Sam is an astronomer on planet Hua, which orbits the distant star Barnard. It has recently been accepted that Hua is spherical in shape, although its exact size is unknown. While studying in the library, in the city of Joy, Sam learns that during equinox, Barnard is directly overhead in the city of Bar, located 1500.0 km north of his location. On the equinox, Sam goes outside and measures the altitude of Barnard at 83 degrees. What is the radius of Hua in km?
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- You are an astronomer on planet Tirth, which orbits a distant star. It has recently been accepted that Tirth is spherical in shape, though no one knows its size. One day, you learn that on the equinox your sun is directly overhead in the city of Tyene, located 450 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 85 ∘∘. What is the circumference of Tirth? Express your answer in kilometers to two significant figures.Consider a star of mass M₁ that hosts a planet of mass M₂ on a circular orbit with semi- major axis a. The mass of the planet is related to the orbital velocity of the star by the expression G M₂1 Μια Using Kepler's 3rd law show that this expression can be written as V₁ = 2πG (27²) ¹/3 9 M²P where P is the orbital period of the planet around the star. V₁ = M₂Determine what the period of revolution of the Earth would be if its distance from the Sun were 3.5 AU rather than 1 AU. Assume that the mass of the Sun remains the same. The final unit should be y in the answer.
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- Two exoplanets, A and B are found revolving around the same star. The period of planet A is 62 days, and that of planet UCF1.02 is 54.5 days. If the average distance of planet A to the sun is 2,374.3 km, what is the average distance of planet B to the sun in km? Please keep four digits after decimal points.The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the Sun. A light-year is the distance that light travels in one year (365 days). How far away, in kilometers, is Proxima Centauri from the Sun?Express your answer using two significant figures.