ASTR 1P01 Exam 2 Practice Questions

Lecture 5 Practice Questions What are the differences and similarities between Copernicus's model and Ptolemy's model? - Copernicus's model was heliocentric, with the Sun at the center. Ptolemy's model was geocentric, with the Earth at the center. However, other than that, both models had epicycles, circular orbits, movement at constant speed along the orbit, and celestial spheres. What did Copernicus's model get right? What did it not get right? - It correctly put the Sun at the center of the solar system. However, the planets were still moving on epicycles in circular orbits around the Sun, which is incorrect - they actually move along ellipses and without epicycles. In addition, we now know that the speed of the planet varies along its orbit (per Kepler's laws) and that there is not actual "celestial sphere", the planets move in empty space. Why do we not feel the Earth move? - Because it is moving at a constant speed (except for negligible variations). We only feel movement when the speed changes, that is, when there is acceleration. Does a planet move faster or slower in its orbit if it's closer to the Sun? - Faster, according to Kepler's 2nd law. What is an example of a prediction that scientists can use to determine experimentally whether Copernicus's model or Ptolemy's model is more accurate? - The phases of Venus are predicted correctly by Copernicus's model, but not by Ptolemy's. If I push an object in empty space with no friction and no other objects to collide with, what will its motion be like? - It will keep moving at constant speed forever, since there will be no forces (like friction or air resistance) to slow it down or speed it up. I drop a 1 kg ball and a 2 kg ball to the ground. What does Aristotle predict about the speed in which each of the ball falls? What does Galileo predict? Which one of them is right? - Aristotle will predict that the heavier ball falls faster. Galileo predicts that both balls fall at the same speed. Galileo is right, as can be demonstrated experimentally. Why did the Catholic Church oppose Copernicus's heliocentric model? - The Church claimed that the Earth is the center of the universe, as in Ptolemy's model, based on the Bible. The heliocentric model claimed that the Earth is just one out of several planets orbiting the Sun, so it's no longer the center of the universe. Copernicus's model challenged the authority of the Church, and if people knew that the Church is wrong about astronomy, they might start questioning the Church's teachings about other topics as well. (Religions often rely on the ignorance of their believers to maintain power; this was true in Galileo's time and remains just as true today.) What were telescopes used for before Galileo started using them for astronomical observations? - For observing far away things on Earth, for example for military purposes. What are the two reasons that Galileo's discovery of the moons of Jupiter strengthen the heliocentric model? - This discovery showed that there are celestial objects that revolve around other planets, not the Earth. This weakened the geocentric claim that all celestial objects revolve around the Earth. It also proved that the Earth can be moving without "losing" the Moon, since if Jupiter can do that, then the Earth also can.

What does the heliocentric model say about humanity's role in the universe? - It shows that (despite what some of us would like to believe) we are not the center of the universe, we are just one form of life living on one planet out of trillions, and there could be other forms of life on other planets. What data did Tycho Brahe collect? - The positions of the Sun, Moon, planets, and stars over many years. What did Kepler discover about the shape of the orbits of the planets that was different from Ptolemy's and even Copernicus's models? - That the orbits were ellipses, not circles, and there were no epicycles. How do the foci of an ellipse compare to the center of a circle? - In a circle, the distance from the center to any point on the circle is always the same, equal to the radius of the circle. But in an ellipse, it's the SUM of distances from the two foci to any point on the ellipse that is always the same. What is the difference between the major axis and the semi-major axis of an ellipse? - The major axis is the widest diameter of the ellipse. It is analogous to the diameter of a circle. The semi- major axis is half the major axis (semi = half). It is analogous to the radius of a circle. A circle is a special case of an ellipse with a specific eccentricity. What is its eccentricity? - Zero. According to Kepler's first law, where is the Sun located in relation to a planet's orbit? - At one of the two foci of the ellipse. In simple terms, what does Kepler's second law say? - A planet moves faster in its orbit when it is closer to the Sun. A planet is moving at constant speed along its entire orbit. What can you say about the shape of this planet's orbit? - It's a perfect circle, so it's always the same distance from the Sun, hence it moves at constant speed according to Kepler's second law. What is the orbital period of the Earth? - By definition, this is exactly 1 year. According to Kepler's third law, is the orbital period of Jupiter longer or shorter than that of Earth? - The orbital period is larger if the semimajor axis is larger. Since Jupiter is farther away from the Sun compared to the Earth, its orbital period must be larger. Indeed, the orbital period of Jupiter is around 12 years. "Kepler's laws explain the fundamental forces of nature responsible for movement in the solar system." True or false? - False. Kepler's laws are just a set of observations; Newton's laws describe the actual underlying forces responsible for the motion. Indeed, Kepler's laws can be mathematically derived from Newton's laws, but not the other way around.

