Tiêu đề GRAVITATION - 5.pdf ✅

CLASS VIII PHYSICS Kepler's laws kepler's first laws: Planets revolve around the sun in elliptical orbits with the sun at one focus. An ellipse with two foci F1 and F2 is shown in figure. The short dimension of the ellipse is called minor axis having length 2 b. The long dimension of the ellipse is called major axis having length 2a. The closest point to the sun, in the orbit is called perihelion. The farthest point to the sun, in the orbit is called aphelion. kepler's second laws: The radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time. i.e., the areal velocity of the planet around the sun is constant. Areal velocity = dA dt = constant Let the planet moves from point A to B in small time interval ' dt ' with orbital velocity v0. The radius vector sweeps an area dθ, in this time interval. The area swept by the radius vector dA = 1 2 r 2dθ Areal velocity dA dt = 1 2 r 2 dθ dt dA dt = 1 2 r 2ω dA dt = 1 2 rv0 dA dt = L 2 m Since L = mv0r Note: Kepler's second law is the consequence of Law of conservation of angular momentum. SYNOPSIS - 5