Question 1

Precession can be detected by noting the

Accepted Answer

Precession is a gradual change in the orientation of the rotational axis of a spinning object, and in astronomy, it refers to the slow rotation of the Earth's rotational axis. This slow rotation causes a change in the celestial coordinates of stars over many years, which can be detected by observing their positions relative to each other and to the celestial poles.

Question 2

Something that is 1000 km away has an angular size of 2 seconds of arc.Approximately how big is it?

Accepted Answer

The angular size in radians can be calculated using the formula: angular size = size / distance. To use this formula, we first convert 2 seconds of arc to radians: 2 seconds of arc = 2/3600 degrees (since there are 3600 arcseconds in a degree) = 2/3600 * π/180 radians (since π radians = 180 degrees). This gives us an angular size of approximately 9.7 x 10^-6 radians. Using the formula angular size = size / distance, we rearrange to find the size = angular size * distance. Substituting the values, we get size = 9.7 x 10^-6 * 1,000,000 meters (since 1000 km = 1,000,000 meters), which gives us a size of approximately 9.7 meters. Therefore, the closest answer is 10 meters (B).

Question 3

How did Eratosthenes determine the circumference of the Earth?

Accepted Answer

Eratosthenes noted that at noon on the summer solstice, the Sun was directly overhead in Syene (located near modern-day Aswan, Egypt), as evidenced by the absence of shadows cast by vertical objects. However, at the same time in Alexandria, located due north of Syene, vertical objects cast shadows at an angle. By measuring the angle of the shadow cast in Alexandria and knowing the distance between Alexandria and Syene, Eratosthenes was able to calculate the circumference of the Earth.

Question 4

What evidence supported Aristotle's argument that the Earth is a sphere?

Accepted Answer

During a lunar eclipse, Aristotle observed that the Earth's shadow on the Moon was curved, which led him to conclude that the Earth must be a spherical shape. The other options are not directly related to Aristotle's argument for the Earth's spherical shape.

Question 5

An astronaut lands on an unknown planet.After walking a distance of 400 km toward the north pole of the planet,she notices that the pole star for that planet is 5 degrees higher in the sky.What is the circumference of the planet?

Accepted Answer

The pole star's elevation change by 5 degrees for a 400 km journey towards the pole indicates that the full 360 degrees would be covered by walking 360/5 times further, which equals 72 times 400 km, giving a total circumference of 28,800 km.

Question 6

The Greek astronomer Thales is reported to have predicted

Accepted Answer

Thales was known for accurately predicting a total solar eclipse, which occurred on May 28, 585 BC. There is no record of Thales predicting the discovery of Uranus, the appearance of a comet or the discovery of variable stars.

Question 7

According to Pythagoras,what was the shape of the Earth?

Accepted Answer

Pythagoras believed that the Earth was a sphere. This was based on his observations of the curved shadow that is cast by the Earth during a lunar eclipse. He also noted that the stars appeared to move in circular patterns in the sky, which further supported his belief that the Earth was a sphere.

Question 8

How did Aristarchus propose that the distance of the Moon could be found?

Accepted Answer

Aristarchus proposed measuring the distance to the Moon by observing the Earth's shadow on the Moon during a lunar eclipse, using geometry to calculate the relative distances.

Question 9

What object was located at the center of Aristarchus's model of the solar system?

Accepted Answer

Aristarchus's model of the solar system was heliocentric, placing the Sun at the center, not the Earth.

Question 10

In Ptolemy's model of the solar system,the circle on which the center of the epicycle moved about the Earth was called the

Accepted Answer

In Ptolemy's model of the solar system, the circle on which the center of the epicycle moved about the Earth was called the deferent. The equant was a point off-center from the Earth where the planet moved at a constant speed, and the eccentric was the deviation of the orbit from a perfect circle. The "capital" is not a term related to Ptolemy's solar system model.

Question 11

What is the angular size of a 2 cm diameter coin at a distance of 1 km?

Accepted Answer

The angular size can be calculated using the formula: angular size (in radians) = diameter / distance. Converting the result to arcseconds, the angular size is approximately 4 arcseconds.

Question 12

When did a planet undergo retrograde motion in Ptolemy's model of the solar system?

Accepted Answer

According to Ptolemy's model, retrograde motion occurred when a planet was on the part of its epicycle that was nearest the Earth. The epicycle was a small circle that a planet's orbit traced as it moved along its deferent, a larger circle around the Earth. During retrograde motion, the planet appeared to move backwards in the sky relative to the stars.

Question 13

What body was located at the center of Ptolemy's model of the solar system?

Accepted Answer

According to Ptolemy's model of the solar system, the Earth was at the center (also known as geocentric model).

Question 14

An object with an angular size of 1 degree moves 10 times farther away.What is its new angular size?

Accepted Answer

The angular size of an object is inversely proportional to its distance from the observer. So, as the object moves 10 times farther, its angular size would reduce to 1/10th of its original size. Therefore, the new angular size would be 6 minutes of arc.

Question 15

What was the main result of Aristarchus's determination of the sizes and distances of the Sun and Moon?

Accepted Answer

Aristarchus's calculations, although not accurate by modern standards, demonstrated that the Sun was much larger than the Earth and suggested that the distances involved in the solar system were vast compared to the Earth's size. This was a significant departure from the Earth-centered universe model that prevailed at the time.

Question 16

What procedure did Aristarchus propose to calculate the distance from the Earth to the Sun?

Accepted Answer

Aristarchus proposed measuring the angle between the Moon and the Sun during a first or last quarter phase, when the angle between the Moon and the Sun is a right angle. Aristarchus reasoned that this angle would be smaller if the Sun was further away from the Earth, and larger if the Sun was closer. By using trigonometry, he was able to estimate the relative distances between the Sun, Earth, and Moon.

Quiz 3: Ancient Astronomy