28. An elliptical orbit can be analyzed using conservation of angular momentum and mechanical energy. The distance between Earth, mass 5.972 × 1024 kg, and Sun, mass 1.989 × 1030 kg, varies from 147 to 152 Gm. (a) Use the formula UG = Gm₁m2/r to find the change in potential energy that occurs moving from the farthest distance to the nearest. (b) Given that the speed of Earth at its farthest point is 29.29 km/s, use conservation of energy to find its speed at the nearest point. (c) Calculate the angular momentum of Earth at each extreme and show that it is equal. 29. Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44 × 1012 m to 7.38 × 1012 m. Hint: use a system of equations based on conservation of energy and angular momentum.
28. An elliptical orbit can be analyzed using conservation of angular momentum and mechanical energy. The distance between Earth, mass 5.972 × 1024 kg, and Sun, mass 1.989 × 1030 kg, varies from 147 to 152 Gm. (a) Use the formula UG = Gm₁m2/r to find the change in potential energy that occurs moving from the farthest distance to the nearest. (b) Given that the speed of Earth at its farthest point is 29.29 km/s, use conservation of energy to find its speed at the nearest point. (c) Calculate the angular momentum of Earth at each extreme and show that it is equal. 29. Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44 × 1012 m to 7.38 × 1012 m. Hint: use a system of equations based on conservation of energy and angular momentum.
28. An elliptical orbit can be analyzed using conservation of angular momentum and mechanical energy. The distance between Earth, mass 5.972 × 1024 kg, and Sun, mass 1.989 × 1030 kg, varies from 147 to 152 Gm. (a) Use the formula UG = Gm₁m2/r to find the change in potential energy that occurs moving from the farthest distance to the nearest. (b) Given that the speed of Earth at its farthest point is 29.29 km/s, use conservation of energy to find its speed at the nearest point. (c) Calculate the angular momentum of Earth at each extreme and show that it is equal. 29. Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44 × 1012 m to 7.38 × 1012 m. Hint: use a system of equations based on conservation of energy and angular momentum.
28. An elliptical orbit can be analyzed using conservation of angular momentum and mechanical energy. The distance between Earth, mass 5.972 × 1024 kg, and Sun, mass 1.989 × 1030 kg, varies from 147 to 152 Gm. (a) Use the formula UG = – Gm1m2/r to find the change in potential energy that occurs moving from the farthest distance to the nearest. (b) Given that the speed of Earth at its farthest point is 29.29 km/s, use conservation of energy to find its speed at the nearest point. (c) Calculate the angular momentum of Earth at each extreme and show that it is equal. 29. Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44 × 1012 m to 7.38 × 1012 m. Hint: use a system of equations based on conservation of energy and angular momentum.
P.S. I already solved 28 but I don't know how to do 29.
Transcribed Image Text:28. An elliptical orbit can be analyzed using conservation of angular momentum and mechanical energy. The distance between Earth, mass 5.972 × 1024 kg, and Sun, mass 1.989 × 1030 kg, varies from 147 to 152 Gm. (a) Use the
formula UG = Gm₁m2/r to find the change in potential energy that occurs moving from the farthest distance to the nearest. (b) Given that the speed of Earth at its farthest point is 29.29 km/s, use conservation of energy to find its
speed at the nearest point. (c) Calculate the angular momentum of Earth at each extreme and show that it is equal.
29. Use concepts from the previous problem to find the speed of Pluto at each extreme of its orbit about the Sun – distance varying from 4.44 × 1012 m to 7.38 × 1012 m. Hint: use a system of equations based on conservation of
energy and angular momentum.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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