# Acceleration due to gravity?

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1. Oct 21, 2015

### faiziqb12

using Newtons equation for gravitational force
one can fling that the acceleration due to gravity, g' above the surface of earth as

g' = g (d/(d+h))

but I find that there is a different equation for the same as

g' = g ( 1- 2h/r )

I know the first formula is right
but I can't doubt the first formula.....
however the unit of h and r in the second formula is km as compared to the m of the first formula

2. Oct 21, 2015

### Staff: Mentor

The first formula is wrong, and the second formula is an approximation to the corrected version of the first formula for small values of h/r.

Chet

3. Oct 21, 2015

### faiziqb12

so as you have said the first formula is wrong
then please show how its wrong

and yes please show the derivation method of the second equation

thanks

4. Oct 21, 2015

### Staff: Mentor

Gravity varies inversely with distance (a) to the first power or (b) to the second power?

5. Oct 21, 2015

### faiziqb12

obviously to the 2nd power

6. Oct 21, 2015

### faiziqb12

I'm sorry but I missed the square in my second formula

the correct one is
g' = g (d / ( d+h )) ^ 2

7. Oct 21, 2015

### Staff: Mentor

Good. Now let x = h/d. Please re-express your equation in terms of x.

8. Oct 21, 2015

### faiziqb12

the new formula is then
g' = g ( 1 / (1+x) ) ^ 2

9. Oct 21, 2015

### faiziqb12

what am I supposed to do further

10. Oct 21, 2015

### Staff: Mentor

Good, this is correct even with all those parentheses. But, here's a piece of advice: if you don't simplify your mathematical expressions when you are at your present stage, you are going to encounter real problems (manipulating the mathematics) when you get to more complicated analyses. So, I'm going to simplify it for you:
$$g'=\frac{g}{(1+x)^2}$$
Have you gotten far enough in calculus to be able to expand this in a Taylor series about x = 0?

Chet

11. Oct 21, 2015

### faiziqb12

I'm sorry
but I can't. I'm just studying in class 9th
isn't there an alternative method

12. Oct 21, 2015

### Staff: Mentor

Yes. From what you learned about geometric progressions, what is the infinite sum 1-x+x2-x3.... equal to?

13. Oct 21, 2015

### Staff: Mentor

Or look up the "binomial approximation." It's a very useful thing to know for situations like this.

14. Oct 21, 2015

### faiziqb12

thanks chestmiller
looks like I can do it now

it would 've your goodness if you show me the whole method involving this progression