# Real Gravitational acceleration of the Earth

#### Mean acceleration of the earth 984.873 cm/s²

Why is the current gravitational acceleration value ( 981.cm/s² ) of the earth wrong ? :

It is a proven fact that the most gravitational acceleration of the earth is on the earth's surface. 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 center will be zero. But the biggest problem is to determine the boundaries of the earth because 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 978.033 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 5.185cm / s². 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. 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,  ш².R.cos²ф = (2л/T)².(6.357×10⁸).(cos0°)² = [ 2л/ (86164.1)]². (6.357 × 10⁸ ).1²  = 3.38 cm/s² Now, taking R =6357 km. = 6.357 × 10⁸. cm, T= 23h 56m 4.1s          = 86164.1 seconds . When R will be 6378 km then,  it will be about 3.39 cm/s². Thus, due to the diurnal motion of the Earth, the maximum gravitational acceleration may decrease by 3.4 cm per second square. 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 ( m neglected )= G.4/3.лR³.р/R² = G.4/3.л.р. R Or, g = c.R here,  c is Constant. Because G, 4/3, л and р are Constants. 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 a avarage gravitational acceleration of the earth :

Polar acceleration, gp = c.Rp

c = gp/Rp = (983.218 cm/s²) ÷ (6.35675×10⁸ cm ) = (1.54673064÷10⁶)/s²                 Thus gravitational acceleration will increase for a radius of 10.7 km  c × 10.7 km = ( 1.54673 ÷ 10⁶ ) × ( 10.7 ×10⁵ ). cm/s²

= 1.655 cm/s².

Therefore, if there was no diurnal motion of the earth, the average gravitational acceleration of the earth at 45° latitude would take place about ( 983.218 + 1.655 )cm/s²

= 984.873 cm/s².

The reason for the low gravitational acceleration in the equatorial region of the earth is the creation of unwanted heights and the speed of rotation of the earth.

 UNWANTED INCREASE IN THE EARTH'S EQUATORIAL AREA
An unwanted increase in the Earth's equator, reduces the Earth's gravitational acceleration by about
2hg/R = 2 × (10.7 ×10⁵ )×983.22/(6.371 ×10⁸). cm/s² = 3.30 cm/s² and  due to the diurnal motion of the Earth, the maximum gravitational acceleration may decrease by 3.39 cm per second square. Thus the gravitational acceleration of the Earth's equatorial region will be.    (984.873 - 3.30 -3.39) =( 984.87 - 6.69 ) = 978.18 cm / s².   This value is consistent with reality. The gravitational acceleration of the Earth's equatorial region is 978.033 cm per second square.
So if the Earth were spherical, and had no diurnal motion, the average gravitational acceleration of the Earth would be about 985 cm/s².
The value of this gravitational acceleration is of considerable importance in determining the exact mass of our earth. Basically, the gravitational acceleration of the earth is about 984.873 cm per second square but due to the fact that the earth is not spherical and the diurnal motion of the earth, it decreases and apparently the gravitational acceleration of the earth is about 980.665 cm per second square.