# Acceleration of Gravity vs Latitude and Elevation

## Variation of acceleration of gravity due to latitude and elevation above sea level

Acceleration of gravity at sea level and elevation related to north-south position on earth (degrees latitude):

### Acceleration of Gravity - *a*_{g} - *m/s*^{2}

_{g}-

^{2}

### Acceleration of Gravity - *a*_{g} - (ft/s^{2})

_{g}- (ft/s

^{2})

### Example - Time for Falling Object to Hit the Ground on the Pole or on the Equator

The distance traveled after some time by a free falling object can be expressed as:

*s = 1/2 a _{g} t^{2}*

*where *

*s = distance (m, ft) *

*a _{g} = acceleration of gravity (m/s^{2}, ft/s^{2}) *

*t = time (s)*

The acceleration of gravity is stronger at the poles than at equator and the equation above can be modified to

*t = (2 s / a _{g})^{1/2}*

The time for an object at level *1 m* to hit the ground on the pole can be calculated as:

*t = (2 (1 m) / (9.832 m/s ^{2}))^{1/2} *

* = 0.4510 s*

The time for an object at level *1 m* to hit the ground on the equator can be calculated as:

*t = (2 (1 m) / (9.78 m/s ^{2}))^{1/2} *

* = 0.4522 s*

### Example - The Weight of a Large Man in Canada vs. Venezuela

The acceleration of gravity in Canada at latitude *60 degrees* is approximately *9.818 m/s ^{2}* and the acceleration of gravity in Venezuela at latitude

*5 degrees*is approximately

*9.782 m/s*.

^{2}The weight - or gravity force - of a large man with mass *100 kg* in Canada can be calculated as

*F _{g} = (100 kg) (9.818 m/s^{2})*

* = 982 N*

The weight the man in Venezuela can be calculated as

*F _{g} = (100 kg) (9.782 m/s^{2})*

* = 978 N*