1. 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?

(Note: this question refers to Newton’s equation for the force of gravity between two objects. How would that change if the radius of the earth or distance were increased by 100,000 meters? To help you answer this question, please review your textbook, chapter 3, Newton’s law of Gravitation section.)

To calculate the acceleration due to gravity for an object 100,000 meters above the ground, we need to modify Newton's equation for the force of gravity between two objects.

In Newton's law of gravitation, the equation is given as:

F = G * (m1 * m2) / r^2

where:
F is the force of gravity between two objects,
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of mass of the two objects.

Now, if we want to calculate the acceleration due to gravity at a height of 100,000 meters above the ground, we need to change the value of the distance (r) in the equation.

In this case, the new distance would be the sum of the radius of the Earth (rE) and the height above the ground (h). So, the new distance (r') becomes:

r' = rE + h

where:
rE is the radius of the Earth (approximately 6,371,000 meters), and
h is the height above the ground (100,000 meters in this case).

Substituting this new value of r' into the equation, we get:

F' = G * (m1 * m2) / (rE + h)^2

To find the acceleration due to gravity at this height, we need to divide the force (F') by the mass of the object (m2), as per Newton's second law:

acceleration due to gravity (g') = F' / m2

Therefore, to calculate the acceleration due to gravity for an object 100,000 meters above the ground, we use the modified equation with the new distance and divide the resulting force by the mass of the object.