Question

(b) Assuming h is small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h isΔg = (2GMeH) / RE³

Answer 1

Vertical distance h isΔg$=\frac{-2GM}{ RE^{3} }$

What is vertical?

• The distance between two vertical places is known as the vertical separation or vertical distance. There are numerous ways to express vertical position using vertical coordinates, including depth, height, altitude, elevation, etc.
• The formula for vertical distance from the ground is y = - g * t2 / 2, where g is the acceleration of gravity and h is a height.
• The vertical distance between the measurement point and the point of observation on Earth's surface. Altitude is the vertical distance from the measurement place to mean sea level.

Assuming h is small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between two points separated by vertical distance h isΔg = (2GMeH) / RE³:

Given:

Separated between two points=h

And, h∠∠$R_{E}$           ($R_{E}$= radius of the Earth)

Now, $\frac{dg}{dr} =$$\frac{-2GM}{ RE^{3} }$

$dg =\frac{-2GM}{ RE^{3} } dr$

Δg$=\frac{-2GM}{ RE^{3} }$  

Therefore, Vertical distance h isΔg$=\frac{-2GM}{ RE^{3} }$  

To learn more about Vertical, refer to:

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