The gravitational acceleration g

In summary, at the surface of the earth, the acceleration due to gravity is approximately 9.8m/s^2. This is calculated by equating the Newton's law of gravitation with Newton's second law and plugging in the mass and radius of the earth, along with the gravitational constant (G). While GM/r^2 is not exactly equal to 9.8, it is a close enough approximation for most practical purposes.
  • #1
manimaran1605
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Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)
 
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Why don't you look up the mass of the earth, the radius of the earth, and G and plug them into Gm/r^2 and see what you get? Is it close to the usual value of g?
 
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  • #3
GMm/R2

Usually

M = mass of planet
m = mass of object/particle

but Newton also says..

F = mg

You can do the rest.
 
  • #4
manimaran1605 said:
Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)
At the surface of the earth, Gm/r^2= g using m= mass of the earth, r= radius of the earth.
 
  • #5
At only one point is GM/r^2 exactly equal to 9.8. However, since r only changes slightly with respect to its value at heights we experience, for all intents and purposes, g=9.8m/s^2.
 
  • #6
manimaran1605 said:
Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)

Like noted above, you get it by equating Newton's gravity law with Newton's second law.
You can plug in some numbers here: Earth's Gravity.
 

Related to The gravitational acceleration g

What is the gravitational acceleration g?

The gravitational acceleration g is a constant value that represents the acceleration due to Earth's gravity. It is approximately 9.8 meters per second squared (m/s²).

How is gravitational acceleration g calculated?

Gravitational acceleration g is calculated by dividing the force of Earth's gravity on an object by the object's mass. It can also be calculated by multiplying the universal gravitational constant (G) by the mass of Earth and dividing by the radius of Earth squared.

Does the gravitational acceleration g vary on different planets?

Yes, the gravitational acceleration g varies on different planets depending on their mass and radius. For example, the gravitational acceleration on Mars is approximately 3.7 m/s², while on Jupiter it is approximately 24.8 m/s².

How does altitude affect gravitational acceleration g?

The higher the altitude, the further an object is from Earth's center of mass, resulting in a decrease in gravitational acceleration g. This is because the force of gravity decreases with distance.

Can gravitational acceleration g be altered?

Gravitational acceleration g cannot be altered by humans. It is a natural constant determined by the mass and size of a planet. However, objects can experience a different acceleration due to other forces such as air resistance or the force of a rocket engine.

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