Esther Hoffman

2022-04-25

What is Difference between Acceleration due to Gravity and Gravitational Field Intensity?

I have read that gravitational field intensity and acceleration due to gravity are two different physical quantities that have the same direction, magnitude, and units. So, if all the units, magnitudes, and directions are the same for the two quantities (and also, physically, both essentially mean the acceleration produced in a point mass at a point) then what is the difference between them?

Edit (Comment)

As a couple of answers point out, physically, the two quantities are different as the former (the field intensity) is the quantity that describes the physical entity that the gravitational field is at a certain point whereas the latter (the acceleration due to gravity) describes the acceleration (a characteristic of the motion) of the particle put in the field.

I would like to point out that the curious fact that these two (meant to be different) quantities generically turn out to be the same in their values is thus a non-trivial fact--in other words, a law of nature. The popular name for this law is, of course, the (weak) equivalence principle. The fact that this is, in fact, non-trivial can be seen via comparing the situation to the situation in electrostatics where the electric field intensity at a point and the acceleration produced (due to the electric field) in a charged particle put at that point are clearly two different quantities. The relation between these two quantities depends on the ratio of the electric charge and the inertial mass of the particle in question. And this ratio, as we know, turns out to be different for different particles--unlike the gravitational scenario where the ratio of the gravitational mass and the inertial mass is independent of the particle in question (which is essentially the statement of the weak equivalence principle).

et3atissb

Beginner2022-04-28Added 1 answers

The two quantities are on opposite sides of Newton's second law equation $\overrightarrow{F}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{a}$

The force on a mass $m$ in a gravitation field $\overrightarrow{g}(=g\phantom{\rule{thinmathspace}{0ex}}\hat{d})$ is $\overrightarrow{F}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{g}=m\phantom{\rule{thinmathspace}{0ex}}g\phantom{\rule{thinmathspace}{0ex}}\hat{d}$ where $g$ is the magnitude of the gravitational field strength and $\hat{d}$ is the unit vector in the down direction.

Assuming no air resistance then using this force and Newton's second law you can find the acceleration of the mass in free fall.

$\overrightarrow{F}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{a}\Rightarrow m\phantom{\rule{thinmathspace}{0ex}}g\phantom{\rule{thinmathspace}{0ex}}\hat{d}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{a}=m\phantom{\rule{thinmathspace}{0ex}}a\phantom{\rule{thinmathspace}{0ex}}\hat{d}\Rightarrow \overrightarrow{a}=a\phantom{\rule{thinmathspace}{0ex}}\hat{d}=g\phantom{\rule{thinmathspace}{0ex}}\hat{d}$ where $a$ is the magnitude of the acceleration.

So the acceleration of free fall $\overrightarrow{a}$ has the same magnitude as the gravitational field strength $g$ and is in the same direction $\hat{d}$

To differentiate between the two quantities you can use $\mathrm{N}\phantom{\rule{thinmathspace}{0ex}}\mathrm{k}{\mathrm{g}}^{-1}$ as the unit of gravitational field strength and $\mathrm{m}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{s}}^{-2}$ as the unit of acceleration although dimensionally they are the same.

The force on a mass $m$ in a gravitation field $\overrightarrow{g}(=g\phantom{\rule{thinmathspace}{0ex}}\hat{d})$ is $\overrightarrow{F}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{g}=m\phantom{\rule{thinmathspace}{0ex}}g\phantom{\rule{thinmathspace}{0ex}}\hat{d}$ where $g$ is the magnitude of the gravitational field strength and $\hat{d}$ is the unit vector in the down direction.

Assuming no air resistance then using this force and Newton's second law you can find the acceleration of the mass in free fall.

$\overrightarrow{F}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{a}\Rightarrow m\phantom{\rule{thinmathspace}{0ex}}g\phantom{\rule{thinmathspace}{0ex}}\hat{d}=m\phantom{\rule{thinmathspace}{0ex}}\overrightarrow{a}=m\phantom{\rule{thinmathspace}{0ex}}a\phantom{\rule{thinmathspace}{0ex}}\hat{d}\Rightarrow \overrightarrow{a}=a\phantom{\rule{thinmathspace}{0ex}}\hat{d}=g\phantom{\rule{thinmathspace}{0ex}}\hat{d}$ where $a$ is the magnitude of the acceleration.

So the acceleration of free fall $\overrightarrow{a}$ has the same magnitude as the gravitational field strength $g$ and is in the same direction $\hat{d}$

To differentiate between the two quantities you can use $\mathrm{N}\phantom{\rule{thinmathspace}{0ex}}\mathrm{k}{\mathrm{g}}^{-1}$ as the unit of gravitational field strength and $\mathrm{m}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{s}}^{-2}$ as the unit of acceleration although dimensionally they are the same.

Troszokd95

Beginner2022-04-29Added 1 answers

Gravitational Intensity and Gravitation acceleration , even though have same dimensions are different physical quantities.

Gravitational Intensity of a mass body A at a given point is defined as the force on a unit mass body. It is just a physical quantity that is defined to help us find out the force exerted by the mass body A on any given mass in its field. So, if at any particular instant the gravitational intensity at a given is E , it does not imply that the gravitational acceleration of any mass at that point is equal to E, it's gravitational acceleration corresponds to the resultant force on it due to other bodies . For eg. Consider Moon, to find out the force exerted by the sun on it, we find out the gravitational intensity of the Sun at that point , but that does not mean that it is the gravitational acceleration.

Even for an isolated system of two bodies, gravitational intensity at a point is the property of the gravitational field associated with the mass A in consideration above, while the gravitational acceleration is the property of the other mass which is present in mass A 's gravitational field, that is even if the other body isn't present, gravitational intensity will be defined whereas gravitational acceleration will not be.

Gravitational Intensity of a mass body A at a given point is defined as the force on a unit mass body. It is just a physical quantity that is defined to help us find out the force exerted by the mass body A on any given mass in its field. So, if at any particular instant the gravitational intensity at a given is E , it does not imply that the gravitational acceleration of any mass at that point is equal to E, it's gravitational acceleration corresponds to the resultant force on it due to other bodies . For eg. Consider Moon, to find out the force exerted by the sun on it, we find out the gravitational intensity of the Sun at that point , but that does not mean that it is the gravitational acceleration.

Even for an isolated system of two bodies, gravitational intensity at a point is the property of the gravitational field associated with the mass A in consideration above, while the gravitational acceleration is the property of the other mass which is present in mass A 's gravitational field, that is even if the other body isn't present, gravitational intensity will be defined whereas gravitational acceleration will not be.

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