The acceleration due to gravity, g, is given by g=gmr2, where m is the mass of the earth, r is the distance from the center of the earth, and g is the uniform gravitational constant.
(a) suppose that we increase from our distance from the center of the earth by a distance δr=x. use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: δg≈ g× (your answer will be a function of x and r.)
(b) is this change positive or negative? δg is (think about what this tells you about the acceleration due to gravity.)
(c) what is the percentage change in g when moving from sea level to the top of mount elbert (a mountain over 14,000 feet tall in colorado; in km, its height is 4.29 km; assume the radius of the earth is 6400 km)? percent change =1

(a)

(b) The change in acceleration is negative.

(c) 99.87%

Step-by-step explanation:

(a) Given that the acceleration due to gravity, g, is given by

where M is the mass of the Earth,

           r is the distance from the center of the Earth, and

           G is the uniform gravitational constant.

If we increase from our distance from the center of the Earth by a distance Δr=x. Equation 1 becomes;

where g' is the acceleration due to gravity at the new height (r + Δr) or (r + x)

Dividing equation 2 by 1

       Dividing through by

Using Binomial approximation (Linear approximation),

(b) The change in acceleration is negative. This implies that the higher we move from the earth surface, the smaller the acceleration due to gravity becomes.

(c)  x = 4.29 km

     r = 6400 km

The percentage change in g is given as:

       = 99.87%

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9

step-by-step explanation: