a variety of different particles and gases. To begin forming planets, these particles had to start condensing into larger solids. Rocks and metals were able to condense everywhere except the immediate vicinity of the Sun, but these dense materials were not very abundant in the nebula to start with. Hydrogen compounds such as water, methane, and ammonia were more prevalent than the rocks and metals but could only condense into solids at relatively large distances from the Sun, beyond the frost line. This meant that planetesimals near the sun were formed mostly of rock and metal and gave rise to the inner, terrestrial planets, while the planetesimals outside the frost line were solidified hydrogen compounds that were able to form the outer, jovian planets.
Since the hydrogen compounds were more abundant, the jovian planets quickly grew to larger sizes than terrestrial planets. They created enough gravity to trap some of the loose hydrogen and helium gas in the young solar system. This further increased their sizes and masses, but at the same time gave them a much lower density than the completely solid terrestrial planets. The gravity-driven flow of gas onto the young jovian planets also would have created a small disk of spiraling material, much the same way the original solar nebula had spiraled around the Sun as it was forming. This led to short episodes of planetesimal formation around each jovian planet that ultimately created a number of moons for each one. Since the terrestrial planets were not large enough to gravitationally form a disk, they have fewer, or no, moons.
4. Page 53 #22. Halley Orbit. Halley's Comet orbits the Sun every 76.0 years.
a. Find its average distance from the sun (semimajor axis). (Hint: Use Kepler's third law.)
Kepler's third law is the mathematical relation p2=a3 where p is the orbital period in years and a is the semimajor axis length in astronomical units. To answer this question, solve for a when p=76.0 years.
b. Halley's orbit is a very eccentric (stretched-out) ellipse, so at perihelion Halley's Comet is only about 90 million kilometers from the Sun, compared to more than 5 billion kilometers at aphelion. Does Halley's Comet spend most of its time near its perihelion distance, near its aphelion distance, or halfway in between? Explain.
Answer: near Aphelion Distance
Kepler's second law (equal areas in equal times) means that in the same unit of time, the comet traverses more length in its orbit when near perihelion than near aphelion. When near the sun, it moves quickly, and when far away, it travels at slower speeds.
Also consider Halley's Comet as viewed from Earth. It is only clearly visible to us (i.e. near the Sun) for a very short period of time (a few weeks).
Last Shuttle Mission: STS-132
The most recent space shuttle mission was called STS-132 and lasted from May 14th to May 26th of this year. It was the final flight mission for the space shuttle Atlantis, which will now be retired. During the mission, a number of important items were delivered to and installed on the International Space Station (ISS).
The largest payload carried to the station was the Russian-build Mini Research Module called Rassvet. Through the use of a large robotic arm, the module was successfully attached to the station, providing additional cargo storage and a fourth Russian docking port. As Russia has several different mission programs that require docks on the ISS, this port will likely see a great deal of use.
Also, three spacewalks were performed to replace some of the station's batteries and to install a new Space-to-Ground Antenna. The batteries are charged from the station's solar panels and are only used to provide power when the solar array is offline or in shadow, but they are very important in keeping the station operational during these times. The Space-to-Ground Antenna is an obviously essential feature, but the one installed was not the only one on the ISS.
On November 1st, the space shuttle Discovery will be leaving the surface of the planet for the last time. Following its eleven day mission to the International Space Station (ISS), Discovery will join Atlantis on the list of retired space shuttles. Its final mission may not be groundbreaking, but it will be important for the continued expansion of the ISS.
Discovery will be carrying two key payloads to the station: the Permanent Multipurpose Module (PMM) called Leonardo and the ExPRESS Logistics Carrier 4 (ELC4). Leonardo was one of several multipurpose modules designed only for short-term use. It underwent extensive modification to become the PMM, which will provide important long-term, easy-access supply storage for the astronauts aboard the ISS. The ELC4 is actually the third ELC to be installed on the exterior of the station. These carriers provide an unpressurized environment that can be used to perform scientific experiments in space without the need to launch a specialized satellite.