A planet moves in an elliptical orbit about the Sun, with the Sun at one focus o

ID: 1325566 • Letter: A

Question

A planet moves in an elliptical orbit about the Sun, with the Sun at one focus of the ellipse.

A planet moves in an elliptical orbit about the Sun, with the Sun at one focus of the ellipse. (a) What is the torque about the center of the Sun due to the gravitational force of attraction of the Sun on the planet? vector tau = kg m^2/s^2 (b) At position A, the planet has an orbital radius r1 and is moving with a speed v1 perpendicular to the line from the Sun to the planet. At position B, the planet has an orbital radius r2 and is moving with speed v2, again perpendicular to the line from the Sun to the planet. What is the ratio of v1 to v2 in terms of r1 and r2? (Use the following as necessary: r1 and r2)

Explanation / Answer

a) Fc1 = m1v12 / r1 = GMm1 / r12

Fc2 = m2v22 / r2 = GMm2 / r22

? = r1 x GMm1 / r12 - r2 x GMm2 / r22 = GMm1 / r1 - GMm2 / r2

= GM(m1/r1 - m2/r2)

from Fc1 GM = v1 r1

Fc2 GM = v2 r2

v1 r1 = v2 r2

v1/v2 = r2/r1

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A planet moves in an elliptical orbit about the Sun, with the Sun at one focus o

A planet moves in an elliptical orbit about the Sun, with theSun at one focus of

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A planet moves in an elliptical orbit about the Sun, with the Sun at one focus o

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