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

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) Gravitational force acts along the line jooining theobjects; Sun and the satellite.

So radius vector r is parallel to the forcevector, F.

So,the torque exerted, (Vector product)

                ? = r x F =0.

(B). Since ? = 0,

                ? = dL/dt = 0

Angular moentum

So L = r x p =constant.

But the linear moentum, p =m.v

So, r x mv = constant .

Since, v is at 90 degrees with r.

         rx mv = r.mv =constant

So, r.v is constant.

          r1.v1 = r2.v2

The ratio,

              v1/v2 = r2/r1.

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