The three correct answers are:
1. The Sun is at the center.
2. The stars are fixed to an outer sphere.
3. The planets move in perfect circles.
Which are features of Copernicus's model of the solar system? Select the three correct answers.(2 points)
Responses
The Sun is at the center.
The Sun is at the center.
The stars are fixed to an outer sphere.
The stars are fixed to an outer sphere.
The outer planets move in epicycles.
The outer planets move in epicycles.
All planets orbit the Sun at the same speed.
All planets orbit the Sun at the same speed.
The planets move in perfect circles.
The planets move in perfect circles.
Earth is fixed to a crystalline sphere.
29 answers
In 3–5 sentences, explain how the shape of planetary orbits affects their orbital velocity. Include the proper law of planetary motion as part of your answer.
The shape of planetary orbits affects their orbital velocity through Kepler's second law of planetary motion, also known as the law of equal areas. According to this law, a planet sweeps out equal areas in equal time intervals as it moves along its orbit. Since the shape of an elliptical orbit is not uniform, the distance between the planet and the Sun varies at different points of the orbit. As the planet gets closer to the Sun, it moves faster to cover a greater distance in a shorter time, resulting in an increase in orbital velocity. Conversely, when the planet is farther away from the Sun, it moves slower due to covering a smaller distance in a longer time, resulting in a decrease in orbital velocity.
Which form of Kepler’s third law can you use to relate the period T and radius r of a planet in our solar system as long as the unit year is used for the period and astronomical unit is used for the radius?(1 point)
Responses
T2=r3
cap t squared is equal to r cubed
T=r2
cap t is equal to r squared
T2=r
cap t squared is equal to r
T3=r2
Responses
T2=r3
cap t squared is equal to r cubed
T=r2
cap t is equal to r squared
T2=r
cap t squared is equal to r
T3=r2
The correct answer is: T2=r3 (T squared is equal to r cubed). This form of Kepler's third law relates the period (T) of a planet's orbit around the Sun to the radius (r) of its orbit. In this equation, the period is squared (T2) and the radius is cubed (r3), highlighting the relationship between the two variables.
The mass of an object doubles. What happens to the gravitational force between it and another object whose mass stays the same, assuming they remain the same distance apart?(1 point)
Responses
The amount of the gravitational force quadruples.
The amount of the gravitational force quadruples.
The amount of the gravitational force remains the same.
The amount of the gravitational force remains the same.
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force doubles.
Responses
The amount of the gravitational force quadruples.
The amount of the gravitational force quadruples.
The amount of the gravitational force remains the same.
The amount of the gravitational force remains the same.
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force doubles.
The correct answer is: The amount of the gravitational force doubles. The gravitational force between two objects is directly proportional to the product of their masses. As one object's mass doubles while the other object's mass remains the same, the gravitational force between them will also double. This is because an increase in mass leads to a stronger gravitational attraction between the objects.
In 3-5 sentences, describe how Copernicus developed his model of the solar system. In your answer, include an explanation for why his model was, or was not, readily accepted at the time
Copernicus developed his model of the solar system by combining observations, mathematical calculations, and his own ideas. He proposed that the Sun, not the Earth, was at the center of the universe, and that the planets, including Earth, revolved around it in circular orbits. This model, known as heliocentrism, was a departure from the prevailing geocentric view that had been dominant for centuries.
At the time, Copernicus' model was not readily accepted due to several reasons. Firstly, it challenged the widely accepted religious and philosophical beliefs of the time. It contradicted the teachings of the Catholic Church, which held that Earth was at the center of the universe. Additionally, Copernicus' model did not provide significantly better predictions than the existing geocentric models, which relied on complicated systems of epicycles to explain planetary motions. Furthermore, the lack of solid evidence and technological advancements to support heliocentrism made it difficult for many to fully embrace Copernicus' revolutionary ideas.
It was only later, with the work of Galileo, Kepler, and others, that further evidence and observations helped solidify the heliocentric model and eventually led to its widespread acceptance.
