Galileo\'s telescopes were not of high quality by modern standards. When Jupiter
ID: 106782 • Letter: G
Question
Galileo's telescopes were not of high quality by modern standards. When Jupiter was closest to Earth, he was able to see its disk and moons, but he never reported seeing the disk or features on Mars. What is a good explanation for this difference? (Hints: Use the small-angle formula to find the angular diameter of Mars when it is closest to Earth. How does that compare with the maximum angular diameter of Jupiter? [Assume circular orbits with radii equal to the average distance from the sun.] At its closest, Jupiter is 4 AU from Earth and Mars is 0.5 AU from Earth. Jupiter is 0.000477 AU and Mars is 0.0000226 AU in diameter.)
If a planet has an average distance from the sun of 28 AU, what is its orbital period in years?
If a space probe is sent into an orbit around the sun that brings it as close as 1.0 AU and as far away as 4.4 AU, what will be its orbital period in years?
Mars orbits the sun with a period of 1.87 years. What is its average distance from the sun in AU?
The angular size of Jupiter is smaller than the angular size of Mars. The angular size of Mars is smaller than the angular size of Jupiter. They both have the same angular size. Not enough information is given to say anything about their relative angular sizes. OExplanation / Answer
1.) Question - Galileo's telescopes were not of high quality by modern standards. When Jupiter was closest to Earth, he was able to see its disk and moons, but he never reported seeing the disk or features on Mars. What is a good explanation for this difference? (Hints: Use the small-angle formula to find the angular diameter of Mars when it is closest to Earth. How does that compare with the maximum angular diameter of Jupiter? [Assume circular orbits with radii equal to the average distance from the sun.] At its closest, Jupiter is 4 AU from Earth and Mars is 0.5 AU from Earth. Jupiter is 0.000477 AU and Mars is 0.0000226 AU in diameter.)
Answer - B.) The angular size of Mars is smaller than the angular size of Jupiter.
Reason - Angular diameter of Mars = 206265 X (Actual diameter / Distance)
=206265x (0.0000226/0.5)
=9.323178
- Angular diameter of Jupiter = 206265 X (Actual diameter / Distance)
=206265x (0.000477/4)
=24.59710125
Therefore, the answer.
2.) Question - If a planet has an average distance from the sun of 28 AU, what is its orbital period in years?
Answer - B.) 148 years.
Reason - Square root of Cubed value of the distance from the sun. Cube of 28 = 21952, square root of 21952 = 148.162, Therefore the answer.
3.) Question - If a space probe is sent into an orbit around the sun that brings it as close as 1.0 AU and as far away as 4.4 AU, what will be its orbital period in years?
Answer - C.) 4.4
Reason - First find the average between closest disance and farthest distance = (4.4+1.0)/2 = 2.7
Then by using Kepler's 3rd law, T^2 = R^3 where T = period in earth years and R = semi-major axis of orbit in AU.
T^2 = 2.7^3
T^2 = 19.683
T = 4.4365 . (where square root of 19.683 is 4.4365).
4.) Question - Mars orbits the sun with a period of 1.87 years. What is its average distance from the sun in AU?
Answer - A.) 1.87
Reason - Distance from mars to sun = 227900000 km , therefore 1.52 AU (where 1 AU = approximately 150 million Km), Using kepler's third law P2 = a3,
where
therefore, P2 = 1.52*1.52*1.52
P2 = 3.511808
P = Square root of 3.511808
P = 1.8739.
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