# Acceleration due to gravity or the gravitational field

You see this all the time in textbooks: This is often described as "the acceleration due to gravity". Is this really the best thing to call this? No. A better name would be "the local gravitational field" and list it in units of: Where does g come from? The usual source is from the weight, or gravitational force: This is the best way to write it (in vector notation) but you will often see it written as: which looses the vector nature. In the vector notion, the vector g is a vector pointing towards the center of the Earth.

Why not acceleration due to gravity? Take the following case of a block sitting on a table. Here is the free body diagram. So what's wrong with this? Nothing. The problem is that if you call g the acceleration due to gravity, its just plain weird. The box is NOT accelerating. I think this leads to the confusion that acceleration itself is a force.

Gravitational Field

If g is the gravitational field, things work out better. First using the units of Newtons per kilogram, one can see that the gravitational field gives a force on a mass. The great thing about this is that it is extremely similar to the electric field in units of Newtons per Coloumb (an idea that students seem to have some trouble with). Note that I am not the first to promote this terminology for g, but I think its a great idea.

When is it the acceleration due to gravity?

Take the case of an object with only the force of gravity on it: In this case, the only force is gravity and it depends on mass. Using Newton's second law, I can write: So, in free fall the acceleration has the same magnitude as the gravitational field (and same direction). This is actually something strange. The strange thing is that there are essentially two masses. There is inertial mass (the resistance to change in motion by a force) and there is gravitational mass that is proportional to the gravitational force. To me, it is odd that these two masses are equivalent. Sure there is a way to explain this equivalence in general relativity, but in that area I am no expert (not even close).

The units:

Just as a check it is important to see that gravitational field and acceleration have equivalent units. So, what about the kinematics equation for free fall? In free fall, the acceleration IS g, so one could write the vertical position as the function: so this g could be called the acceleration due to gravity. HEY WAIT! How come there is a negative sign there? This is not a vector equation, this is a one-dimensional equation so that the negative sign is needed. It usually bothers students that we use g as a positive number. This is because g is the magnitude of the vector g so it has to be positive.

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GR does not "explain" the Equivalence Principle (all local vacuum free fall trajectories are identical regardless of mass composition or configuration). GR postulates the EP via Einstein's elevator (photons having twice the massed acceleration). Teleparallelism wholly contains GR as EP=true plus EP violations from angular momentum: physical spin, quantum spins (particle and orbit - magnets), relativistic spin-orbit coupling, and mass distribution chirality.

1.74 solar-mass pulsar PSR J1903+0327 in a 95.17-day 0.437-eccentricity orbit with its 1.05 solar-mass companion. 27% vs. 1.4x10^(-4)% gravitational binding energy, 1.8x10^11 vs. ~30 surface gees, 2x10^8 gauss vs. ~5 gauss magnetic field, neutrons and exotica vs. hydrogen plasma isopin; pulsar equatorial velocity more than 11% lightspeed. GR describes the binary.

Do left and right shoes falsify the EP? Nobody has looked. Solid single crystal spheres of space groups P3(1)21 and P3(2)21 quartz are enantiomorphic atomic mass distributions. Lock and load,

http://www.npl.washington.edu/eotwash/experiments/equivalencePrinciple/…
Browser "view image" to see the tungsten suspensory filament 1/3 hair thickness.

An EP parity violation is strongly allowed. Covariance with respect to reflection in space and time is not required by the PoincarÃ© group of Special Relativity or the Einstein group of General Relativity. Somebody should look.

who can tell the complete concept of the signs of acceleration and velocity when a body is in free fall and during the projectile motion

By neeraj (not verified) on 08 Jan 2009 #permalink

any one who knows the complete concept of the signs of acceleration and velocity when a body is in free fall and during the projectile motion can mail me to say me the information

me id is neeraj.mega7@gmail.com

By neeraj (not verified) on 08 Jan 2009 #permalink

Can you tell me what happens to a flow of liquid when there is a decrease in earths gravity like the one during eclipse. My email id is kpsanjayan@yahoo.co.in

By Sanjayan (not verified) on 28 Jul 2009 #permalink