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