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Finding the mass of 55 Cancri

  1. Oct 28, 2016 #1
    1. The problem statement, all variables and given/known data
    I have to find the mass of 55 Cancri in kg using the average orbits of 3 orbiting planets. Specifically, "Using the average of the values of R^3/T^2 that you filled in just for planets c, f, and d in #2, approximately what is the mass of 55 Cancri in kg?
    planet c = 3.14 x 10^18
    planet f = 3.16 x 10^18
    planet d = 3.10 x 10^18

    Then to convert the mass in kg to solar masses.

    2. Relevant equations
    M=(4pi^2/G)(R^3/T^2) With T equaling the period


    3. The attempt at a solution
    (3.14 x 10^18) + (3.16 x 10^18) + (3.10 x 10^18) / 3 = 7.3 x 10^31
    M= (4pi^2/6.67x10^11)(7.3x10^18) = 1.73x10^31 kg

    Is this correct? Or is this value in another form that I need to convert to kg?

    And then would it convert to 8.70 Ms (solar masses)?

    Please help!! Thank you all!!
     
  2. jcsd
  3. Oct 28, 2016 #2

    gneill

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    Staff: Mentor

    All of your data values are close to 3 x 1018, so I would expect their average to be similar. Check your average calculation.
     
  4. Oct 28, 2016 #3
    Thanks gneill! I redid the calculations. You were right. For my average I got 3.13x10^18. I plugged that into the formula to calculate mass and got 1.85x10^30 kg. Is this correct?
     
  5. Oct 28, 2016 #4

    gneill

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    Staff: Mentor

    Yes, that looks much better.
     
  6. Oct 28, 2016 #5
    Cool! And just to be sure, this is in kilograms, right? I wasn't sure if there was a conversion that I needed to do that was missing.

    Also, I redid the conversion to solar masses from kilograms and got .93Ms.
     
  7. Oct 28, 2016 #6

    gneill

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    Staff: Mentor

    Your problem statement didn't mention what units the R^3/T^2 values were given in so I can't say decisively, but it would make sense that they'd be in ##m^3/s^2##, giving you a result in kg.
    That looks reasonable.
     
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