At the time, Copernicus' model was not readily accepted due to several reasons. Firstly, it challenged the widely accepted religious and philosophical beliefs of the time. It contradicted the teachings of the Catholic Church, which held that Earth was at the center of the universe. Additionally, Copernicus' model did not provide significantly better predictions than the existing geocentric models, which relied on complicated systems of epicycles to explain planetary motions. Furthermore, the lack of solid evidence and technological advancements to support heliocentrism made it difficult for many to fully embrace Copernicus' revolutionary ideas.
It was only later, with the work of Galileo, Kepler, and others, that further evidence and observations helped solidify the heliocentric model and eventually led to its widespread acceptance.
Which of the following statements about Newton's theory of universal gravitation are true? Select the three correct answers.(2 points)
Responses
The theory applies only to objects on Earth.
The theory applies only to objects on Earth.
The theory applies to all objects in the universe.
The theory applies to all objects in the universe.
Gravitational force increases as the distance between objects increases.
Gravitational force increases as the distance between objects increases.
Gravitational force increases as mass of objects decreases.
Gravitational force increases as mass of objects decreases.
Gravitational force increases as the distance between objects decreases.
Gravitational force increases as the distance between objects decreases.
Gravitational force increases as the mass of objects increases.
Responses
The theory applies only to objects on Earth.
The theory applies only to objects on Earth.
The theory applies to all objects in the universe.
The theory applies to all objects in the universe.
Gravitational force increases as the distance between objects increases.
Gravitational force increases as the distance between objects increases.
Gravitational force increases as mass of objects decreases.
Gravitational force increases as mass of objects decreases.
Gravitational force increases as the distance between objects decreases.
Gravitational force increases as the distance between objects decreases.
Gravitational force increases as the mass of objects increases.
The three correct answers are:
1. The theory applies to all objects in the universe.
2. Gravitational force increases as the mass of objects increases.
3. Gravitational force increases as the distance between objects decreases.
1. The theory applies to all objects in the universe.
2. Gravitational force increases as the mass of objects increases.
3. Gravitational force increases as the distance between objects decreases.
A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 5r?(1 point)
Responses
15√v
the fraction with numerator 1 and denominator square root of 5 v
15v
1 fifth v
5–√v
square root of 5 v
5v
Responses
15√v
the fraction with numerator 1 and denominator square root of 5 v
15v
1 fifth v
5–√v
square root of 5 v
5v
The correct answer is: 5√v (square root of 5v). When the satellite is moved to an orbital radius of 5r, the velocity of the satellite is given by the equation v' = √(GM/5r), where v' represents the new velocity, G is the gravitational constant, and M is the mass of the Earth. Simplifying this equation, we get v' = (1/√5)√v, which can be written as √(5v)/√5 or 5√v.
Based on Kepler's observations about planetary motion, what is the relationship between a planet's orbital velocity and its distance from the sun?(1 point)
Responses
As distance is cut in half, orbital velocity decreases.
As distance is cut in half, orbital velocity decreases.
The greater the distance, the slower the orbital velocity.
The greater the distance, the slower the orbital velocity.
The greater the distance, the greater the orbital velocity.
The greater the distance, the greater the orbital velocity.
Distance has no effect on orbital velocity.
Responses
As distance is cut in half, orbital velocity decreases.
As distance is cut in half, orbital velocity decreases.
The greater the distance, the slower the orbital velocity.
The greater the distance, the slower the orbital velocity.
The greater the distance, the greater the orbital velocity.
The greater the distance, the greater the orbital velocity.
Distance has no effect on orbital velocity.
The correct answer is: The greater the distance, the slower the orbital velocity. According to Kepler's observations about planetary motion, as a planet's distance from the Sun increases, its orbital velocity decreases. This relationship is known as Kepler's second law of planetary motion or the law of equal areas. It states that a planet sweeps out equal areas in equal time intervals as it moves along its elliptical orbit, resulting in a slower orbital velocity when farther from the Sun.
Which did Kepler notice about planetary motion that caused him to propose Kepler’s first law of orbital motion?(1 point)
Responses
The distance to the sun varies.
The distance to the sun varies.
The planets have circular orbits.
The planets have circular orbits.
Most planets have highly elliptical orbits.
