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E) From D) what is the angular speed of the Earth in orbit? F) From E) and the estimates above, what is the linear speed v of Earth in its orbit? G) From F) and the estimates what is the acceleration of Earth in its orbit?

E) From D) what is the angular speed of the Earth in orbit? F) From E) and the estimates above, what is the linear speed v of Earth in its orbit? G) From F) and the estimates what is the acceleration of Earth in its orbit?

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please answer parts E, F, and G
In Newton's late 17th century era, there were relatively accurate estimates, from terrestrial and astronomical observations and experiments, of the distance of the Earth to the Sun (dEs = 150 million 1. %3D kilometers) and the circumference of the Earth (CE = 40,000 kilometers [the meter was later defined during the late 18th century French revolution in relation to the size of the Earth]). Newton further estimated, likely based on the density of rocks, that the Earth was a solid sphere with a density about 6 times the density of water, which has density of pwater = 1 g/cm3. A) Based on these estimates, what is the mass of the Earth Mp? B) From Newton's 2"d law, what is the magnitude of the force on a 1 kg mass falling freely near the surface of the Earth? C) The force in B) is due to Earth's gravity, which from Newton's law of universal law of gravitation is given by Fg = G mMg where the radius of the Earth Rg serves as the distance RE2 between the two masses. Use this formula, the result in B), the mass of the Earth from A), and the estimates above to deduce a value for the universal constant G. Check that it reasonably agrees with the modern "textbook" value. D) What is the period of the Earth's orbit around the sun (here assumed to be circular and uniform)? E) From D) what is the angular speed of the Earth in orbit? F) From E) and the estimates above, what is the linear speed v of Earth in its orbit? G) From F) and the estimates what is the acceleration of Earth in its orbit? H) From Newton's 2nd law and G) what is the force on the Earth in its orbit? I) If the force in H) is due to the gravitational pull of the sun, use the values you've calculated so far and Newton's universal law of gravitation to find the mass of the sun Ms. J) How far from the (center of the) sun is the center of mass of the Earth-Sun system? Note that this is the point, and not the sun, that is in fact fixed in the com frame of this system. Is this distance larger or smaller than the radius of the sun, RĘ ~ 700,000 km? [A nice mnemonic to help develop your sense of scale at the planetary level is that Jupiter's radius is about 10 times bigger than Earth's and the Sun's radius is about 10 times bigger than Jupiter's.]
Transcribed Image Text:In Newton's late 17th century era, there were relatively accurate estimates, from terrestrial and astronomical observations and experiments, of the distance of the Earth to the Sun (dEs = 150 million 1. %3D kilometers) and the circumference of the Earth (CE = 40,000 kilometers [the meter was later defined during the late 18th century French revolution in relation to the size of the Earth]). Newton further estimated, likely based on the density of rocks, that the Earth was a solid sphere with a density about 6 times the density of water, which has density of pwater = 1 g/cm3. A) Based on these estimates, what is the mass of the Earth Mp? B) From Newton's 2"d law, what is the magnitude of the force on a 1 kg mass falling freely near the surface of the Earth? C) The force in B) is due to Earth's gravity, which from Newton's law of universal law of gravitation is given by Fg = G mMg where the radius of the Earth Rg serves as the distance RE2 between the two masses. Use this formula, the result in B), the mass of the Earth from A), and the estimates above to deduce a value for the universal constant G. Check that it reasonably agrees with the modern "textbook" value. D) What is the period of the Earth's orbit around the sun (here assumed to be circular and uniform)? E) From D) what is the angular speed of the Earth in orbit? F) From E) and the estimates above, what is the linear speed v of Earth in its orbit? G) From F) and the estimates what is the acceleration of Earth in its orbit? H) From Newton's 2nd law and G) what is the force on the Earth in its orbit? I) If the force in H) is due to the gravitational pull of the sun, use the values you've calculated so far and Newton's universal law of gravitation to find the mass of the sun Ms. J) How far from the (center of the) sun is the center of mass of the Earth-Sun system? Note that this is the point, and not the sun, that is in fact fixed in the com frame of this system. Is this distance larger or smaller than the radius of the sun, RĘ ~ 700,000 km? [A nice mnemonic to help develop your sense of scale at the planetary level is that Jupiter's radius is about 10 times bigger than Earth's and the Sun's radius is about 10 times bigger than Jupiter's.]
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