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 3r?(1 point) Responses 3v 3 v 3–√v square root of 3 v 13v 1 third v 13√v
For which project would knowledge of Kepler's laws prove most useful?(1 point) Responses calculating the mass of Earth calculating the mass of Earth measuring the distance between Earth and the moon measuring the distance between Earth and the moon putting a communications satellite in Earth orbit putting a communications satellite in Earth orbit determining the structure of the solar system's planets
The correct answer is "determining the structure of the solar system's planets".
A satellite is orbiting Earth at an orbital radius of 7.3×104 m. What is its velocity in terms of G and the mass of Earth, mp ? (Ignore units in the answer.)(1 point) Responses (2.7×102)Gmp−−−−√ open paren 2 point 7 times 10 squared close paren times square root of cap g m sub p end root (3.7×10−3)Gmp−−−−√ open paren 3 point 7 times 10 to the negative 3 power close paren times square root of cap g m sub p end root (7.3×104)Gmp−−−−√ open paren 7 point 3 times 10 to the 4th power close paren times square root of cap g m sub p end root (1.4×10−5)Gmp−−−−√
The correct answer is "(7.3×104)Gmp−−−−√", which means the orbital velocity is equal to the square root of G times the mass of Earth, mp, divided by the orbital radius (7.3×104 m).
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 affects their orbital velocity through Kepler's Second Law of Planetary Motion, also known as the Law of Areas. According to this law, a planet sweeps out equal areas in equal time intervals as it moves along its elliptical orbit, which means that a planet travels faster when it is closer to the Sun and slower when it is farther away. This means that as a planet moves through its elliptical orbit, its distance from the Sun changes, resulting in variations in its orbital velocity.
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, known as the heliocentric model, by challenging the prevailing geocentric model that placed Earth at the center of the universe. He proposed that the Sun, not Earth, was the center around which the planets revolved. Copernicus relied on observations, mathematical calculations, and his understanding of the movements of celestial bodies to support his heliocentric model. However, his model was not readily accepted at the time due to a combination of factors including religious beliefs, societal norms, and the lack of direct evidence or conclusive proof for his claims. It took several decades and the work of subsequent astronomers like Galileo and Kepler to further validate and popularize the heliocentric model.
The gravitational force between two objects is 360 Newtons. The objects move such that their distance is now three times their original distance. What is the new gravitational force between the objects?(1 point)
