# Gravitational field vs. acceleration due to gravity

• thecommexokid
In summary, the electric field is different than the acceleration due to gravity. The equivalence of inertial and gravitational mass is a happy coincidence that comes out of the application of the equivalence principle.

#### thecommexokid

"Gravitational field" vs. "acceleration due to gravity"

So I'm pretty sure the following paragraph is all true. Do the citizens of PhysicsForums agree? Please confirm and/or correct and/or clarify, as needed.

In electostatics, the electric field E is a completely different quantity than the acceleration due to an electric force aE, which you could calculate as aE = qE E / m (where qE E is the electric charge). But the gravitational field Φ and the acceleration due to gravitational force aG are the same thing. By analogy with the electric case, aG = qG Φ / m, but qG, the "gravitational charge", is itself just m. So it all comes down to the familiar fact that inertial mass and gravitational mass are the same thing...which is an unexplained coincidence in the context of Newtonian mechanics (though it possibly has firmer footing in general relativity).

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Completely correct (excpet for the slight typo in the first parentheses :tongue2:). This happy coincidence you speak of is commonly called the equivalence of inertial and gravitational mass; i.e. that the m appearing in Newton's Second Law is the same m that appears in Newton's Law of Universal Gravitation. In the electrostatic analogy, we could think of the "electric charge" as an "electric mass," which is completely unrelated the inertial/gravitational mass. Of course, this is completely equivalent to your explanation.

One word of warning, the above is true when you formulate gravity as a non-relativistic field theory in analogy to electrostatics. There might be some subtleties when you go into proper General Relativity (I'm truthfully not sure); but never mind that since we're not posting in the Relativity Forums.

Yep, it's all fine within the non-relativistic (Newtonian) approximation.

Concerning General Relativity (GR) (which is a classical theory after all and thus belongs also to this subforum although there is a more specialized one on relativity), one should emphasize that here the sources of the gravitational field is not the mass distribution but all kinds of energy and momentum, to which according to GR the gravitational field couples universally. That comes directly out of the application of the here discussed equivalence principle, leading to a geometrical reinterpretation of the gravtiational field as the curvature of the four-dimensional pseudo-Riemannian space-time manifold.

## What is the difference between gravitational field and acceleration due to gravity?

The gravitational field is a measure of the force per unit mass exerted by a massive object, while acceleration due to gravity is a measure of the rate at which an object falls towards the Earth's surface. In other words, the gravitational field tells us how strong the force of gravity is at a certain point, while acceleration due to gravity tells us how quickly an object will accelerate towards the Earth.

## How do gravitational field and acceleration due to gravity affect objects?

The gravitational field and acceleration due to gravity both play a crucial role in determining the motion of objects. The gravitational field determines the strength of the force of gravity on an object, while the acceleration due to gravity determines the rate at which the object will accelerate towards the Earth. Together, these factors determine the path and speed of an object in a gravitational field.

## Are gravitational field and acceleration due to gravity the same everywhere?

No, the values of gravitational field and acceleration due to gravity can vary depending on the location and mass of the objects involved. The strength of the gravitational field is directly proportional to the mass of the object, while the acceleration due to gravity is also affected by the distance between the objects.

## How can we measure gravitational field and acceleration due to gravity?

Gravitational field and acceleration due to gravity can be measured using various methods such as pendulum experiments, projectile motion experiments, or through mathematical calculations using the mass and distance between objects. These measurements are important for understanding the behavior of objects in a gravitational field and for accurate predictions in the fields of physics and astronomy.

## Is the value of acceleration due to gravity constant?

No, the value of acceleration due to gravity is not constant and can vary depending on the location and mass of the objects involved. On Earth, the standard value of acceleration due to gravity is 9.8 meters per second squared, but this can change at different points on the Earth's surface and in space due to factors such as altitude and the presence of other massive objects.