Does the Andromeda galaxy, 2.5 million light years away, exert any gravity on you personally? - In principle, yes. Both the Andromeda galaxy and you have mass, and anything that has mass anywhere in the universe attracts anything else with mass anywhere in the universe, so the Andromeda galaxy and you attract each other gravitationally. However, this force is so tiny that you will never be able to measure it. "The astronauts on the International Space Station do not experience any gravity." True or false? - False. They feel weightless, since they are in free fall, so technically they are falling all the time. However, gravity is still acting on them, which is exactly why the space station stays in orbit. "A planet moves fastest when it is at the perihelion (the point closest to the Sun) compared to any other point, due to Kepler's second law". True or false? - True. Kepler's second law says a planet moves faster in its orbit when it is closer to the Sun, and the perihelion is the point where the planet is closest to the Sun. Which planet has the most eccentric orbit? And what does this mean for the shape of its orbit? - Mercury has the most eccentric orbit. This means that the shape of Mercury's orbit is the most different from a circle (or "the most elliptic") compared to the other planets. Where is the Kuiper belt located? - 30-50 AU away from the Sun. If Superman throws a ball with enough force, can he send that ball into an orbit around Earth? - Yes. More force means more acceleration and thus larger velocity. If thrown in just the right direction with just the right force, the ball can be made to "fall" around the Earth, which is exactly what an orbit is. "Kepler's laws give a 100% precise description of the orbits of planets in the solar system." True or false? - False. Kepler's laws only take the gravitational effects of the Sun into account. However, due to Newton's law of gravitation, now we know that the planets also exert gravity on each other, and this is not taken into account in Kepler's laws. This causes subtle differences in the orbits of the planets compared to what Kepler's laws say. In addition, today we know that Newton's laws aren't 100% precise either, and general relativity provides a much more precise description of the orbits. What has more momentum: a 1 kg ball moving at 5 m/s or a 5 kg ball moving at 1 m/s? - Momentum is mass times velocity. In both cases, the product of mass and velocity is 5, so in fact, both ball have the same momentum. A ball was moving at a velocity of 3 m/s. It then accelerated with an acceleration of 6 m/s 2 for 2 seconds. What was its final velocity? - 3 + 2 × 6 = 15 m/s. During a plane flight, when is the plane's frame an inertial frame and when is it not an inertial frame? - Remember that an inertial frame is one that doesn't rotate or accelerate. When the plane is taking off and landing, it's accelerating, so it's not an inertial frame. Once it's in the air, as long as it's maintaining constant speed (no acceleration) and constant direction (no rotation), it's an inertial frame.

Lecture 7 Practice Questions How many great circles are on a sphere? - An infinite number. Any circle whose center is at the center of the sphere is a great circle, and you can place that circle in any orientation you want. The distance between me and the North Pole is equal to the distance between me and the South Pole. Where am I? - On the equator. The coordinates of Brock University are 43.1176° N, 79.2477° W. What do these coordinates mean? - The first number is latitude: the university is located 43.1176 degrees to the north of the equator. The second number of longitude: the university is located 79.2477 degrees west of the Prime Meridian (passing through Greenwich, England). Is declination analogous to latitude or longitude? Is right ascension analogous to latitude or longitude? - Declination is the angle to the north or south of the celestial equator, so that's analogous to latitude. Right ascension is the angle to the east of the March equinox, so it's analogous to longitude. What did Foucault prove with his pendulum? - From the fact that the pendulum's direction of oscillation was slowly rotating over time, it follows that the Earth is rotating around its axis. This is a great example of a simple experiment that literally anyone can do, and yet can prove something that people have denied for thousands of years! "The seasons are due to the distance between the Earth and the Sun changing throughout the year." True or false? - False. This is actually a common misconception. The real reason for the seasons is the Earth's axial tilt. If the distance to the Sun was the cause for the season, then we would have two summers and two winters during each year! Which two effects are responsible for the seasons, and how? - The Sun's rays hit the ground at different angles throughout the year, due to the Earth's axial tilt. When the Sun hits the ground at a small angle, the rays spread out and each point on the ground gets less heat, resulting in a winter. When the Sun hits the ground at a large angle, the rays hit the ground more directly and each point on the ground gets more heat, resulting in a summer. When it's summer in the northern hemisphere it's winter in the southern hemisphere, and vice versa, since when one hemisphere "leans into" the Sun, the other "leans out". - In addition to rays hitting the ground more directly, in the summer the Sun spends more time in the sky, so it has more time to heat the ground before night falls. Which solstice happens in June? What does it mean in each hemisphere? - The June solstice happens every year around June 21. In the northern hemisphere, it's the summer solstice: the day where the Sun is highest in the sky and the day is the longest. In the southern hemisphere, it's the winter solstice: the day where the Sun is lowest in the sky and the day is the shortest. What are the two tropics, and what do they mean? - The Northern Tropic (Tropic of Cancer) is the northmost latitude where the Sun can be directly overhead (at the zenith). The Southern Tropic (Tropic of Capricorn) is the southmost latitude where the Sun can be directly overhead (at the zenith).

