Explanation Given information: The path of particle is defined as, y = x 2 4 r 0 ε = 1 Equation 12.35 is defined as, d 2 u d θ 2 + u = F m h 2 u 2 Where, u = 1 r Equation 12.27 is defined as, 1 r = G M h 2 ( 1 + ε cos θ ) Calculation: At the given instant, y = x 2 4 r 0 r 0 − r cos θ = r 2 sin 2 θ 4 r 0 r 2 sin 2 θ + 4 r 0 r cos θ − 4 r 0 2 = 0 By solving, we get r = 2 r 0 ( 1 − cos θ ) sin 2 θ = 2 r 0 ( 1 − cos θ ) 1 − cos 2 θ = 2 r 0 1 + cos θ According to the above explanation, u = 1 r Then, u = 1 r = 1 + cos θ 2 r 0 Differentiate, d u d θ = − sin θ 2 r 0 d 2 u d θ 2 = − cos θ 2 r 0 According to equation 12

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Chapter 12.3, Problem 12.97P

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Using equation 12.35 and 12.37 that the central force F is inversely proportional to r2 and h=2GMr0.

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Chapter 12.3, Problem 12.96P

Chapter 12.3, Problem 12.98P

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Using equation 12.35 and 12.37 that the central force F is inversely proportional to r 2 and h = 2 G M r 0 .

Solution Summary: The author explains that the central force F is inversely proportional to r2.

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Using equation 12.35 and 12.37 that the central force F is inversely proportional to r2 and h=2GMr0.

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