Problem 7. Why did summer go so quickly? Scientists are studying a planet in a faraway galaxy that has the potential to sustain life. It has the same mass 5.97 × 10²4 kg as our Earth, and orbits a star with the same mass 1.99 x 1030 kg as our sun. However, its orbit has appreciable eccentricity, so that the distance between this planet and its star varies between 1.20 x 1011 m and 1.80 × 1011 m during its perihelion and aphelion, respectively. (a) Find the semimajor axis and the eccentricity of this planet. What is its period of orbit in Earth days? (b) Find the speeds (both linear and angular) of this planet at its perihelion and aphelion.
Problem 7. Why did summer go so quickly? Scientists are studying a planet in a faraway galaxy that has the potential to sustain life. It has the same mass 5.97 × 10²4 kg as our Earth, and orbits a star with the same mass 1.99 x 1030 kg as our sun. However, its orbit has appreciable eccentricity, so that the distance between this planet and its star varies between 1.20 x 1011 m and 1.80 × 1011 m during its perihelion and aphelion, respectively. (a) Find the semimajor axis and the eccentricity of this planet. What is its period of orbit in Earth days? (b) Find the speeds (both linear and angular) of this planet at its perihelion and aphelion.
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