How is a solar eclipse created? What about a lunar eclipse? - A solar eclipse happens when the Moon casts a shadow on the Earth, or in other words, the Moon fully or partially blocks light from the Sun from reaching the Earth. A lunar eclipse is the opposite: it happens when the Earth casts a shadow on the Moon, or in other words, the Earth fully or partially blocks light from the Sun from reaching Moon. Does every planet with a moon experience total solar eclipses? - No. The apparent size (i.e. the size in the sky, not the actual size) of both the Sun and the Moon needs to be approximately the same for that to happen. What are the umbra and penumbra? - The umbra is the central cone where the shadow from a spherical body (e.g. the Moon or the Earth) is darkest. A person within the umbra will see the light from the Sun completely blocked, and will experience a total eclipse. The penumbra is the outer part of the cone, where the shadow is lighter. A person within the penumbra will see the light from the Sun partially blocked and will experience a partial eclipse. Is a solar eclipse visible from everywhere in the same hemisphere? - No, only if you are in the small area that's inside the umbra of the Moon's shadow. Is a lunar eclipse visible from everywhere in the same hemisphere? - Yes, because the shadow is not on you, it's on the Moon, so everyone sees the same thing as long as they can see the Moon. "During a solar eclipse, it is safe to look directly at the Sun." True or false? - False, except during totality - the short time when the Sun is totally eclipsed by the Moon, which lasts a few minutes at the most. At that time, and ONLY at that time, it is safe to look directly at the Sun. However, it might be hard to tell exactly when the Sun is 100% eclipsed, so it is highly recommended not to look directly at the Sun if you are on your own, even during totality. Instead, you should attend an official eclipse event led by qualified people, such as professional astronomers or physicists. An example of such an event is the one planned for the total solar eclipse of April 8, 2024 at Brock University, where qualified experts, including the professor of this course, will be on site to ensure everyone is viewing the eclipse safely by distributing eclipse glasses and letting you know exactly when it is safe to look directly at the Sun without the glasses.

Exam 2 Practice Questions During the winter: - The Sun is high in the sky. - The Sun is low in the sky. - The Sun is farthest away from the Earth. The Tropic of Capricorn... - Is at a latitude of approximately 23° N. - Is at a longitude of approximately 23° W. - Is at a latitude of approximately 23° S. Planet A has an orbital period of 100 Earth days. Planet B has an orbital period of 200 Earth days. Which planet is closer to the Sun? - Planet B. - Planet A. - There is not enough information to answer this question. If I double the mass of an object, its momentum will be... - The same. - Twice as large. - Half as large. The law of inertia says that... - Objects naturally tend to keep moving at a constant speed unless a force acts on them. - Objects naturally tend to speed up with time unless a force acts on them. - Objects naturally tend to slow down with time unless a force acts on them. What is the difference between mass and weight? - Mass is the gravitational force on the object, weight is the amount of matter in the object. - There is no difference; they are two words that mean the same thing. - Mass is the amount of matter in the object, weight is the gravitational force on the object. Where on Earth can a solar eclipse be seen from? - Anywhere. - Anywhere where the Moon is visible. - Only inside the shadow of the Moon. Who collected the accurate orbital data on planetary motions? - Johannes Kepler. - Galileo Galilei. - Tycho Brahe. Which book was the first to accurately describe how gravity works? - Mathematical Principles of Natural Philosophy. - Almagest. - On the Revolution of the Celestial Spheres. During a full moon... - The Moon is between Earth and the Sun. - Earth is between the Moon and the Sun. - The Sun is between Earth and the Moon.

