# Can't understand gravitation

1. Sep 7, 2016

### Deebu R

1. The problem statement, all variables and given/known data
If we take the gravitational acceleration at the earths surface as 10,/s^2 and the radius of the earth as 6400km, decrease in the value of the gravitational acceleration g at a depth of 64 km from its surface would be ......,/s^2

2. The attempt at a solution
I was never really good in physics or maths so forgive me if this sound too stupid.
I tried using acceleration due to gravity at a distence d to the center,

Gd= Go [ 1-d/R], where Go is the acceleration due to gravity at the surface of earth.
But when I did this the solution became very messed up. Thank you very much for your help.

2. Sep 7, 2016

### Merlin3189

Perhaps you could show your calculation. Your formula seems reasonable and when I substitute your values in, I get a simple answer without any complications.

3. Sep 7, 2016

### drvrm

i think your equation is good -try to understand the relation...see
https://en.wikipedia.org/wiki/Gravity_of_Earth#Depth
as you move inside the earth's surface g decreases from the surface value and is now proportional to (R-d) and then you can proceed further..
this decrease is due tl less mass being enclosed by the spherical volume of radius (R-d).

4. Sep 7, 2016

### Deebu R

I got this,
Gd= 10 [1-64/6400]
Gd= 10 [99/100] = 9.9

Last edited: Sep 7, 2016
5. Sep 7, 2016

### Merlin3189

Your G0 must be wrong, since we know it to be around 9.8 m/sec2. This is probably what you spotted originally.

Looking at the values substituted in your formula, I can't see anything which could be the mass of the earth.
You seem to have put M=6.13 x 10-4kg - a bit light for an earth!

Also I don't agree with your value for R = 6400 m. You are mixing your units. You were told R = 6400 km. You must convert everything to a consistent set of units. Here that needs to be metres to match the G constant. So R= 6.4 x 106 m

I think the gravitational constant G=6.67 x 10-11 Nm2/kg2
and earth mass M=5.97 x 1024 kg

Of course, once you have calculated g0 your calculation for gp is ok. But you started with a bad value for g0

BUT you were told to use g0 = 10 m/sec2 so you just have to put this into your second equation and you'll get the right answer.

Well done for spotting that your Gp must be wrong with an acceleration of 10-22 m/sec2