Question

State and explain Kepler’s second law of planitary motion.​

Answer 1

Answer:

Kepler's second law states that a planet moves in its ellipse so that the line between it and the Sun placed at a focus sweeps out equal areas in equal times.

Answer 2

Explanation:

Kepler’s second law states ” The radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time”

As the orbit is not circular, the planet’s kinetic energy is not constant in its path. It has more kinetic energy near perihelion and less kinetic energy near aphelion implies more speed at perihelion and less speed (vmin) at aphelion. If r is the distance of planet from sun, at perihelion (rmin) and at aphelion (rmax), then,

rmin + rmax = 2a × (length of major axis of an ellipse) . . . . . . . (1) .

For an infinitesimal movement of the planet in a time interval in an elliptical orbit, the area swept by the planet in time is given by;

dA/dt = d/dt [ 1/2 × r × (v dt)]= 1/2 × rv . . . . . (2)

At perihelion r = rmin, v = vmax then from Equation 2;

dA/dt = 1/2 × rmin × vmax) = [m × vmax × rmin]/2m = L/2m;

At aphelion r = rmax, v = vmin then from Equation 2;

dA/dt = 1/2 × vmin × rmax = [m × vmin × rmax]/2m = L/2m

Kepler’s second law can also be stated as “The areal velocity of a planet revolving around the sun in elliptical orbit remains constant which implies the angular momentum of a planet remains constant”. As the angular momentum is constant all planetary motions are planar motions, which is a direct consequence of central force.

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