Acceleration due to gravity: Difference between revisions

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Considering a body with the mass ''M'' as a source of a gravitational field, the strength of that field, or the
Under Newtonian gravity, the gravitational field strength, or gravitational acceleration, due to a point mass ''M'' is given by <math>\vec g = -G \frac{M}{r^2} \frac{\vec{r}}{r}</math>.  
gravitational acceleration, is given by <math>\vec g = -G \frac{M}{r^2} \frac{\vec{r}}{r}</math>.  
The modulus of ''g'' is <math>|g| = G \frac{M}{r^2}</math>.
The modulus of ''g'' is <math>g = G \frac{M}{r^2}</math>.


Here ''G'' is the gravitational constant, ''G'' = 6.67428&times;10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup>, ''r'' is the distance between a body of mass ''m'' and the center of the gravitational field, <math>\vec r</math> is the vector radius of that body having the mass ''m''.
Here ''G'' is the gravitational constant, ''G'' = 6.67428&times;10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup>, <math>\vec r</math> is the position vector in the field, relative to the point mass ''M'', and has a magnitude ''r''.
If the source of the gravitational field has a spherical shape, then ''r'' is the sphere’s radius. Taking into
account that the Earth is an oblate spheroid, the distance ''r'' is not that of a sphere and varies from the
equator to the poles.
 
[[Image:OblateSpheroidAngles.png]]
 
A normal section (on the equatorial plane) is almost an ellipse, so, ''r'' can be done by:
 
<math>r = \sqrt{{r_e}^2 cos^2 \theta + {r_p}^2 sin^2 \theta}</math>
 
 
where ''r<sub>e</sub>'' and ''r<sub>p</sub>'' are the equatorial radius and polar radius, respectively and ''θ'' is the latitude, or
the angle made by ''r'' with the equatorial plane.
 
References
 
1. V. Dorobantu and Simona Pretorian, Physics between fear and respect, Vol. 3, Edited by Politehnica                                          Timisoara, 2007, ISBN 978-973-625-493-2

Revision as of 16:57, 24 February 2008

Under Newtonian gravity, the gravitational field strength, or gravitational acceleration, due to a point mass M is given by . The modulus of g is .

Here G is the gravitational constant, G = 6.67428×10-11 Nm2/kg2, is the position vector in the field, relative to the point mass M, and has a magnitude r.

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