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Finding Altitude When Given g = g0(Re/Re+A)^2

  1. Sep 9, 2016 #1
    1. The problem statement, all variables and given/known data

    g = g0(Re/(Re + A))2

    g is the acceleration due to gravity. g0 is the acceleration of gravity at the surface of the earth, A is altitude, and Re is the radius, approximately 6380 km. Assume g0 = 9.8 meters per second squared. If the value of g is 9 meters per second squared, what is the Altitude in units of miles?


    2. Relevant equations

    g = g0(Re/(Re + A))2

    3. The attempt at a solution

    First, I plugged what I knew into the given equation:

    9m/sec2 = 9.8m/sec2(6380km/(6380km +A))2

    Second, I divided m/sec from the right:

    (9m/sec2)/(9.8m/sec2) = 0.9583
    0.9583 = (6380/(6380 + A))2


    Third, I took the square root of both sides:

    0.9583 = 6380km/(6380km + A)

    Fourth, I multiplied both sides by the denominator:

    (6380km + A)(.9583) = (6380km/(6380km + A))(6380km + A)
    6113.954km + .9583A = 6380km


    Finally, I subtracted, divided, and converted units:

    .9583A = 266.046km
    A = 277.6229km

    277.6229km *(.621 mi/ 1km) = 172.404 miles

    My Questions:
    So while typing this problem up I started to understood more of what it is I needed to do and it became much easier. However, I still have some questions about converting the units and so forth.First, during the second step where I divided m/sec on the right side from the left side I canceled the units out during division as if they were a variable, I am pretty sure this is legal but I want to make sure that I am right in this assumption, otherwise I would have to convert m/sec^2 to km and I have no idea where to start on that one. Second, is taking the square root of both sides to get rid of the exponent a viable option? Once again I feel like this is true, but I am very paranoid and cautious when it comes to these things. Thanks in advance for any help given
     
  2. jcsd
  3. Sep 9, 2016 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    Yes, that is what you need to do. It gives you an answer that is a dimensionless ratio
    Yes, take the square-root of everything under a single big square-root sign, for each side.

    this means it has no units
     
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