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brinethery

  • 3 years ago

Scientists want to place a 2800.0 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2695.0 m/s in a perfectly circular orbit. Here is some information that may help solve this problem: mass of mars = 6.4191 x 10^23 kg radius of mars = 3.397 x 10^6 m G = 6.67428 x 10^-11 N-m^2/kg^2 What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.)

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  1. Algebraic!
    • 3 years ago
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    \[G\frac{ M _{mars} }{ r^2 } = \frac{ V^2 }{ r}\]

  2. Algebraic!
    • 3 years ago
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    \[G\frac{ M _{mars} }{ V^2 } = r\]

  3. brinethery
    • 3 years ago
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    @Algebraic! Thank you very much, just one quick question... why is little m (mass of satellite) not included?

  4. Algebraic!
    • 3 years ago
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    yeah, it's a bit weird to think about... but there you have it: the force due to gravity is proportional to satellite mass as is the centripetal force... so, it's immaterial what the satellite's mass is...

  5. Algebraic!
    • 3 years ago
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    This is actually only approximately true though, for satellite mass << mass of mars... if the satellite is very massive then mars and the satellite both orbit the center of mass of the system... but that's not a concern here.

  6. brinethery
    • 3 years ago
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    Thanks... I feel like I need some major hand-holding through this chapter we're doing :-(

  7. Algebraic!
    • 3 years ago
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    No problem:)

  8. brinethery
    • 3 years ago
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    I'd give ya 3 medals if I could. My dad and I just went through the derivation and I can see that the little m on each side cancels out. I will live another day!

  9. Algebraic!
    • 3 years ago
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    :)

  10. Algebraic!
    • 3 years ago
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    for sparta!

  11. brinethery
    • 3 years ago
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    I have one more question having to do with this problem: I could open up a new thread if you want me to? What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

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