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Help with circular velocity question (unit conversions?)

  1. Apr 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider a satellite in circular low Mars orbit 300km above the planetary surface.
    R = 3396km
    M = 6.419 x 1023kg
    G = 6.674 x 10-11m3/kg/s2
    Find the orbital velocity of the satellite (using the given values, I assume, as there is some inaccuracy in the real-life mass value. Consider it irrelevant).

    2. Relevant equations
    Vc2 = GM/R

    3. The attempt at a solution

    I understand the radius of this equation to refer to M2's (satellite) distance from the center of M1 (Mars), and so simply added the mars radius and given orbital distance from the surface together.
    To get R = 3696km
    As it is given, I know the mass of mars to be 6.419e+23 (or 6.419 x 1023) (is this how notation works?)


    Given my limited math ability, I'm having trouble interpreting (in the mental sense) the numerous measures at the end of the "gravitational constant". Those being: m3, kg, and s2

    How do i go about plugging all this into a calculator? Do I ignore the units of measurement and treat everything as their values alone?

    Multiplying the mass of mars by the gravitational constant gave me:
    4.2840406e+13, which i then divided by the radius of 3696
    This gave me
    11591018939.4
    I then took the square root of this (on account of the given equation), which equaled:
    107661.594542
    This seems a bad number, considering known orbital velocities (I also dont understand this number. Would that read as 107661 km? or 10.7661 km? Even still this velocity would eject the satellite, no?)

    I suspect I am faulting in the units of measurement and the misinterpretation of the scientific notation.

    Somebody please help me, or otherwise professionally solve the equation with the given values, and then deconstruct your process for me.
     
  2. jcsd
  3. Apr 5, 2015 #2

    FactChecker

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    Gold Member

    You must pay attention to the units of the numbers and make sure that they cancel out to give the units of the desired answer. Notice that km = 1000m. Put that factor of 1000 in your calculations and your answer should be right. Also notice how all the units in numerators and denominators cancel out to leave the units m2/s2. Those are the proper units for V2
     
  4. Apr 5, 2015 #3
    Thankyou. That is what I suspected.
    I think I need further explanation, however. You may underestimate my inproficiency at math. How precisely do go about doing as you've suggested? Where do I change the values?
     
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