Question

At what altitude above the earth's surface would the acceleration due to gravity be 4.9 m/s²? Assume the mean radius of the earth is 6.4x10⁶ metres and the acceleration due to gravity 9.8m/s² on the surface of the earth.

Answer 1

The altitude above Earth's surface where the acceleration due to gravity is 4.9 m/s² is approximately 6.4 x 10¶ meters, calculated by using the gravitational acceleration formula and Earth's mean radius.

Step-by-step explanation:

Calculating the Altitude for Reduced Acceleration due to Gravity

To calculate the altitude above Earth's surface where the acceleration due to gravity is 4.9 m/s², we can use the formula for gravitational acceleration g at a distance r from the center of the Earth.

The formula is g = (G × M) / r², where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center to the object. Knowing that the acceleration due to gravity on the surface of the Earth (gsurface) is 9.8 m/s² and given Earth's mean radius (R), we set up the equation 4.9 m/s² = (G × M) / (R + h)², with h being the altitude above Earth's surface. We then solve for h using the initial conditions of G × M and R. After rearranging the equation and solving for h, we find that the altitude where gravity is 4.9 m/s² is approximately 6.4 x 10¶ meters above Earth's surface.