Acceleration due to gravity: Difference between revisions
imported>Roger Moore No edit summary |
imported>Michael Underwood (Expanded a little and added common definition of g=9.807 m/s^2) |
||
| Line 1: | Line 1: | ||
In the [[science]]s the term '''acceleration due to gravity''' commonly refers to the value | |||
:<math>g=9.807\ \text{m/s}^2\ .</math> | |||
Any object near the [[earth]] is subject to a [[force]] in the downward direction that causes an [[acceleration]] of magnitude ''g'' toward the surface of the earth. This value serves as an excellent approximation for the local acceleration due to gravity at the surface of the earth, although it is not exact and the actual acceleration varies slightly between different locations around the world. | |||
Here ''G'' is the gravitational constant, ''G'' = 6.67428×10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup>, <math>\vec r</math> is the position | More generally the acceleration due to gravity refers to the magnitude and direction of the acceleration of some test object due to the [[mass]] of another object. | ||
Under [[Newtonian gravity]] the gravitational field strength, or gravitational acceleration, due to a [[spherical symmetry|spherically symmetric]] object of mass ''M'' is given by | |||
:<math>\vec g = -G \frac{M}{r^2} \frac{\vec{r}}{r}\ .</math> | |||
The magnitude of the acceleration is <math>g = GM/r^2</math>, with [[SI]] units of [[meter]]s per [[second]] squared. | |||
Here ''G'' is the [[gravitational constant]], ''G'' = 6.67428×10<sup>-11</sup> Nm<sup>2</sup>/kg<sup>2</sup>, <math>\vec r</math> is the position of the test object in the field relative to the centre of mass ''M'', and ''r'' is the magnitude of <math>\vec{r}</math>. | |||
Revision as of 17:40, 24 February 2008
In the sciences the term acceleration due to gravity commonly refers to the value
Any object near the earth is subject to a force in the downward direction that causes an acceleration of magnitude g toward the surface of the earth. This value serves as an excellent approximation for the local acceleration due to gravity at the surface of the earth, although it is not exact and the actual acceleration varies slightly between different locations around the world.
More generally the acceleration due to gravity refers to the magnitude and direction of the acceleration of some test object due to the mass of another object. Under Newtonian gravity the gravitational field strength, or gravitational acceleration, due to a spherically symmetric object of mass M is given by
The magnitude of the acceleration is , with SI units of meters per second squared.
Here G is the gravitational constant, G = 6.67428×10-11 Nm2/kg2, is the position of the test object in the field relative to the centre of mass M, and r is the magnitude of .
