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SUBMITTED BY:
LUYAS, ERGELYN B. SIBUCO, JAMES T.
FERNANDEZ, CHRISS JOHN N. GLOVA, JOHINA S.
ANTIQUE, DAVE FRANCIS A. YANAG, JOHN MARK B.
GOCOTANO, ROXANNE P.
1. From where on Earth could you observe all of the stars during the course of a year?
What fraction of the sky can be seen from the North Pole?
You can observe all the stars from Earth's equator over a year. From the North Pole, you can see only half of the sky
2. Give four ways to demonstrate that Earth is spherical.
Ship disappearing bottom-up over the horizon, curvature of Earth's shadow during lunar eclipses, observations of stars from different latitudes, and circumnavigation.
3. Explain, according to both geocentric and heliocentric cosmologies, why we see
retrograde motion of the planets.
Geocentric: Retrograde motion explained by planets' orbits around Earth. Heliocentric: Retrograde motion due to Earth's orbit overtaking outer planets.
4. In what ways did the work of Copernicus and Galileo differ from the views of the ancient
Greeks and of their contemporaries?
Copernicus proposed heliocentrism, challenging geocentric views. Galileo supported heliocentrism with telescopic observations, unlike ancient Greek and contemporary views.
5. What were four of Galileo’s discoveries that were important to astronomy?
Moons of Jupiter, phases of Venus, sunspots, and mountains on the Moon.
6. Explain the origin of the magnitude designation for determining the brightness of stars.
Why does it seem to go backward, with smaller numbers indicating brighter stars?
Magnitude scale originates from ancient Greek astronomers. Smaller numbers indicate brighter stars due to their logarithmic nature, with each unit representing a factor of 2.5 change in brightness.
7. Ursa Minor contains the pole star, Polaris, and the asterism known as the Little Dipper.
From most locations in the Northern Hemisphere, all of the stars in Ursa Minor are
circumpolar. Does that mean these stars are also above the horizon during the day?
Explain.
Yes, stars in Ursa Minor, being circumpolar, remain above the horizon throughout the day, especially in high latitudes. However, they may be difficult to observe during daylight due to the Sun's brightness.
8. How many degrees does the Sun move per day relative to the fixed stars? How many
days does it take for the Sun to return to its original location relative to the fixed stars?
The Sun moves approximately 1 degree per day relative to the fixed stars. It takes about 365.25 days for the Sun to return to its original location relative to the fixed stars, which is why we have a leap year every four years to account for the extra fraction of a day.
9. How many degrees does the Moon move per day relative to the fixed stars? How many
days does it take for the Moon to return to its original location relative to the fixed stars?
The Moon moves about 12 to 13 degrees per day relative to the fixed stars. It takes about 27.3 days for the Moon to return to its original location relative to the fixed stars, which is why we have roughly a month.
10. Explain how the zodiacal constellations are different from the other constellations.
The zodiacal constellations are a specific group of constellations through which the Sun, Moon, and planets appear to move in the sky over the course of a year. They are important in astrology. Other constellations are not part of this specific path.
11. The Sun was once thought to be a planet. Explain why.
The Sun was once thought to be a planet because, from Earth, it appears to move across the sky along with the other planets, rather than remaining fixed like the stars. Ancient astronomers categorized it as one of the "wandering stars" (planets) due to its apparent motion.
12. Is the ecliptic the same thing as the celestial equator? Explain.
No, the ecliptic and the celestial equator are not the same. The ecliptic is the apparent path that the Sun follows through the sky over the course of a year, while the celestial equator is the projection of Earth's equator onto the celestial sphere. They intersect at two points, the vernal and autumnal equinoxes.
13. What is an asterism? Can you name an example?
An asterism refers to a distinctive arrangement of stars either within a single constellation or extending across multiple constellations. These configurations tend to be more compact and conspicuous compared to the constellations they inhabit. Although they might be commonly identified by specific names, they lack official recognition as constellations by astronomical authorities. One example of an asterism is the Big Dipper, which is part of the constellation Ursa Major. The Big Dipper consists of seven bright stars arranged in a distinctive shape resembling a ladle or dipper. While it's technically just a part of the larger Ursa Major constellation, it's one of the most recognizable and frequently observed asterisms in the night sky.
geocentric model remained dominant until Copernicus proposed the heliocentric model, offering a simpler explanation for celestial motions.
