Conservation Of Angular Momentum

A scientific experimental satellite moves in an elliptical orbit with the Earth's center at one focus. The altitude at perigee is $h_1 = 266$ km, and the altitude at apogee is $h_2 = 1826$ km. The satellite's speed at perigee is $v_1 = 8.13$ km/s. The Earth's radius is $R = 6.37 \times 10^3$ km. Air resistance is negligible.

The Moon's orbit around the Earth can be approximated as a circle. The Earth's mass is $M_e$, the Moon's mass is $M_m$, and the distance between them is $r_0$.

An object is in uniform linear motion.

A planet orbits the Sun.

On a smooth horizontal table, a small ball is attached to a string that passes through a central hole O. Initially, the ball undergoes uniform circular motion with speed $v_1$ and radius $r_1$. The string is then slowly pulled downwards until the ball moves in a circle of radius $r_2$.

Two artificial satellites, each with mass $m = 200$ kg, are in the same circular orbit at an altitude equal to the Earth's radius, $h=R$. They are moving in opposite directions and eventually collide. The collision is perfectly inelastic. Gravitational forces between the satellites and air resistance are negligible. Use Earth's radius $R = 6.4 \times 10^6$ m and surface gravity $g = 10$ m/s$^2$.