91Ó°ÊÓ

The inverse square law is a fundamental principle in physics that describes how a force, in this case, gravitational force, is affected by distance. According to this law, the intensity of gravitational acceleration decreases proportionally to the square of the distance from the source of the gravitational field, which is the center of the Earth in this scenario.
This means that if you are twice as far from the center of the Earth, the gravitational acceleration is not just half, but a quarter of what it is at the first distance. This relationship is crucial in understanding how gravitational force diminishes with distance, and it's why you need to calculate ratios as shown in the exercise to find changes in gravity based on distance.
Therefore, using the inverse square law, you set up a ratio between gravitational accelerations at different distances to solve for the unknown distance above Earth's surface.

Earth's radius, often represented as \( R_e \), is the distance from the Earth's center to its surface. The average value used in calculations is roughly 6,371 kilometers. This value is important because it factors into many calculations involving Earth's gravitational field.
For example, in the exercise, when calculating how the gravitational force changes at different altitudes, knowing the Earth's radius helps you determine how far from the Earth's surface you are in terms of the total distance from the Earth's center. When solving the problem, you converted the change in gravitational acceleration to a change in distance using the ratio of Earth's radius and the unknown distance \( r_2 \).
Earth’s radius is a standard reference for many geological and astronomical calculations involving the Earth and forms the baseline for approximating distances related to the Earth's gravitational influence.

The gravitational constant, often denoted as \( G \), is a crucial part of the formula for determining gravity's force. Its value is approximately \( 6.674 \times 10^{-11} \, \mathrm{Nm^2/kg^2} \). This constant reflects the strength of gravity and is used in the universal law of gravitation to calculate gravitational forces between two masses anywhere in the universe.
Within the context of Earth's gravity, the gravitational constant helps determine the gravitational pull that the Earth exerts on objects at or near its surface. Although \( G \) itself is not directly used in every step of the calculation in basic exercises, it underlies the concept that gravity decreases as we move away from Earth’s center, as shown by the inverse square law.
The gravitational constant is what allows us to link mass and distance into a meaningful force, giving mathematic expression to the gravitational pull between masses at various distances.

The mass of the Earth, represented as \( M \), is a critical factor when calculating gravitational acceleration. It is approximately \( 5.972 \times 10^{24} \, \mathrm{kg} \), providing the bulk of the gravitational pull experienced at the Earth's surface.
In the formula \( g = \frac{GM}{r^2} \), where \( G \) is the gravitational constant and \( r \) is the distance from Earth's center, Earth's mass \( M \) combines with \( G \) to show how gravity's strength decreases with distance. This is key in exercises like the one above, as it helps us understand why gravity weakens as altitude increases.
The large mass of the Earth contributes to its ability to hold the atmosphere and exert a significant gravitational pull, maintaining equilibrium for objects that exist within its gravitational field. This concept helps in understanding how gravitational force varies with distance, work that is crucial when addressing problems involving changes in gravity over different altitudinal distances.