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 they would on Earth? e. Planet Y orbits the same star as Planet X. The semi major axis of its orbit is 1.5 AU, and the eccentricity of its orbit is 0.1. Which planet, if either, is moving at the highest orbital speed at perihelion? At aphelion? (In other words, when both planets are at perihelion, which has the higher orbital speed? When both planets are at aphelion, which has the higher orbital speed?)
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 they would on Earth?
e. Planet Y orbits the same star as Planet X. The semi major axis of its orbit is 1.5 AU, and the eccentricity of its orbit is 0.1. Which planet, if either, is moving at the highest orbital speed at perihelion? At aphelion? (In other words, when both planets are at perihelion, which has the higher orbital speed? When both planets are at aphelion, which has the higher orbital speed?)
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