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Believe it or not — the world does not revolve around you. Accept this harsh truth, then calculate the beguiling dance of objects in orbit, from binary stars to the symphony of our Solar System.

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 \(G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.\)

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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 \(G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.\)

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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 \(G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.\)

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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?

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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.

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