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Scientists want to place a 2600-kg satellite in orbit around Mars. They plan to have the...

Question:

Scientists want to place a 2600-kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 1.7 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

mass (mars) = {eq}6.4191 \times 10^{23} {/eq} kg, radius (mars) = {eq}3.397 \times 10^6 {/eq} m, G = {eq}6.67428 \times 10^{-11} {/eq} N{eq}\cdot {/eq}m{eq}^2 {/eq}/kg{eq}^2 {/eq}

1) What is the force of attraction between Mars and the satellite?

2) What speed should the satellite have to be in a perfectly circular orbit?

3) How much time does it take the satellite to complete one revolution?

4) Which quantities would change the speed the satellite needs to orbit at?

5) What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

Orbital Speed:

Orbital speed is the speed by which an object or body in space sweeps or covers the distance of its orbit in a particular time period. Orbital speed depends on the mass of the body and its radius. Its value is expressed in meter per second.

Answer and Explanation:

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Given data

  • The mass of satellite is: {eq}M = 2600\;{\rm{kg}}{/eq}
  • The mass of mars is: {eq}{m_m} = 6.4191 \times {10^{23}}\;{\rm{kg}}{/eq}
  • The...

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Kepler's Three Laws of Planetary Motion

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Chapter 22 / Lesson 12
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