<P> If it is desirable to model an object's weight on Earth as a function of latitude, one could use the following (p. 41): </P> <Dl> <Dd> g = g 45 − 1 2 (g p o l e s − g e q u a t o r) cos ⁡ (2 l a t π 180) (\ displaystyle g = g_ (45) - (\ tfrac (1) (2)) (g_ (\ mathrm (poles)) - g_ (\ mathrm (equator))) \ cos \ left (2 \, lat \, (\ frac (\ pi) (180)) \ right)) </Dd> </Dl> <Dd> g = g 45 − 1 2 (g p o l e s − g e q u a t o r) cos ⁡ (2 l a t π 180) (\ displaystyle g = g_ (45) - (\ tfrac (1) (2)) (g_ (\ mathrm (poles)) - g_ (\ mathrm (equator))) \ cos \ left (2 \, lat \, (\ frac (\ pi) (180)) \ right)) </Dd> <Ul> <Li> g p o l e s (\ displaystyle g_ (\ mathrm (poles))) = 9.832 metres (32.26 ft) per s </Li> <Li> g 45 (\ displaystyle g_ (45)) = 9.806 metres (32.17 ft) per s </Li> <Li> g e q u a t o r (\ displaystyle g_ (\ mathrm (equator))) = 9.780 metres (32.09 ft) per s </Li> <Li> lat = latitude, between − 90 and 90 degrees </Li> </Ul>

What is the relative error in the determination of the gravitational acceleration g