If the Earth had an orbital radius half as large, how would the force of gravity between the Earth and the Sun change? - It would increase by a factor of 4. - It would decrease by a factor of 4. - It would increase by a factor of 2. What is the rate of change of position called? - Acceleration. - Velocity. - Momentum. A star is 40° east of the March equinox. This means the star is at ... - Right ascension 40° - Longitude 40° - Declination 40° An ellipse has... - One focal point. - Two focal points. - Three focal points. Which of the following is always conserved? - Force - Mass - Angular momentum Who collected the accurate orbital data on planetary motions? - Johannes Kepler. - Nicolaus Copernicus. - Tycho Brahe. The far side of the Moon is... - Always dark. - Sometimes dark and sometimes not dark. - Never dark. A star is 40° north of the celestial equator. This means the star is at ... - Declination 40° - Right ascension 40° - Latitude 40° If the Earth had an orbital radius twice as large, how would the force of gravity between the Earth and the Sun change? - It would increase by a factor of 2. - It would decrease by a factor of 4. - It would increase by a factor of 4.

Planet A has an orbital period of 200 Earth days. Planet B has an orbital period of 100 Earth days. Which planet is closer to the Sun? - Planet A. - There is not enough information to answer this question. - Planet B. In which latitudes does the Sun shine for 24 or more hours? - Between 66.6° N and 90° N. - Between 0° and 23.4° N. - Between 23.4° N and 66.6° N. If the Sun had a mass twice as large, how would the force of gravity between the Earth and the Sun change? - It would increase by a factor of 4. - It would increase by a factor of 2. - It would decrease by a factor of 2. Which of the following aspects of Copernicus's heliocentric model was correct? - It assumed the planets orbited the Sun. - It assumed the epicycles moved at a constant speed. - It assumed the planets moved in epicycles. Which is longer on Earth? - A sidereal day. - Both are the same length. - A synodic day. During a new moon... - Earth is between the Moon and the Sun. - The Sun is between Earth and the Moon. - The Moon is between Earth and the Sun. An object in the Oort cloud... - Experiences more gravity from the Sun than an object of the same mass in the Kuiper belt. - Experiences less gravity from the Sun than an object of the same mass in the Kuiper belt. - Experiences the same amount of gravity from the Sun as an object of the same mass in the Kuiper belt. Which book was the first to describe a heliocentric model? - Almagest. - On the Revolution of the Celestial Spheres. - Mathematical Principles of Natural Philosophy. When the Earth is farthest from the Sun... - It moves at the same rate as when it is at any other point. - It moves the slowest. - It moves the fastest. During the winter: - The Sun's rays hit the ground at a large angle relative to the surface. - The Sun's rays hit the ground at a zero angle relative to the surface. - The Sun's rays hit the ground at a small angle relative to the surface.

The far side of the Moon is... - Always facing away from Earth. - Always facing towards Earth. - Sometimes facing away from Earth and sometimes towards it. During the June solstice, in the northern hemisphere... - The day is the longest day of the year. - The day and night are the same length. - The day is the shortest day of the year. A sidereal day is... - A body's rotation period with respect to the fixed stars. - A body's rotation period with respect to itself. - A body's rotation period with respect to the Sun. According to Aristotle, the natural state of matter is... - Moving at a constant speed. - Either being at rest or moving at a constant speed. - Being at rest. Galileo's discoveries which supported the Copernican model included: - The moons of Jupiter and the phases of Venus. - The phases of the Moon and the fact that the Milky Way is composed of many individual stars. - The phases of Venus and the phases of the Moon. Why were Galileo's books banned? - Because scientists of the time rejected his theories. - Because the Catholic Church feared his scientific discoveries would undermine the Church's authority. - Because the Catholic Church feared the wrath of God due to his blasphemy against the holy scriptures. In which latitudes can the Sun be at the zenith? - Between 0° and 23.4° N. - Between 23.4° N and 66.6° N. - Between 66.6° N and 90° N. The Tropic of Cancer... - Is at a latitude of approximately 23° S. - Is at a longitude of approximately 23° W. - Is at a latitude of approximately 23° N. During the summer: - The Sun is low in the sky. - The Sun is high in the sky. - The Sun is closest to the Earth. When I throw a ball while sitting on a spinning carousel, the ball will seem to me to have a curved path. The reason for that is... - The Coriolis force. - That Earth is rotating around the Sun. - That Earth is rotating around its axis.

During the December solstice, in the northern hemisphere... - The day is the shortest day of the year. - The day and night are the same length. - The day is the longest day of the year. Where on Earth can a lunar eclipse be seen from? - Only inside the shadow of the Moon. - Anywhere where the Moon is visible. - Anywhere.