19. Why did Copernicus want to develop a completely new system for predicting planetary
positions? Provide two reasons.
Copernicus sought to develop a completely new system for predicting planetary positions for two main reasons:
- Geometric Simplicity: Copernicus aimed to simplify the mathematical description of planetary motion. In the geocentric model, proposed by Ptolemy, the observed motions of planets were explained through complex combinations of epicycles and deferent. Copernicus believed that a heliocentric model, with the Sun at the center and planets orbiting in circular or nearly circular paths, would offer a more elegant and mathematically straightforward explanation of planetary motion.
- Observational Accuracy: Copernicus recognized certain inconsistencies in the geocentric model, such as the varying speeds and retrograde motions of planets. He sought to develop a model that better aligned with observed astronomical phenomena. By placing the Sun at the center of the solar system, Copernicus aimed to create a model that could accurately predict the positions of planets over time, thereby improving the understanding and prediction of celestial events.
20. What two factors made it difficult, at first, for astronomers to choose between the
Copernican heliocentric model and the Ptolemaic geocentric model?
At first, astronomers struggled to choose between the Copernican heliocentric model and the Ptolemaic geocentric model due to the lack of observable evidence distinguishing between them. Both models could explain celestial phenomena, such as the apparent motion of the planets, with comparable accuracy. Additionally, the prevailing Aristotelian worldview favored a stationary Earth at the center of the universe, which made it challenging for astronomers to accept the heliocentric concept. Furthermore, technological limitations hindered astronomers' ability to observe and measure celestial phenomena with the precision needed to discern between the two models.
21. What phases would Venus show if the geocentric model were correct?
In the geocentric model, Venus would exhibit phases similar to those of the Moon. As Venus orbits the Earth, its illuminated portion would vary, resulting in phases ranging from crescent to full and back again. When Venus is on the far side of the Sun from Earth, it would appear fully illuminated, akin to a full moon. As it moves closer to Earth, its illuminated portion would decrease, resembling crescent phases, until it reaches a point between Earth and the Sun, where it would appear as a thin crescent. This cyclic variation in Venus's appearance would align with the geocentric model's prediction of its orbit around Earth.
Thought Questions
22. Describe a practical way to determine in which constellation the Sun is found at any
time of the year.
One practical way to determine the constellation in which the Sun is found at any time of the year is through the use of an astronomical tool called an analemma. An analemma is a diagram that shows the position of the Sun in the sky at the same time each day throughout the year. By observing the position of the Sun relative to the analemma, one can identify the constellation it is located in. Additionally, tools such as a planisphere or a star chart can help locate the constellations visible at a given time. By referencing these resources and accounting for the Earth's axial tilt and its orbit around the Sun, one can determine the constellation in which the Sun resides.
23. What is a constellation as astronomers define it today? What does it mean when an
astronomer says, “I saw a comet in Orion last night”?
A constellation, as astronomers define it today, is a specific area of the celestial sphere containing recognizable patterns of stars that form imaginary outlines or shapes. These patterns are traditionally named after mythological figures, animals, or objects. When an astronomer says, "I saw a comet in Orion last night," they are referring to the comet's apparent position in the sky relative to the constellation of Orion. This means that the astronomer observed the comet within the region of the sky where the stars forming the constellation Orion are located, using Orion as a reference point for describing the comet's position.
24. Draw a picture that explains why Venus goes through phases the way the Moon does,
according to the heliocentric cosmology. Does Jupiter also go through phases as seen from
Earth? Why?
VENUS JUPITER
In the heliocentric cosmology, Venus orbits
the Sun, and its phases as seen from Earth
are determined by its relative position to the
Sun and Earth. When Venus is on the opposite
side of the Sun from Earth, it appears fully
illuminated, resembling a full moon. As it
moves closer to Earth in its orbit, its
illuminated portion decreases, showing
crescent phases. When Venus is between
Earth and the Sun, it appears as a thin
crescent.
