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- When Sedna was discovered in 2003, it was the most distant object known to orbit the Sun. Currently, it is moving toward the inner solar system. Its period is 10,500 years. Its perihelion distance is 75 AU. a. What is its semimajor axis in astronomical units? b. What is its aphelion distance?Check Your Understanding The nearly circular orbit of Saturn has an average radius of about 9.5 AU and has a period of 30 years, whereas Uranus averages about 19 AU and has a period of 84 years. Is this consistent with our results for Halley’s comet?The orbital period of the Earth and Mars are Pg = 365.26 d and P respectively. Assuming circular orbits, the synodic period P, for two planets to be at the same angular position from the Sun can be found using the equation 1 = 686.97 d, %3D Pe Pe a) The last opposition of Mars occurred on 13 Oct 2020. Using the information above, calculate the interval between two consecutive Martian oppositions, and estimate the date of its next opposition. b) It is said that Mars at oppositions near its perihelion occur roughly once every 15 years, with the last event occurring on 27 Jul 2018. Using the synodie period derived, find a more accurate interval, and estimate the date for the next time this event occurs. c) The actual dates for the next Martian opposition and opposition at perihelion are 8 Dec 2022 and 15 Sep 2035, respectively. State two reasons why your estimations may have differed from these dates. In stage 10 of the evolution of a Sun-like star, helium fusion occurs. Write down the…
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- Planet X with a radius of 4.0 Rearth⊕ is found orbiting a star of mass 0.80M⊙ . The eccentricity of its orbit is 0.05, and at its farthest approach to the star, it is 0.63 AU away, while at its closest approach to the star, it is 0.57 AU away. a. How long does it take Planet X to make a complete orbit around its star in years? b.The semi major axis of the planet is changed such that its closest approach to the star is now 2.9 AU. Would the gravitational force exerted by the star on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor? c. The mass of the star was increased to 2.4M⊙ . Would the gravitational force exerted by it on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor? d. What must the mass of Planet X be in Mearth⊕ such that an astronaut on its surface would have the same weight as…Universal Gravitational Constant, G=6,6742867E-11 m3 kg / s2(Note that the exponent is negative)Radius of Earth, RE: 6,3781366E+06 mMass of Earth, ME: 5,9721426E+24 kg Two celestial bodies whose masses are m1 and m2 are revolving around their common center of mass and the distance between them is L. Assuming that they are both point masses, Find the angular speed, tangential speeds of the masses m1 and m2, and period of the motion. m1=7,27210x10^12kg m2=3,85280x10^11kg L=6,16500x10^8m35. Ellipsoid Earth. to its rotation, producing an apparent "centrifugal force" pulling the equator outwards. You, at the north pole, and your friend, at latitude 0, decide to drill through the center of the Earth all the way to the other side. Ignoring the different layers of the Earth, and given that the Earth has a radius R along the poles, rotates along the equator at a speed v, has a constant density o everywhere, the difference between the time it takes to fall to the other side of the Earth through the poles and through latitude 0 is given by: The Earth is actually closer to being an ellipsoid than a sphere due -(e cos! 0 – 5) ) - egR' + v^(e cos/ 0 - f), cgR* At = VazG"o" egR® where a, b, c, d, e, f, a, B, y, e are dimensionless constants and G, g, # are their respective constants. Find Ja|ll + 2|3| +3/5|| + 4|e|". Hint: Don't let that complicated expression taunt you! What can you say about the units of the final expression?