# B What is the value of acceleration due to gravity

1. Sep 9, 2016

### parshyaa

Upto what maximum height, value of g remains equal to 9.8 or close to it.
• g = GM/r^2
• And g' = GM/(r+h)^2 = g/(1+ h/r)^2
• Therefore when h ≥ r , g' decreases
• Again if h < r , g' agin decreases
• BUT I want to know what is the maximum height at which g' ≈ 9.8
• From my calculation maximum height ≈ 19.3 km, I think I am wrong, so what is the corrrct value of maximum height.

2. Sep 9, 2016

### Staff: Mentor

What do you consider a strong enough deviation? 1%?

3. Sep 9, 2016

### parshyaa

I want to know upto what height the value of g remains unchange.

4. Sep 9, 2016

### davenn

it doesn't remain unchanged, it's constantly changing with height
hence @DrClaude 's question which you didn't answer

5. Sep 9, 2016

### Tazerfish

It might be useful to do a linear approximation to the function $g'(h)=g \cdot (1+\frac {h}{r})^{-2}$
Then you would get $g'(h) \approx g'(0) + \frac {d(g'(0))}{dh} \cdot h$ Sorry for the convoluted notation.
this works out to be
$g' \approx g(1-\frac{2h}{r})$ Or in other words gravity decreases about 1 percent every $\frac {1}{200}$ of earths radius (which is roughly 32 kilometers).
EDIT: The approximation diverges pretty quickly but it gives at least some idea about the change in gravity with height.

Last edited: Sep 9, 2016
6. Sep 9, 2016

### parshyaa

Thanks tazerfish

Last edited by a moderator: Sep 9, 2016
7. Sep 9, 2016

### ZapperZ

Staff Emeritus
This is puzzling. How did that answer your question, when you were insistent on finding the height where "... the value of g remains unchange (sic)..."? tazerfish answer was exactly what DrClaude was asking you about, and you never did fully address.

Or are you even aware of what just happened here?

Zz.

8. Sep 9, 2016

### parshyaa

Actually I didn't understand what Dr.cloude asked. my question is simple , upto which height their is not much deviation in value of g , it remains between 9.8 to 10 . So what is the height

9. Sep 9, 2016

### parshyaa

Value of g remains in between 9.8 and 10

10. Sep 9, 2016

### ZapperZ

Staff Emeritus
Well then me explain. YOU need to specify the RANGE of values where you consider that it has not changed! Some people think a variation of 10% is sufficient. Some 1%. And if you are doing LIGO experiment, the variation can be orders of magnitude smaller!

Can't you even see what's going on here? You want something within some accuracy, but YOU never specified the level of accuracy that you are looking for!

Why is this so difficult to comprehend?

Zz.

11. Sep 9, 2016

### parshyaa

Just now I told you that the value should be inbetween 9.8 and 10

toldto

12. Sep 9, 2016

### ZapperZ

Staff Emeritus
That makes even LESS sense. As you go higher in height, the value of "g" drops! So if you are insisting that the value stays betweeen 9.8 and 10 (btw, my students get penalized for not writing down units) m/s^2, then you'll never find such a value, will you?

Why can't you just specify a percentage drop of when you consider to be within your acceptable range?

Zz.

13. Sep 9, 2016

### parshyaa

Suppose I am at the top of burj khalifa , it is at a height of 830 m , the value of g acting on me is approximately equals 9.7679 ≈ 9.8 , I want to know upto what such heights, the value of g remains closer to 9.8, suppose some budy asked a question that what is the force of attraction of earth on a object which is at a height of 200 km or 300 km or etc etc but not much larger from the earth surface.Then upto what value of h , without using the newtons gravitational formula I can directly take g ≈ 10. And find the force by multiplying it to the mass of a object.

14. Sep 9, 2016

### Staff: Mentor

Just use the equation from Newton's theory of gravitation:

https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

It's the equation part-way down the page under "Modern" version. The distance r that you use is measured from the center of the Earth, so be sure to add that distance to the distance your object is above the surface of the Earth.

15. Sep 9, 2016

### jbriggs444

So 9.7679 is acceptably close to 9.8 for your purposes.
Would 9.7402 be unacceptably low for your purposes?

16. Sep 9, 2016

### bsheikho

Why dont you substitute the value which you deem to be the first not acceptable answer for gravity, and work it backwards to get your distance?

17. Sep 9, 2016

### parshyaa

Yes value between 9.6 to10 will be accepetable

18. Sep 10, 2016

### davenn

you didn't read ZZ's post #12 did you ?

19. Sep 10, 2016

Staff Emeritus
How long is a piece of string?