Jupiter, however, does not go through
phases as seen from Earth. This is because
Jupiter orbits the Sun outside of Earth's
orbit, meaning its relative positions with
respect to the Sun and Earth do not lead to
observable changes in its illuminated
portion. Since Jupiter's orbit lies beyond
Earth's orbit, its position relative to Earth
does not cause changes in the amount of
sunlight it reflects back to Earth, resulting in
no discernible phases.
25. Show with a simple diagram how the lower parts of a ship disappear first as it sails
away from you on a spherical Earth. Use the same diagram to show why lookouts on old
sailing ships could see farther from the masthead than from the deck. Would there be any
advantage to posting lookouts on the mast if Earth were flat? (Note that these nautical
arguments for a spherical Earth were quite familiar to Columbus and other mariners of
his time.)
28. Consider three cosmological perspectives—the geocentric perspective, the heliocentric
perspective, and the modern perspective—in which the Sun is a minor star on the outskirts
of one galaxy among billions. Discuss some of the cultural and philosophical implications
of each point of view.
Each cosmological perspective has profound cultural and philosophical implications, shaping human perceptions of the cosmos and our place within it. From reinforcing traditional beliefs to challenging established paradigms and fostering existential reflections, these perspectives have influenced the course of human thought and civilization.
29. The north celestial pole appears at an altitude above the horizon that is equal to the
observer’s latitude. Identify Polaris, the North Star, which lies very close to the north
celestial pole. Measure its altitude. (This can be done with a protractor. Alternatively,
your fist, extended at arm’s length, spans a distance approximately equal to 10°.)
Compare this estimate with your latitude. (Note that this experiment cannot be performed
easily in the Southern Hemisphere because Polaris itself is not visible in the south and no
bright star is located near the south celestial pole.)
To measure the altitude of Polaris, the North Star, one can extend their arm and use their fist as a rough estimate, where the width of the fist at arm's length spans about 10 degrees of the sky. By sighting Polaris and estimating its angle above the horizon using this method, one can compare it to their known latitude. For example, if Polaris appears at an altitude of approximately three fists above the horizon, it suggests a latitude of around 30 degrees. This phenomenon aligns with the principle that the altitude of Polaris above the horizon is roughly equal to the observer's latitude. However, this experiment is more feasible in the Northern Hemisphere, as Polaris is not visible in the Southern Hemisphere, making it challenging to determine the south celestial pole's altitude using a similar method.
30. What were two arguments or lines of evidence in support of the geocentric model?
- Apparent Motion of Celestial Bodies: Ancient astronomers observed the apparent motion of celestial bodies, such as the Sun, Moon, planets, and stars, across the sky. From Earth's perspective, these objects appeared to move around the Earth in regular patterns. This observation seemed to support the idea that Earth was stationary at the center of the universe, with celestial bodies revolving around it.
- Lack of Stellar Parallax: Ancient astronomers did not detect stellar parallax, the apparent shift in the positions of stars due to Earth's motion around the Sun. Despite observing the stars throughout the year, they noticed no significant changes in their positions relative to each other. This lack of parallax was interpreted as evidence that the stars were fixed on a celestial sphere surrounding the stationary Earth, rather than being distant objects in space.
31. Although the Copernican system was largely correct to place the Sun at the center of
all planetary motion, the model still gave inaccurate predictions for planetary positions.
Explain the flaw in the Copernican model that hindered its accuracy.
The flaw in the Copernican model that hindered its accuracy stemmed from its adherence to the idea of perfectly circular orbits for the planets. Copernicus proposed that the planets moved in circular orbits around the Sun, with Earth itself also orbiting the Sun. However, later observations revealed that planetary orbits are not perfect circles but rather ellipses, with the Sun located at one of the foci of each ellipse. This deviation from circular orbits introduced inaccuracies in the Copernican model's predictions for planetary positions. Since Copernicus's model assumed circular orbits, it failed to account for the varying speeds at which planets move along their elliptical paths, resulting in discrepancies
between predicted and observed planetary positions. It wasn't until Johannes Kepler proposed his laws of planetary motion, which described the elliptical orbits of the planets and the varying speeds at which they move, that more accurate predictions of planetary positions became possible.
32. During a retrograde loop of Mars, would you expect Mars to be brighter than usual in
the sky, about average in brightness, or fainter than usual in the sky? Explain.
