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

In summary, the local gravitational field or free fall acceleration, g=9.81m/s^2, is calculated by assuming the Earth is a perfect sphere and using Newton's law of universal gravitation. The equation used to obtain g is G(M_E*m)/R_E^2=mg, with input parameters being the gravitational constant, Earth's mass, and Earth's radius.
  • #1
Kat007
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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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  • #2
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.
 
  • #3
So what is the actual equation used to obtain the g (with the values)?
Just out of general interest.
 
  • #4
[tex]G\frac{M_E\:m}{R_E^2}=mg[/tex]

Solve for g.
 
  • #5
OK thank you for your time.
:)
 

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

How is g calculated?

The value of g, or the acceleration due to gravity, is calculated using the formula g = G * (M / r^2), where G is the universal gravitational constant, M is the mass of the larger object, and r is the distance between the two objects.

Why is g equal to 9.81m/s^2?

The value of g is not a constant and can vary depending on location and altitude. However, 9.81m/s^2 is a commonly used approximation for the average value of g at sea level on Earth.

How does altitude affect the value of g?

As altitude increases, the distance between an object and the center of the Earth increases, resulting in a decrease in the value of g. This is because the gravitational force between two objects decreases as the distance between them increases.

Does the value of g differ on other planets?

Yes, the value of g can differ on other planets depending on their mass and radius. For example, the value of g on Mars is approximately 3.71m/s^2, while on Jupiter it is approximately 24.79m/s^2.

How is the value of g used in physics?

The value of g is an important factor in many physics equations, such as calculating the force of gravity between two objects, determining the weight of an object, and understanding the motion of objects in free fall. It is also used in fields such as astrophysics, geology, and engineering.

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