well, uh, g, plug in the numbers!
20 miles = 32.2 km, so
A(32.2) = 9.81(6380/(6380+32.2))^2 = 9.71 m/s^2
constant. However, g is actually dependent upon the distance from the center of the
Earth. A more accurate expression for g is: g=g0(Re/Re+A)^2
Here, g0 is the acceleration of gravity at the surface of the Earth, A is the altitude, and Re
is the radius of the Earth, approximately 6,380 kilometers. What is the value of g at an
altitude of 20 miles in units of meters per second squared?
20 miles = 32.2 km, so
A(32.2) = 9.81(6380/(6380+32.2))^2 = 9.71 m/s^2
1 mile is approximately equal to 1.609 kilometers.
So, 20 miles is equal to 20 x 1.609 = 32.18 kilometers.
Now, we can use the formula: g = g0(Re/Re+A)^2
Given:
g0 = acceleration due to gravity at the surface of the Earth = 9.8 m/s^2
Re = radius of the Earth = 6,380 kilometers = 6,380,000 meters
A = altitude = 32.18 kilometers = 32,180 meters
Plugging in these values into the formula, we get:
g = 9.8 * (6,380,000 / (6,380,000 + 32,180))^2
Calculating this expression, we find:
g ≈ 9.8 * (0.99694)^2
g ≈ 9.8 * 0.99388
g ≈ 9.741 m/s^2
Therefore, the value of g at an altitude of 20 miles is approximately 9.741 meters per second squared.
g = g0(Re / (Re + A))^2
First, let's convert the altitude from miles to meters. We know that 1 mile is approximately equal to 1,609.34 meters. So, 20 miles is equal to 20 * 1,609.34 = 32,186.8 meters.
Next, we'll substitute the given values into the formula:
g = g0(Re / (Re + A))^2
g = g0(6,380,000 / (6,380,000 + 32,186.8))^2
Now, let's substitute the known values:
g0 = acceleration of gravity at the surface of the Earth = 9.8 m/s^2
Re = radius of the Earth = 6,380,000 meters
g = 9.8 * (6,380,000 / (6,380,000 + 32,186.8))^2
Now, let's calculate the value of g:
g = 9.8 * (6,380,000 / 6,412,186.8)^2
g = 9.8 * (0.9948)^2
g = 9.8 * 0.9896
g ≈ 9.689 m/s^2
Therefore, the value of g at an altitude of 20 miles is approximately 9.689 meters per second squared.