The acceleration due to gravity calculated this way works well for objects near the Earth’s surface. How would you have to change the above equation if the object was 100,000 meters above the ground?
To calculate the acceleration due to gravity for an object that is 100,000 meters above the ground, you would need to take into account the variation of gravity with distance from the Earth's surface. The acceleration due to gravity decreases as you move farther away from the Earth's center.
The equation to calculate the acceleration due to gravity near the Earth's surface is:
g = GM/r^2
where:
g is the acceleration due to gravity
G is the universal gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
M is the mass of the Earth
r is the distance between the object and the center of the Earth
At a distance of 100,000 meters above the ground, the distance between the object and the center of the Earth would be the radius of the Earth plus the distance above the ground.
The radius of the Earth is approximately 6,371,000 meters.
So, the equation would be modified as follows:
g = GM/(r + h)^2
where:
h is the distance above the ground (100,000 meters in this case)
r is the radius of the Earth (6,371,000 meters)
By plugging in these values, you can calculate the new acceleration due to gravity for the object 100,000 meters above the ground.