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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, Rg = 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.]

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, Rg = 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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M of earth = 6.48x10^24 kg G = 6.136x10^-11 m3/kg s2 T = 31.6x10^6 s w (angular speed) = 198.83x10^-9 rad/s v of earth in orbit = 29.82x10^3 m/s a of earth in orbit = 5.93x10^-3 m/s2 F on earth in orbit = 3.84x10^22 N
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 1. = 150 million 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.
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 1. = 150 million 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.
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, Rg - 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: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, Rg - 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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