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
1/5√v
1/5√v
1/5v
1/5v
√5v
√5v
5v
1/5v
The correct answer is 5v. When a satellite is moved to a new orbital radius, its velocity remains constant. Therefore, if the original velocity was v, then when the satellite is moved to an orbital radius of 5r, its velocity will still be 5v.
To determine the velocity of a satellite when it is moved to an orbital radius of 5r, we can use the concept of conservation of angular momentum for objects in circular motion.
The angular momentum of an object in circular motion is given by the product of its moment of inertia (mass x radius squared) and its angular velocity. Since the mass of the satellite remains the same, the angular momentum will also remain constant.
Mathematically, the angular momentum can be expressed as:
L = m * r * v
where L is the angular momentum, m is the mass of the satellite, r is the orbital radius, and v is the velocity.
To find the velocity when the satellite is moved to an orbital radius of 5r, we can set up the equation for the initial and final states:
L1 = m * r * v
L2 = m * (5r) * v2
Since the angular momentum is conserved, we can equate L1 and L2:
m * r * v = m * (5r) * v2
The mass (m) can be canceled out from both sides of the equation, giving:
r * v = 5r * v2
Dividing both sides of the equation by r and simplifying, we get:
v = 5v2
Therefore, the velocity (v2) of the satellite when it is moved to an orbital radius of 5r is equal to 5 times the original velocity (v).
Hence, the correct option is 5v.
What shape is the moon's orbit around Earth?(1 point)
Responses
a spiral
a spiral
a circle
a circle
an ellipse that is almost circular
an ellipse that is almost circular
an ellipse that is elongated
an ellipse that is almost circular
Which statements about the geocentric model are false? Select the two correct answers.(1 point)
Responses
It shows the orbits of the planets as circular.
It shows the orbits of the planets as circular.
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 Earth at the center of the solar system.
It shows Earth at the center of the solar system.
It shows the Sun at the center of the solar system.
The two correct answers are:
It shows the orbits of the planets as circular.
It shows the Sun at the center of the solar system.
The geocentric model does not accurately depict the orbits of the planets as circular. In reality, the planets orbit the Sun in elliptical paths. Additionally, the geocentric model places Earth at the center of the solar system, not the Sun.
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.(4 points)
Copernicus developed his model of the solar system by proposing that the Sun is at the center, with the planets including Earth revolving around it in circular orbits. This heliocentric model challenged the prevailing geocentric model, which placed Earth at the center. Copernicus' model was based on detailed observations of planetary motions and mathematical calculations.
At the time, Copernicus' model faced significant opposition and was not readily accepted because it contradicted long-held beliefs and challenged religious and philosophical views. The geocentric model had been widely accepted for centuries, and Copernicus' heliocentric model required a paradigm shift in thinking. It took time for his ideas to gain wider acceptance, with astronomers like Galileo providing further evidence supporting the heliocentric model and eventually leading to its widespread adoption.
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
T^3=r^2
t^3=r^2
T^2=r
T^2=r
T^2=r^3
T^2=r^3
T=r^2
T=r^2
T^2=r^3
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.
Gravitational force increases as mass of objects decreases.
Gravitational force increases as mass of objects decreases.
The theory applies to all objects in the universe.
The theory applies to all objects in the universe.
Gravitational force increases as the mass of objects increases.
Gravitational force increases as the mass of objects increases.
Gravitational force increases as the distance between objects increases.
Gravitational force increases as the distance between objects increases.
Gravitational force increases as the distance between objects decreases.
The three correct statements about Newton's theory of universal gravitation are:
1. The theory applies to all objects in the universe.
2. Gravitational force increases as the mass of objects increases.
3. Gravitational force decreases as the distance between objects increases.
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.(4 points)
The shape of planetary orbits, specifically referring to their eccentricity or how elongated they are, directly affects their orbital velocity. This is described by Kepler's Second Law of Planetary Motion, also known as the Law of Equal Areas. According to this law, a planet will sweep out equal areas in equal time intervals as it moves around its orbit.
When a planet is closer to the Sun, it moves faster in its orbit. This is because as it sweeps out an equal area in a shorter time, it covers a larger arc in the same time interval. Conversely, when a planet is farther from the Sun, it moves slower in its orbit. This is due to the need to cover a smaller arc in the same time interval in order to sweep out equal areas.
Therefore, a more eccentric or elongated orbit will result in varying distances between the planet and the Sun along its orbit, leading to corresponding changes in orbital velocity. Planets with more circular orbits will have a fairly constant orbital velocity, while those with more elliptical orbits will experience greater variations in velocity throughout their orbit.
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 decreases by one-half.
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force quadruples.
The amount of the gravitational force quadruples.
The amount of the gravitational force doubles.
The amount of the gravitational force doubles.
The amount of the gravitational force remains the same.
The amount of the gravitational force doubles. According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses. Therefore, if one object's mass doubles while the other object's mass remains the same, the gravitational force between them will double as well.
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.
The planets have circular orbits.
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 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 enters a stable elliptical orbit around the sun.
The asteroid enters a stable elliptical orbit around the sun.
