Suppose the Sun were somehow replaced by a star with five times as much mass. How long would the Earth year last in this last case? (hint: Newton’s version of Kepler’s 3rd Law)
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Suppose the Sun were somehow replaced by a star with five times as much mass. How long would the Earth year last in this last case? (hint: Newton’s version of Kepler’s 3rd Law)
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- In a distant star system there are many inhabitable planets. One of these planets is named Qomar. Qomar is 3.2 AU's from its star and takes 6.5 Earth years to go around its star once. There is another planet in the same star system called Ferenginar. Ferenginar is 0.9 AUs from the star. What is the length of a Ferengi year (on Ferenginar) in terms of Earth years?Two exoplanets, UCF1.01 and UCF1.02 are found revolving around the same star. The period of planet UCF1.01 is 92.4 days, and that of planet UCF1.02 is 7.1 days. If the average distance of UCF1.01 to the sun is 5,828.0 km, what is the average distance of UCF1.02 to the sun in km? Please keep four digits after decimal points.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?
- (a) Jupiter's third-largest natural satellite, Io, follows an orbit with a semimajor axis of 422,000 km (4.22 ✕ 105 km) and a period of 1.77 Earth days (PIo = 1.77 d). To use Kepler's Third Law, we first must convert Io's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 ✕ 108 km). Convert Io's a value to AU and record the result. aIo = AU (b) One Earth year is about 365 days. Convert Io's orbital period to Earth years and record the result. PIo = yr (c) Use the Kepler's Third Law Calculator to calculate Jupiter's mass in solar units. Record the result. MJup(Io) = MSun (d) Based on this result, Jupiter's mass is about that of the Sun. Jupiter has a similar fraction of the Sun's volume. The two objects therefore have rather similar density! In fact, Jupiter has a fairly similar composition as well: most of its mass is in the form of hydrogen and helium.Mars' period (its "year") was noted by Kepler to be about 687 days (Earth days), which is (687d / 365 d) = 1.88 yr. Determine the distance of Mars from the Sun using the Earth as reference. (The distance of Earth from the Sun is 1.50 x 10 m) !3! Thu TMS IMS TE TES TES TE 2 28 x 10 m TES yr After reading and understanding the concept Gravity, please do the following problems: 1. What keeps a satellite up in its orbit around the Earth?Consider a planet of radius 10 x 106 m for which the length of a sidereal day is 5 x 104 s. Calculate the speed you would have with respect to the center of the planet, in m/s, if you were at a latitude of 5 degrees north. (Please answer to the fourth decimal place - i.e 14.3225)
- A planet with mass 8.07x1023 kg orbits a star with mass 1.18x1030 kg. The orbit is circular, and the distance from the planet to the sun is 121x106 km. What is the length of a year on this planet? Give your answer in earth years (1 earth year = 31,557,600 seconds).(to two decimal places): (what is ‘h’?) Eccentricity of earth orbit is 0.0167 µ(sun) = 1.32712E+11 km^3/s^ semimajor axis of Earth orbit = 1.49598E+08 need to figure out what ‘h’ is. a) Calculate the speed of the earth around the sun at aphelion? (29.29 KM/S) b) At perihelion? (30.29 KM/S)Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.
- The value of Gme/re2, where me is the mass of the earth, re is the radius of the earth, and G is the universal gravitational constant is (enter your answer with three significant figures)A new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of 12 AU and takes 117 days to orbit the star. Determine the mass of the star. State your answer with appropriate mks units. [NOTE: AU ..stands.for...astronomical unit". It is the average distance between Earth & the Sun. 1 AU≈ 1.496 x 1011 m.] Enter a number with units. I be quite large and your calculator will display the answer as a power of 10. If, as an example, your answer was 8.54 x 1056, you would type "8.54e56" into the answer box (remember to state your units with your answer).]On the evening of an autumnal equinox day Siddhant noticed that Mars was exactly along the north-south meridian in his sky at the exact moment when the sun was setting. In other words, the Sun and Mars subtended an angle of exactly 90° as measured from the Earth. If the orbital radius of Mars is 1.52 au, What will be the approximate rise time of the mars on the next autumnal equinox day?