During a retrograde loop of Mars, you would expect Mars to be brighter than usual in the sky. Retrograde motion occurs when Earth, in its orbit around the Sun, overtakes and passes by another outer planet like Mars. As Earth moves between Mars and the Sun during this period, Mars appears to temporarily move backward in the sky relative to the background stars. This retrograde motion typically coincides with Mars being at opposition, which means it is closest to Earth and fully illuminated by the Sun. As a result, Mars appears larger and brighter in the sky during its retrograde loop compared to other times in its orbit. Therefore, during a retrograde loop, Mars would be brighter than usual in the sky.
33. The Great Pyramid of Giza was constructed nearly 5000 years ago. Within the
pyramid, archaeologists discovered a shaft leading from the central chamber out of the
pyramid, oriented for favorable viewing of the bright star Thuban at that time. Thinking
about Earth’s precession, explain why Thuban might have been an important star to the
ancient Egyptians.
Due to Earth's precession, the North Star (the fixed point around which the night sky appears to rotate) slowly changes over thousands of years. Around 5000 years ago, Thuban was the North Star. The alignment of the pyramid shaft towards Thuban suggests the Egyptians used it for navigation or aligning structures with the heavens, making Thuban a significant star for them.
34. Explain why more stars are circumpolar for observers at higher latitudes.
As your latitude increases (move further north), the north celestial pole gets higher in the sky. This is because you're tilting your perspective more towards the pole, causing more circumpolar stars (those never setting below the horizon) to become visible.
35. What is the altitude of the north celestial pole in the sky from your latitude? If you do
not know your latitude, look it up. If you are in the Southern Hemisphere, answer this
question for the south celestial pole, since the north celestial pole is not visible from your
location.
The altitude of the north celestial pole in the sky would range from approximately 9° to 10° from my location.
36. If you were to drive to some city south of your current location, how would the altitude
of the celestial pole in the sky change?
Driving south, the altitude of the north celestial pole would decrease. As your latitude gets lower, the pole dips closer to the horizon.
37. Hipparchus could have warned us that the dates associated with each of the natal
astrology sun signs would eventually be wrong. Explain why.
Hipparchus could have foreseen astrology's sign dates shifting because of precession. The constellations used for birth signs slowly drift westward due to precession, meaning the Sun's position relative to constellations during birth would gradually change over time.
42. Suppose Eratosthenes’ results for Earth’s circumference were quite accurate. If the
diameter of Earth is 12,740 km, what is the length of his stadium in kilometers?
To find the length of Eratosthenes' stadium in kilometers, we can use the formula for the circumference of a circle: Circumference = π×Diameter Given that the diameter of Earth is 12,740 km and Eratosthenes' estimated circumference is 250, stadia, we can set up the proportion: 250,000 stadia = π * 12,740 km Now, solve for the length of one stadium: 1 stadium = (π × 12,740 km) / 250, 1 stadium = (π × 12,740 km) / 250,000 = 0.16152 km So, the length of Eratosthenes' stadium, if his results were quite accurate, would be approximately 0.16152 kilometers.
43. Suppose you are on a strange planet and observe, at night, that the stars do not rise
and set, but circle parallel to the horizon. Next, you walk in a constant direction for 8000
miles, and at your new location on the planet, you find that all stars rise straight up in
the east and set straight down in the west, perpendicular to the horizon. How could you
determine the circumference of the planet without any further observations? What is the
circumference, in miles, of the planet?
To determine the circumference of the strange planet without further observations after walking 8000 miles and noticing the change in the stars' movement, you can use the concept of angular displacement. When the stars circle parallel to the horizon, it indicates that you are at the planet's equator. After walking 8000 miles and observing the stars rise straight up in the east and set straight down in the west, perpendicular to the horizon, you have reached one of the planet's poles. Given that the stars circle parallel to the horizon at the equator and rise straight up and set straight down at the poles, the distance between the equator and the pole is a quarter of the planet's circumference. Therefore, by walking 8000 miles from the equator to the pole, you have covered a quarter of the planet's circumference. To find the circumference of the planet, you can multiply the distance you walked by 4 since you have traveled a quarter of the planet's circumference. Thus, the circumference of the planet would be 32,000 miles. Therefore, based on your observations and the distance you walked, the circumference of the strange planet would be 32,000 miles.
