24. The distance between Earth and the Sun is 149.6 million km, and the distance between...

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24. The distance between Earth and the Sun is 149.6 million km, and the distance between Venus and the Sun is 108.2 million km. How long does it take Venus to orbit once around the Sun? 25. A spacecraft of mass 1,000 kilograms is in an elliptical orbit about the Earth, as shown below. At point a, the spacecraft is at a distance TA-1.2 x 10 meters from the center of the Earth and its velocity, of magnitude v, -7.1 x 10 meters per second, is perpendicular to the line connecting the center of the Earth to the spacecraft. The mass and radius of the Earth are Mg = 6.0 x 1024 kilograms and re-6.4 x 10 meters, respectively. G = 6.674 x 10-11 m³ kg-¹ s-2 b (1) When the spacecraft is at point a, determine the total mechanical energy of the spacecraft, assuming that the gravitational potential energy is zero at an infinite distance from the Earth. (II) Suppose that a different spacecraft is at point a, a distance r = 1.2 X 107 meters from the center of the Earth. Determine the minimum speed of the spacecraft at point a if it is to escape completely from the Earth. 24. The distance between Earth and the Sun is 149.6 million km, and the distance between Venus and the Sun is 108.2 million km. How long does it take Venus to orbit once around the Sun? 25. A spacecraft of mass 1,000 kilograms is in an elliptical orbit about the Earth, as shown below. At point a, the spacecraft is at a distance TA-1.2 x 10 meters from the center of the Earth and its velocity, of magnitude v, -7.1 x 10 meters per second, is perpendicular to the line connecting the center of the Earth to the spacecraft. The mass and radius of the Earth are Mg = 6.0 x 1024 kilograms and re-6.4 x 10 meters, respectively. G = 6.674 x 10-11 m³ kg-¹ s-2 b (1) When the spacecraft is at point a, determine the total mechanical energy of the spacecraft, assuming that the gravitational potential energy is zero at an infinite distance from the Earth. (II) Suppose that a different spacecraft is at point a, a distance r = 1.2 X 107 meters from the center of the Earth. Determine the minimum speed of the spacecraft at point a if it is to escape completely from the Earth.

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