What is the relationship for g at a very small height h above the Earth's surface?
Understand the Problem
The question is asking about how the acceleration due to gravity (g) changes when measured at a very small height (h) above the Earth's surface in relation to its value at the surface. It prompts for an explanation of the relationship between g and height, which typically involves understanding the inverse square law of gravitation as well as how gravity decreases with height.
Answer
g' = g * R^2 / (R+h)^2
The value of acceleration due to gravity (g) at a height h above the Earth's surface is given by the formula: g' = g * (R^2 / (R+h)^2), where R is the Earth's radius and g is the acceleration due to gravity at the surface.
Answer for screen readers
The value of acceleration due to gravity (g) at a height h above the Earth's surface is given by the formula: g' = g * (R^2 / (R+h)^2), where R is the Earth's radius and g is the acceleration due to gravity at the surface.
More Information
This formula is derived based on the inverse square law for gravity, which shows that the gravitational force decreases with the square of the distance from Earth's center.
Tips
A common mistake is forgetting to square both (R+h) and R in the formula, leading to incorrect calculations.
Sources
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