The asteroid spirals into the sun.
The asteroid spirals into the sun.
The asteroid continues out of the solar system.
The asteroid continues out of the solar system.
The asteroid falls into an irregular orbit around Jupiter.
The asteroid falls into an irregular orbit around Jupiter.
The asteroid slows down as it passes around Jupiter.
The three correct answers are:
1. The asteroid adopts an unusual orbit around the sun, such as an egg shape.
2. The asteroid enters a stable elliptical orbit around the sun.
3. The asteroid continues out of the solar system.
When an asteroid approaches Jupiter closely, it can be affected by Jupiter's gravity and be slung into a new trajectory. Depending on the specific conditions and the interaction between the asteroid and Jupiter, it is possible for the asteroid to adopt an orbit that is unusual and not perfectly circular, such as an egg shape (1). It is also possible for the asteroid to enter a stable elliptical orbit around the sun (2) if its velocity and trajectory are adjusted by Jupiter's gravity. Additionally, if the asteroid gains enough velocity from the gravitational encounter with Jupiter, it may continue on a trajectory that carries it out of the solar system (3).
Which are features of Copernicus's model of the solar system? Select the three correct answers.(2 points)
Responses
Earth is fixed to a crystalline sphere.
Earth is fixed to a crystalline sphere.
The planets move in perfect circles.
The planets move in perfect circles.
All planets orbit the Sun at the same speed.
All planets orbit the Sun at the same speed.
The outer planets move in epicycles.
The outer planets move in epicycles.
The stars are fixed to an outer sphere.
The stars are fixed to an outer sphere.
The Sun is at the center.
The three correct features of Copernicus's model of the solar system are:
1. The planets move in perfect circles.
2. All planets orbit the Sun at the same speed.
3. The Sun is at the center.
In Copernicus's heliocentric model, he proposed that the planets moved in perfect circles around the Sun, which was placed at the center of the solar system. He also suggested that all planets moved at the same speed in their orbits around the Sun. However, it is important to note that these features were later revised and refined by Johannes Kepler, who introduced the concept of elliptical orbits and varying planetary speeds.
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 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 distance from the sun to the planet while it sweeps out the areas
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 remains constant. According to Kepler's Second Law of Planetary Motion, also known as the Law of Equal Areas, a line that connects a planet to the Sun will sweep out equal areas in equal time intervals. This means that, regardless of where the planet is in its orbit, the time required to sweep out a given area remains the same.
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
0.65
0.65
0.27
0.27
0.57
0.57
0.48
The moon's orbital eccentricity is 0.65. Orbital eccentricity is determined by the ratio of the difference between the shortest distance (rp) and the longest distance (ra) between the moon and its planet, divided by the sum of those distances. In this case, if rp is equal to 0.27ra, the difference between rp and ra is 0.73ra. Dividing this by the sum of rp and ra (which is 1.27ra) gives a quotient of approximately 0.57, which represents the eccentricity. However, none of the given options match this value, so there seems to be a discrepancy in the provided answers.
n 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.(4 points)
Copernicus developed his model of the solar system by proposing a heliocentric system, in which the Sun was at the center and the planets, including Earth, revolved around it in circular orbits. He studied ancient Greek texts, astronomical observations, and mathematical principles to formulate his model. However, his model was not readily accepted at the time due to several reasons. First, the prevailing geocentric model, with Earth at the center, was supported by religious and philosophical beliefs. Second, Copernicus' model presented significant challenges to existing astronomical theories and required a paradigm shift in thinking. Lastly, the lack of direct observational evidence and the absence of accurate mathematical calculations hindered the immediate acceptance of his model. It took time, further observations by later astronomers like Kepler and Galileo, and additional evidence to gradually shift and establish the acceptance of Copernicus' heliocentric model.
Which statements about the geocentric model are false? Select the two correct answers.(1 point)
Responses
It shows Earth at the center of the solar system.
It shows Earth at the center of the solar system.
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.
The two false statements about the geocentric model are:
1. It shows the Sun at the center of the solar system.
2. It shows the orbits of the planets as circular.
In the geocentric model, Earth is believed to be at the center of the universe, not the Sun. Additionally, the geocentric model proposed that the planets moved in circular orbits around Earth, which we now know is not accurate.
In 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.(4 points)
Aristotle's and Ptolemy's geocentric models were accepted and believed for more than a thousand years due to a combination of factors. Firstly, the models were consistent with people's observations of the apparent motion of celestial bodies. Second, these models were aligned with prevailing philosophical and religious beliefs, with the Earth being viewed as the center of the universe. Additionally, the geocentric models provided a sense of stability and order in the cosmos. Moreover, the lack of alternative models and the limited availability of accurate measurements and observations impeded the development and acceptance of new theories.
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
Distance has no effect on orbital velocity.
Distance has no effect on orbital velocity.
The greater the distance, the slower the orbital velocity.
The greater the distance, the slower the orbital velocity.
As distance is cut in half, orbital velocity decreases.
As distance is cut in half, orbital velocity decreases.
The greater the distance, the greater the orbital velocity.