A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is 7.0×10−3 less than that at sea level.

What is the observatory's altitude?

(1-7.0E-1)=(re/(re+alt))^2

That is the inverse square relationship.

My Prof. used the equation ---- (G*Me)/((Re+h)^2)=g'

He said to solve for h which is what I did but it didn't work. Suggestions?

To determine the altitude of the observatory, we need to understand the relationship between altitude and the gravitational acceleration. The gravitational acceleration decreases as altitude increases due to the decrease in Earth's gravitational field strength.

We can start by using the given information that the free-fall acceleration at the observatory is 7.0×10^(-3) less than that at sea level. Let's denote the free-fall acceleration at sea level as "g" and the free-fall acceleration at the observatory as "g'".

We can set up the equation as follows:

g' = g - 7.0×10^(-3)

Next, we need to determine the value of "g" which represents the free-fall acceleration at sea level. The standard value for the acceleration due to gravity at sea level is approximately 9.8 m/s^2.

Therefore, we can substitute this value into the equation:

g' = 9.8 - 7.0×10^(-3)

Now, we can solve for "g'":

g' = 9.8 - 0.007

g' = 9.793 m/s^2

Since we have obtained the value for "g'", which represents the free-fall acceleration at the observatory, we can now determine the altitude of the observatory using the relationship between gravitational acceleration and altitude.

The formula relating gravitational acceleration to altitude is:

g' = g(1 - 2h/RE)

Where:
g' is the free-fall acceleration at the observatory,
g is the free-fall acceleration at sea level,
h is the altitude of the observatory,
RE is the radius of the Earth.

By rearranging the equation, we can solve for the altitude (h):

h = (RE/2) * (1 - (g'/g))

Substituting the known values:

h = (6371 km / 2) * (1 - (9.793 m/s^2 / 9.8 m/s^2))

h = 3185.5 km * (1 - 0.999282)

h = 3185.5 km * 0.000718

h ≈ 2.29 km

Therefore, the observatory's altitude is approximately 2.29 km.