At what height above the surface of the earth does the acceleration due to gravity reduces by 64% .radius of earth 6400 km
.64=(re/(re+h))^2
solve for h
1600km
To determine the height above the surface of the Earth where the acceleration due to gravity reduces by 64%, we can utilize the principle that the acceleration due to gravity decreases with distance from the Earth's center.
Here are the steps to find the answer:
1. Calculate the decrease in acceleration due to gravity by 64% of its original value.
- If we assume the original value of acceleration due to gravity as g, then the decrease in acceleration would be 0.64 * g.
2. Use the formula for gravitational acceleration as a function of distance from the Earth's center.
- The formula can be expressed as:
g(h) = g / (1 + (h / R)^2)
where:
g(h) is the acceleration due to gravity at the height h above the surface,
g is the acceleration due to gravity at the Earth's surface,
h is the height above the surface, and
R is the radius of the Earth.
3. Substitute the decrease in acceleration found in step 1 into the formula from step 2.
- Replace g(h) with 0.64 * g and solve for h.
4. Rearrange the equation to solve for h.
- Rearranging the equation in terms of h gives:
h = R * sqrt(((1 / (0.64 * g)) - 1)
where sqrt represents the square root function.
5. Substitute the given values into the equation from step 4.
- Replace R with the radius of the Earth, which is 6400 km, and g with the acceleration due to gravity at the surface of the Earth (approximately 9.8 m/s^2).
6. Calculate the height h using the equation derived in step 4.
By following these steps, you can find the height above the Earth's surface where the acceleration due to gravity reduces by 64%.