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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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