Most planets have highly elliptical orbits.
The distance between Mars and the sun is constant.
Responses
The distance to the sun varies.
The distance to the sun varies.
The planets have circular orbits.
The planets have circular orbits.
Most planets have highly elliptical orbits.
Most planets have highly elliptical orbits.
The distance between Mars and the sun is constant.
The correct answer is: The planets have circular orbits. Kepler noticed that the planets did not have perfect circular orbits, but rather elliptical ones. This observation led him to propose Kepler's first law of orbital motion, which states that the planets move around the Sun in elliptical orbits, with the Sun located at one of the foci of the ellipse. This was a significant departure from the previous belief that planetary orbits were perfectly circular.
n 3-5 sentences, analyze why Aristotle's and Ptolemy's models were accepted for more than a thousand years in spite of being completely incorrect. In your answer, use the term geocentric
Aristotle's and Ptolemy's geocentric models of the universe were accepted for more than a thousand years for several reasons. Firstly, these models aligned with the prevailing religious and philosophical beliefs of the time, which held Earth as the center of the universe. Additionally, the geocentric models provided a satisfactory explanation for the observed motions of the celestial bodies using complex systems of epicycles, deferents, and equants. These models also had a long-standing reputation and authority, as they were based on the works of respected philosophers, including Aristotle. It was not until Copernicus introduced the heliocentric model, supported by observational evidence, that the geocentric worldview was significantly challenged.
What shape is the moon's orbit around Earth?(1 point)
Responses
a circle
a circle
an ellipse that is almost circular
an ellipse that is almost circular
a spiral
a spiral
an ellipse that is elongated
Responses
a circle
a circle
an ellipse that is almost circular
an ellipse that is almost circular
a spiral
a spiral
an ellipse that is elongated
The correct answer is: an ellipse that is almost circular. The moon's orbit around Earth is not a perfect circle but rather an elliptical shape. While the orbit is not a perfect circle, it is very close to being circular. This means that the distance between the moon and Earth varies slightly as it moves along its orbit, but the overall shape is more circular than elongated.
An asteroid approaches Jupiter and is slung around into a new trajectory across the solar system. Which of the following are possible? Select the three correct answers.(2 points)
Responses
The asteroid enters a stable elliptical orbit around the sun.
The asteroid enters a stable elliptical orbit around the sun.
The asteroid adopts an unusual orbit around the sun, such as an egg shape.
The asteroid adopts an unusual orbit around the sun, such as an egg shape.
The asteroid spirals into the sun.
The asteroid spirals into the sun.
The asteroid falls into an irregular orbit around Jupiter.
The asteroid falls into an irregular orbit around Jupiter.
The asteroid continues out of the solar system.
The asteroid continues out of the solar system.
The asteroid slows down as it passes around Jupiter.
Responses
The asteroid enters a stable elliptical orbit around the sun.
The asteroid enters a stable elliptical orbit around the sun.
The asteroid adopts an unusual orbit around the sun, such as an egg shape.
The asteroid adopts an unusual orbit around the sun, such as an egg shape.
The asteroid spirals into the sun.
The asteroid spirals into the sun.
The asteroid falls into an irregular orbit around Jupiter.
The asteroid falls into an irregular orbit around Jupiter.
The asteroid continues out of the solar system.
The asteroid continues out of the solar system.
The asteroid slows down as it passes around Jupiter.
The three correct answers are:
1. The asteroid enters a stable elliptical orbit around the sun.
2. The asteroid continues out of the solar system.
3. The asteroid slows down as it passes around Jupiter.
When an asteroid approaches Jupiter and is influenced by its gravitational pull, it can be slung into a new trajectory. Depending on the specific conditions and the angle of approach, the asteroid can either enter a stable elliptical orbit around the sun, continue on a trajectory out of the solar system, or experience a deceleration as it passes around Jupiter. The other options of falling into an irregular orbit around Jupiter, spiraling into the sun, or adopting an unusual orbit such as an egg shape are less likely outcomes based on the scenario described.
