Classical Mechanics
# Orbits

A satellite with mass $m = 3.00 \times 10 ^4 \text{ kg}$ goes around a planet with mass $M = 6.00 \times 10 ^{17} \text{ kg}$ in a circular orbit of radius $R = 4.00 \times 10^6 \text{ m}.$ Find the approximate orbital speed $v$ for the satellite.

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

A satellite of mass $m = 4.00 \times 10 ^4 \text{ kg}$ orbtis around a planet of mass $M = 6.00 \times 10 ^{17} \text{ kg}.$ If the satellite's gravitational potential energy is $U=-4.00 \times 10^5 \text{ J},$ what is the approximate kinetic energy of the satellite?

**Details**

- The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

A satellite with mass $m = 2.00 \times 10 ^4 \text{ kg}$ goes around a planet with mass $M = 8.00 \times 10 ^{17} \text{ kg}$ in a circular orbit of radius $R.$ If the speed of the satellite is $v = 5.17 \text{ m/s},$ whatis the approximate angular momentum of the satellite?

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

A satellite of mass $m = 4.00 \times 10^4 \text{ kg}$ orbits around a planet while maintaining a height of $h = 500 \text{ km}$ from its surface. If the planet has mass $M = 9.00 \times 10 ^{17} \text{ kg}$ and radius $R = 1.50 \times 10^6 \text{ m},$ what is the approximate kinetic energy of the satellite?

A satellite is moving around the earth in a stable circular orbit. Which of the following statements is WRONG about this satellite?

(a) It is moving at a constant speed.

(b) It is acted upon by a force directed away from the center of the earth which counter-balances the gravitational pull of the earth.

(c) Its angular momentum remains constant.

(d) It behaves as if it were a free-falling body.