Question

state and prove Kepler's second law using vector notation​

Answer 1

Explanation:

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. His astronomy thus made pressing and practical the otherwise merely difficult problem of the…

Statement:-The line that joins a planet to the sun sweeps out equal areas in equal intervals of time.

Area covered by the planet while revolving around the sun will be equal in equal intervals of time. This means the rate of change of area with time is constant.

Suppose position and momentum of planet is denoted by ‘r’ and ‘p’ and the time taken will be Δt.

ΔA=1/2xrxvΔt (where vΔt is distance travelled by a planet in Δt time.)

ΔA / Δt =1/2(rxv)

where

(Linear momentum) p=mv or we can write as

v =p/m

=1/2m(rxp)

=1/2 L/2m where L= angular momentum(It is constant for any central force)

ΔA / Δt = constant (This means equal areas are covered in equal intervals of time).