Question

Circular orbits in Equation 13.10 for conic sections must have eccentricity zero. From this, and using Newton’s second law applied to centripetal acceleration, show that the value of α in Equation 13.10 is given by α=L2GMm2 where L is the angular momentum of the orbiting body. The value of α is constant and given by this expression regardless of the type of orbit.

(a) ( α = frac{L²GMm}{2} )
(b) ( α = frac{L²}{GMm} )
(c) ( α = frac{GMm}{L²} )
(d) ( α = frac{2}{L²GMm} )

Answer 1

The value of α in Equation 13.10 is given by α = L2GMm2 where L is the angular momentum of the orbiting body.

Step-by-step explanation:

The value of α in Equation 13.10 is given by α = L2GMm2 where L is the angular momentum of the orbiting body. To derive this expression, we start with Newton's second law applied to centripetal acceleration.

The centripetal force necessary to keep an object in circular motion is provided by the gravitational force between the two masses. Equating these two forces and solving for α, we obtain the expression for α in terms of angular momentum L.