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Orbits

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.

Characteristics of Circular 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?

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

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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