Calculating Local Gravity: How is g = 9.81m/s^2?

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Homework Help Overview

The discussion revolves around the calculation of the local gravitational field, specifically the value of g = 9.81 m/s². Participants are exploring the principles and assumptions behind this value, particularly in relation to Earth's characteristics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the assumption of Earth as a perfect sphere and the application of Newton's law of universal gravitation. Questions arise about the specific equation used to derive the value of g and the parameters involved in the calculation.

Discussion Status

The conversation is ongoing, with participants providing insights into the calculation process and seeking further clarification on the specific equation and values used. There is an exchange of information without a clear consensus on the final interpretation.

Contextual Notes

Participants are operating under the constraints of a homework context, focusing on understanding the derivation of gravitational acceleration without providing complete solutions.

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Homework Statement


I am wondering how did the local graviational field (free fall acceleration) g = 9.81m/s^2 is calculated?


Homework Equations





The Attempt at a Solution



 
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It is usually calculated by assuming that the Earth is a perfect sphere and then by using Newton's law of universal gravitation to find the force on an object at the surface of the Earth. Input parameters are the gravitational constant and the radius and mass of the Earth.
 
So what is the actual equation used to obtain the g (with the values)?
Just out of general interest.
 
[tex]G\frac{M_E\:m}{R_E^2}=mg[/tex]

Solve for g.
 
OK thank you for your time.
:)
 

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