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A short class with Sarah and her students. The other ways are under More.
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Let's explore how gravity changes when we move above the Earth's surface. Can anyone tell me how the distance to the center of Earth affects gravity?
I think the further you go from the Earth, the less gravity you feel!
Exactly! The force can be calculated using the formula . What happens to as increases?
It decreases, right?
Correct! As you go higher, gravity decreases less significantly according to our surface gravity equation . Let's remember this pattern: the higher you go, the less you weigh — 'h' for height and 'h' for lesser gravity!
Now let's switch gears and discuss gravity beneath Earth's surface. Who can guess how gravitational pull changes when we dig down?
I think it decreases too!
Very close! The force due to gravity below the surface is calculated with . How does this look compared to our earlier equation?
It seems like we're using a different radius!
Exactly! As we go deeper, we use the radius minus our depth. The acceleration becomes . So, deeper means less gravity, and we can remember this: 'Deep Equals Decreased gravity — DED.'
Up in the sky, gravity's shy, down below, it helps us flow.
Imagine climbing a tall mountain, feeling lighter; when you dig into the Earth, it feels heavier at first, but then it lightens as you go deeper.
H.E.L.P: Height Equals Lesser Pull.
G.R.A.D.E: Gravity Reduces Above and Down Everywhere.
Term
Acceleration due to Gravity
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Term
Gravitational Force at Height
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Term
Gravitational Force at Depth
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Term
Decrease in Gravity
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The distance above the Earth's surface.
The distance below the Earth's surface.
A fundamental constant used in the calculation of gravitational force.
A measure of the amount of matter in an object.
The acceleration due to gravity at the surface of the Earth.
This section discusses how acceleration due to gravity changes with height above and depth below the Earth's surface.
The section explains the mathematical relationship for gravitational acceleration at various heights above and below the Earth's surface. It delineates how gravity decreases at height and depth and provides equations to calculate it, emphasizing the unique characteristics of gravitational force in these contexts.
This section elaborates on the concept of gravitational acceleration (g) at different positions relative to Earth’s surface. It separates the discussion into two main areas: acceleration at heights above the Earth's surface and acceleration at depths below the surface.
When a mass m is positioned at a height h above the Earth, the gravitational force acting on it can be described by the formula:
where G is the gravitational constant and is the radius of the Earth. From this force, we derive acceleration due to gravity:
This indicates that as h increases, g(h) decreases relative to the surface gravity, diminishing with height.
For small heights (), we can approximate g(h) using a binomial expansion:
where g is the gravitational acceleration at the Earth's surface.
Conversely, at a depth d below the surface, the calculation changes. The force on a mass m at that depth can be expressed as:
where is the mass of the smaller sphere of radius that contributes to the gravitational pull. The total gravitational acceleration then becomes:
This depicts how gravitational acceleration diminishes linearly as one travels deeper into the Earth. Notably, gravity is maximal at the surface and decreases consistently as one moves both upward to heights and downward into depths. Thus, the behavior of gravitational acceleration is fundamental for understanding various physical phenomena related to gravity.