Gravitational acceleration 'What is difference between free fall acceleration g and gravitational acceleration a?***a is with subscript g.In my textbook it is written that "free fall acceleration = gravitational acceleration - centripetal acceleration." so i'm confused if there is any difference between these two?
 A: In the second law of Newton appears the acceleration $a$. It refers to a generic acceleration due to any phenomenon. $g$ has the same role of $a$, but it refers specifically to the acceleration of gravity (free fall particular case) on the Earth. Usually we approximate $g$ to be constant $\left(9.81\, \mathrm{m}/\mathrm{s}^2\right)$, but in the real case the value of $g$ change at different altitudes (as mentioned by Edward Newgate).
A: Newton devised a very good law of gravity (until Einstein came along) where the force between the two bodies is scaled by a very small number usually written as a capital G. It's a general law that applies to any two bodies. But if you plug in the mass of the earth, the mass of a test ball, and the distance between the center of earth and the test ball, then plug in the experimentally determined G you will deduce the force on that test object. Next if you plug the calculated force on the test object along with its mass into another of Newton's laws F=ma and solve for a you will get the acceleration that the ball will experience at earths surface due to gravity. Since it is known that the calculated acceleration is independent of mass (it pretty much comes out the same for all test balls unless you do something ridiculous like plug in the moon but then you've got a radius issue) they give it a special symbol little g and give you the approximation 9.8 some odd meters per second per second. 
Edit: In the text book images above a seems to be the usual g and g is shown to include other accelerations. Another way you could complicate the equation is to consider the acceleration imposed by various other planets on the test ball. Also give it a charge and imagine some other charges pulling it in various other directions. Then you'd get an equation like mg=ma+fifty other things... But for almost all practical purposes g=a so you want to look at F=mg only. Here's an example of a situation that breaks that rule: in the equation above the extra term subtracts from ma resulting in smaller mg (weight) when you're lifting things it's easier to lift smaller dumb bells than larger ones right? Well in the space rocket industry easier equates to less fuel. which means less costs. So to maximize that second term they tend to build space centers nearer to the equator.
A: I think you are confused between gravitational CONSTANT g, and gravitational acceleration a which can be thought of as a VARIABLE.
Gravitation acceleration g is around 9.81m/s^2 near sea level. But as you go higher the gravitational acceleration is no longer g, but another number, let's say a. a is a more generic gravitational acceleration that is not necessarily g. 
Also, a is not only gravitational acceleration, but can be acceleration due to other phenomena (ex. Tension force).
