Real gravitational acceleration of the earth

To be honest, determining the true gravitational acceleration of the Earth is very complicated but not impossible. Why is the gravitational acceleration value ( 981.cm/s² ) of the earth

 wrong ?

  It is a proven fact that the most gravitational acceleration of the earth exist on the earth's surface.

Perfect value of acceleration of  🌎 

              is 983.218 cm/sec²

 As the gravitational acceleration decreases as we go up from the earth, its value will be zero at one time and the gravitational acceleration will decrease as we go down the earth and the value of the Earth's center will be zero. But the biggest problem is to determine the boundaries of the earth because the earth is not spherical but it is rotating and ecliptical and the atmosphere is located within the boundaries of the earth. Whatever it is, we hold the earth's sea level to the earth's borders for convenience. Earth's gravitational acceleration in the polar region is 983.218 cm/s². The gravitational acceleration of the Earth at a latitude of 45° is 980.665 cm/s². And the Earth's gravitational acceleration at the equator is 978.033z cm per second square. In India the datum adapted for the Great Trigonometrical Survey (GTS) is the mean sea level at Karachi it's latitude of 45°. 

 The difference between the gravitational acceleration of the Earth's polar and equatorial regions is about ( 983.218 - 978.033 ) = 5.185 cm/sec² 

Other hand, we know that polar radius of the earth is 6356.7523 km and equatorial radius of the earth is 6378.1370 km. The difference between the two is about 21.3847 km.

Average radius of the earth is about 6371.009 km 

 

Change in gravitational acceleration due to Earth's diurnal motion

 Considering all this information, it is easy to conclude that this shape is due to the diurnal motion of the earth. Due to the diurnal motion of the Earth, the gravitational acceleration of the Earth decreases by about 3.4 cm per second square. Here,   ω².R.cos²ф = (2л/T)².(6.357×10⁸).(cos²0°) = [ 2л/ (86164.1)]². (6.378137 × 10⁸ ).1²  = 3.392 cm/s² Now, taking R =6378.137 km. = 6.378137 × 10⁸. cm, T= 23h 56m 4.1s = 86164.1 seconds . Thus, due to the diurnal motion of the Earth, the highest gravitational acceleration may decrease by 3.392 cm/sec². Note that this calculation only shows the difference between the gravitational acceleration of the polar region and the equatorial region and does not specify the value of the actual gravitational acceleration.

       On the other hand we know that g = G.(M+m)/R² = G.M/R² ( where m neglected )

= G.4/3.лR³.р/R² = G.4/3.л.р. R 

Or, g = k.R  -------  ( 1 )

 here,  k is Constant. Because G, 4/3, л and р are Constants.  So we get from the equation 

g ∝ R

Thus the gravitational acceleration of the earth (g) is directly proportional to the radius of the earth (R). The avarage radius of the earth is about 10.70 km greater than the radius of the polar region and the radius of the equatorial region is about 10.70 km greater than the average radius of the earth.  The value of the earth's gravitational acceleration in the polar region is correct because there is no effects on the diurnal motion of the earth. On the other hand, the value of the gravitational acceleration of the earth's equatorial region is not entirely accurate because it is here that the effects of the earth's diurnal motion are greatest.

  Now let's see what is the equatorial acceleration of the earth :

 We know that,  g = G.M/r²

Here G and M are constants, 

     g  = k/r²

   ∴   g ∝ 1/r²

   ∴  k = gr²

 k = 983.218 × ( 6371.009 )²

     =9.9909 × 10¹⁰ cm³/s²

 

Hence there will be acceleration of gravity in the equatorial region   k/(6378.137km)²

             =981.022 cm/s²

 Hence the gravitational acceleration of the earth decreases by 2.196 cm/s² due to unwanted distance increase. 

 Hence due to diurnal motion of earth and unwanted distance increase in equatorial region gravitational acceleration decreases ( 3.392 + 2.196 ) 

= 5.588 cm/s²

 

Hence the gravitational acceleration of Earth's equatorial region is ( 983.218  - 5.588 ) =  977.630 cm/s² But we find the gravitational acceleration at the equator is 978. 033 cm/s². So we can easily assume that this slight increase of 0.403 cm/s² may be due to inflation of the equatorial region. Therefore, for general convenience, the average gravitational acceleration of the earth can be taken as the gravitational acceleration of the polar regions.

So the gravitational acceleration at the polar regions is 983.218 cm/s² Earth's average gravitational acceleration

 FAQ

     

What is the average gravitational acceleration of the earth?

Gravitational acceleration of the earth can be basically divided into two parts namely apparent gravitational acceleration and real gravitational acceleration. Apparent gravitational acceleration in the polar region is 983.218 cm/s², earth's gravitational acceleration at the equator is 978.033 cm/s² and the avarage earth's gravitational acceleration at a latitude of 45° is 980.665 cm/s² but Earth's actual gravitational acceleration is about 983 cm/s²

How much does the value of gravitational acceleration decrease due to the diurnal motion of the earth?

Due to the diurnal motion of the Earth, the highest gravitational acceleration may decrease by 3.392 cm/sec².

Does the Earth's oval shape cause the acceleration of gravity to be less or more?

Gravitational acceleration is only slightly affected by the Earth's oval shape

  So if the Earth were spherical, and had no diurnal motion,

 the average gravitational acceleration of the Earth will be about 983.218 cm/s².

  The value of this gravitational acceleration is of considerable importance in determining the exact mass of our earth. Gravitational acceleration of earth is about 983.218 cm/s² but earth is not spherical and due to daily motion of earth it decreases and actually average gravitational acceleration of earth is about 983.218 cm/s² not less but more.  So the average gravitational acceleration of the earth is about 983.218 cm/s².