First Law (Orbits): Planets move in ellipses with the Sun at one focus. Circular orbit is a special case (e = 0). Most JEE problems assume circular orbits.

Second Law (Areas): dA/dt = L/(2m) = constant. This IS conservation of angular momentum. At perihelion: maximum speed. At aphelion: minimum speed. v_pr_p = v_ar_a.

Third Law (Periods): T^2 = 4pi^2a^3/(GM). For two satellites around the same body: T_1^2/T_2^2 = r_1^3/r_2^3. This is the most frequently tested law.

Application example: If satellite A has period T and radius r, satellite B at radius 4r has period T_B = T*4^{3/2} = 8T.

Binary star system: T = 2pisqrt(d^3/(G(m_1+m_2))), where d is the separation. Both orbit the common CM.