Variation of g with Altitude, Depth and Latitude
Acceleration due to gravity falls as g(1 - 2h/R) with altitude, as g(1 - d/R) with depth, and varies with latitude due to the Earth's rotation.
What is Variation of g with Altitude, Depth and Latitude?
Acceleration due to gravity falls as g(1 - 2h/R) with altitude, as g(1 - d/R) with depth, and varies with latitude due to the Earth's rotation.
Key formula / rule: g = GM/R2 at the surface.
Key points
- Compute g at a given altitude and depth.
- Analyse why the depth and altitude dependencies differ.
Common exam trap
Using the same formula for altitude and depth.
Definitions
- Term
Variation of g with Altitude, Depth and Latitude
- Meaning
Acceleration due to gravity falls as g(1 - 2h/R) with altitude, as g(1 - d/R) with depth, and varies with latitude due to the Earth's rotation.
- Term
Variation of g with Altitude, Depth and Latitude — explanation
- Meaning
The two variations differ in form because above the surface the whole mass acts from the centre, while below it only the enclosed mass contributes.
Learning objectives
Compute g at a given altitude and depth.
Analyse why the depth and altitude dependencies differ.
Formulae
- Key point
g = GM/R2 at the surface.
- Key point
Altitude: gh = g(1 - 2h/R) for h << R; depth: gd = g(1 - d/R).
- Key point
g is zero at the centre and maximum at the poles.
Prerequisites
PHY-U2-GRAV-T1-S1-C1
Common mistakes
Using the same formula for altitude and depth.
Ignoring that the altitude formula is an approximation for small h.
Keywords
Variation
Altitude
Depth
Latitude
Practice preview
At what depth (d) below the Earth's surface will the acceleration due to gravity be 75% of its value on the surface? (Assume R is the radius of Earth).…
medium
How does the acceleration due to gravity (g) change as we move to a higher altitude from the Earth's surface?…
easy
At what altitude 'h' will the acceleration due to gravity be the same as at a depth 'd = R/2' below the Earth's surface? (Assume h << R for altitude formula approximation).…
medium