1. The asteroid enters a stable elliptical orbit around the sun.
2. The asteroid continues out of the solar system.
3. The asteroid slows down as it passes around Jupiter.
When an asteroid approaches Jupiter and is influenced by its gravitational pull, it can be slung into a new trajectory. Depending on the specific conditions and the angle of approach, the asteroid can either enter a stable elliptical orbit around the sun, continue on a trajectory out of the solar system, or experience a deceleration as it passes around Jupiter. The other options of falling into an irregular orbit around Jupiter, spiraling into the sun, or adopting an unusual orbit such as an egg shape are less likely outcomes based on the scenario described.
For a moon orbiting its planet, rp
is the shortest distance between the moon and its planet and ra
is the longest distance between the moon and its planet. What is a moon's orbital eccentricity if rp
is equal to 0.27ra
?(1 point)
Responses
0.57
0.57
0.65
0.65
0.27
0.27
0.48
is the shortest distance between the moon and its planet and ra
is the longest distance between the moon and its planet. What is a moon's orbital eccentricity if rp
is equal to 0.27ra
?(1 point)
Responses
0.57
0.57
0.65
0.65
0.27
0.27
0.48
The correct answer is: 0.57. Orbital eccentricity is calculated as (ra - rp) / (ra + rp). Given that rp is equal to 0.27ra, we can substitute these values into the formula: (ra - 0.27ra) / (ra + 0.27ra) = 0.73ra / 1.27ra = 0.57. Therefore, the moon's orbital eccentricity is 0.57 in this scenario.
Which statements about the geocentric model are false? Select the two correct answers.(1 point)
Responses
It explains why Mars appears to move backward for a few months approximately every two years.
It explains why Mars appears to move backward for a few months approximately every two years.
It shows the Sun at the center of the solar system.
It shows the Sun at the center of the solar system.
It shows the orbits of the planets as circular.
It shows the orbits of the planets as circular.
It shows Earth at the center of the solar system.
Responses
It explains why Mars appears to move backward for a few months approximately every two years.
It explains why Mars appears to move backward for a few months approximately every two years.
It shows the Sun at the center of the solar system.
It shows the Sun at the center of the solar system.
It shows the orbits of the planets as circular.
It shows the orbits of the planets as circular.
It shows Earth at the center of the solar system.
The two correct answers are:
1. It shows the Sun at the center of the solar system.
2. It shows the orbits of the planets as circular.
The geocentric model actually shows Earth at the center of the solar system, not the Sun. Additionally, the geocentric model depicts the orbits of the planets as circular, which is not accurate according to Kepler's observations of elliptical orbits. The false statements are that the geocentric model shows the Sun at the center of the solar system and that it shows the orbits of the planets as circular.
1. It shows the Sun at the center of the solar system.
2. It shows the orbits of the planets as circular.
The geocentric model actually shows Earth at the center of the solar system, not the Sun. Additionally, the geocentric model depicts the orbits of the planets as circular, which is not accurate according to Kepler's observations of elliptical orbits. The false statements are that the geocentric model shows the Sun at the center of the solar system and that it shows the orbits of the planets as circular.
A line between a planet and the sun sweeps out two equal areas at different places as it moves along its orbit. Which factor remains constant as this happens?(1 point)
Responses
the distance the planet moves along its orbit while it sweeps out the area
the distance the planet moves along its orbit while it sweeps out the area
the time required to sweep out the areas
the time required to sweep out the areas
the planet’s speed as it sweeps out the areas
the planet’s speed as it sweeps out the areas
the distance from the sun to the planet while it sweeps out the areas
Responses
the distance the planet moves along its orbit while it sweeps out the area
the distance the planet moves along its orbit while it sweeps out the area
the time required to sweep out the areas
the time required to sweep out the areas
the planet’s speed as it sweeps out the areas
the planet’s speed as it sweeps out the areas
the distance from the sun to the planet while it sweeps out the areas
The correct answer is: the time required to sweep out the areas. According to Kepler's second law of planetary motion, which is also known as the law of equal areas, a line connecting a planet to the Sun will sweep out equal areas in equal time intervals. This means that as the planet moves along its orbit and sweeps out different areas, the time required to do so remains constant.
3 answers