Assume Earth is on a circular orbit around the sun with radius of a.) 1.000001 AU and a period of Pe = 1.000017 years. (The AU was defined as 149,597,870.7 km before the true value was determined; and the "year" here is the Julian year, defined as 365.25 days of 86,400 s each, which differs from the orbital period.) Assume Venus is on a co-planar eircular orbit around the Sun, with radius 0.723332 AU. Let o be the angle between the Earth-Sun line and the Earth-Venus line. Calculate the maximum possible value of ø. When o is at its maximum value, we call this greatest elongation. b.) When Venus is on the side of Earth visible before sunrise, we call this greatest western elongation, and when it's visible after sunset, we call this greatest eastern elongation. When Venus is at greatest eastern elongation, how many hours can it potentially be seen above the horizon after the Sun sets? (If you're a stickler for such things, assume you are on Earth's equator and both Sun and Venus have zero declination.) c.) expressed in Julian years to six digits? d.) is) Using 2= 27/2, what is the orbital frequency of Earth, g, and Venus, 2y? Again, retain at least six digits. s) Using Kepler's laws, what is the orbital period of Venus, Py, %3D
Assume Earth is on a circular orbit around the sun with radius of a.) 1.000001 AU and a period of Pe = 1.000017 years. (The AU was defined as 149,597,870.7 km before the true value was determined; and the "year" here is the Julian year, defined as 365.25 days of 86,400 s each, which differs from the orbital period.) Assume Venus is on a co-planar eircular orbit around the Sun, with radius 0.723332 AU. Let o be the angle between the Earth-Sun line and the Earth-Venus line. Calculate the maximum possible value of ø. When o is at its maximum value, we call this greatest elongation. b.) When Venus is on the side of Earth visible before sunrise, we call this greatest western elongation, and when it's visible after sunset, we call this greatest eastern elongation. When Venus is at greatest eastern elongation, how many hours can it potentially be seen above the horizon after the Sun sets? (If you're a stickler for such things, assume you are on Earth's equator and both Sun and Venus have zero declination.) c.) expressed in Julian years to six digits? d.) is) Using 2= 27/2, what is the orbital frequency of Earth, g, and Venus, 2y? Again, retain at least six digits. s) Using Kepler's laws, what is the orbital period of Venus, Py, %3D
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Transcribed Image Text:Assume Earth is on a circular orbit around the sun with radius of
a.)
1.000001 AU and a period of Pe = 1.000017 years. (The AU was defined as
149,597,870.7 km before the true value was determined; and the "year" here
is the Julian year, defined as 365.25 days of 86,400 s each, which differs from
the orbital period.) Assume Venus is on a co-planar eircular orbit around
the Sun, with radius 0.723332 AU. Let o be the angle between the Earth-Sun
line and the Earth-Venus line. Calculate the maximum possible value of o.
When o is at its maximum value, we call this greatest elongation.
b.)
When Venus is on the side of Earth visible before sunrise, we call this greatest
western elongation, and when it's visible after sunset, we call this greatest
eastern elongation. When Venus is at greatest eastern elongation, how many
hours can it potentially be seen above the horizon after the Sun sets? (If
you're a stickler for such things, assume you are on Earth's equator and both
Sun and Venus have zero declination.)
Using Kepler's laws, what is the orbital period of Venus, Py,
c.)
expressed in Julian years to six digits?
d.) ) Using 2 = 27/S2, what is the orbital frequency of Earth, S2p, and
Venus, 2y? Again, retain at least six digits.
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