12 12 points Tipler6 10P048 My Notes Ask Your Teacher A plan

12. -12 points Tipler6 10.P048. My Notes Ask Your Teacher A planet moves in an elliptical orbit about the Sun, with the Sun at one focus of the ellipse. (a) What ls the torque about the center of the Sun due to the gravltatlonal force of attractlon of the Sun on the planet? = kg m2/s2 (b) At position A, the planet has an orbltal radlus r1 and Is moving with a speed v perpendicular to the lne from the Sun to the planet. At position B, the planet has an orbltal radius /2 and ls moving with speed v2, again perpendicular to the lne from the Sun to the planet. What Is the ratlo of v1 to v2 In terms of r1 and r27(Use the followlng as necessary: and r2) eBook

Solution

Part (A)

Gravitational force acts along the line joining the objects, the Sun and the satellite.

So radius vector \'r\' is parallel to the force vector, \'F\'.

So, the torque exerted,

T = r x F = 0

T = 0 kg m²/s²

Part (B)

Since torque T = 0, &

T = dL/dt = 0

Angular moentum, L = r x p = constant.

But the linear moentum, p = mv

So, r * mv = constant .

Since, v is at 90^o with r, we have

         r * mv = rmv = constant

Therefore,

r₁ v₁ = r₂ v₂

The ratio of  v₁ & v₂ is given by

              v₁ / v₂ = r₂ / r₁