What is the gravitational acceleration?

Question

The gravitational acceleration at the surface of a planet is 25.5 m/s2. Find the acceleration at a height above the surface equal to half the planet's radius.

Answer 1

If you recall that the force of gravity varies inversely proportional to the square of the distance (r) between the centers of mass (m and M), then you can immediately write g = k(1/r^2) = 25.5 m/sec^2 and G = k(1/R^2); where r = 1 and R = 1.5r, which is 1.5X the planet's radius r. The k's are constants of proportionality.

Thus, we have G/g = k(1/R^2)/k(1/r^2); so that G = g(r^2/R^2) = g(1/1.5)^2 = 25.5(1/2.25), you can do the math. But you can see that the new G is less than half of g = 25.5.

Lesson: When asked to compare the value of something (like g and G) at two different states (like r and R), this is best done by starting with a ratio (like G/g). This results because most of the factors going into G and g are the same values; so they cancel out in a ratio.

Answer 2

The g.a. decrease with the 2power of distance d.Increasing:d+1/2d=3/2*d.So the g.a. will be9/4smaller than:22,5,than=10

Answer 3

http://en.wikipedia.org/wiki/Gravitational_acceleration