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 = $\frac{L}{2m}$ = constant. This IS conservation of angular momentum. At perihelion: maximum speed. At aphelion: minimum speed. $v_p$$r_p$ = $v_a$$r_a$.

Third Law (Periods): $T^2$ = 4*$pi^2$*a^$\frac{3}{GM}$. 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^$\frac{3}{G(m_1+m_2}$)), where d is the separation. Both orbit the common CM.