According to Laplace, how is the sphere of influence defined?

Correct Answer : Option (C) :   Elliptic

Explanation : In the heliocentric phase of the patched conic method, the spacecraft follows the elliptical transfer orbit where sun is considered as the primary gravitational body. The interplanetary cruise is analyzed by two-body mechanics in heliocentric0ecliptic coordinate frame.

Correct Answer : Option (C) :   Ratio of perturbing acceleration and central-body acceleration

Explanation : According to Laplace, Sphere of Influence (SOI) is described as the ratio of perturbing acceleration and central-body acceleration.

Correct Answer : Option (A) :   Hyperbolic

Explanation : The arrival trajectory inside the target planet’s sphere of influence is done using a hyperbolic orbit which is analyzed in inertial planet-centered frame. As soon as the spacecraft enters the target planet’s sphere of influence, the sun’s gravity is turned off and planet’s gravity is turned on.