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Objects in orbit

  1. Feb 17, 2013 #1
    1. The problem statement, all variables and given/known data
    As a spacecraft of diameter 2.8km approaches Mars, the astronauts want to experience what their Mars-bound weight will be. What should the period of rotation be to simulate an acceleration due to gravity of magnitude 3.8 m/s2 ?

    Mass of Mars = 6.37*1023
    Radius of Mars = 3.40*106

    2. Relevant equations
    (1) Fg = (GMm)/r2

    (2) ac = (mv2)/r

    (3) T = (2∏r)/v

    3. The attempt at a solution

    Fg = ac
    (GMm)/r2 = (mv2)/r

    Solving for v
    v = √((GM)/r)

    Sub v into eqn. (3)
    T = (2∏r)*(√(r)/√(GM))
    T = (2∏r(3/2))/√(GM)

    And that's as far as i got cause i'm not sure what to do with the given information... The answer is 1.2*102s.
     
  2. jcsd
  3. Feb 17, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    You don't need to do anything with G or those mass figures. They already gave you the acceleration required. So the force produced will be F=ma=m*(3.8m/s^2). Equate that to mv^2/r.
     
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