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

1. Sep 9, 2016

Oannes

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. Sep 9, 2016

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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