How Does Latitude Affect Observed Gravity?

[physics_lover]

When an observer stand on at the place with a angle "a" of the latitude,
the observed value of the gravity will be affected by the motion of the rotation.SO what is the value of the obversed gravity at that time?

 

[Kurdt]

The force of gravity is counteracted by the centrifugal force so the observed value of gravity is less than the true value. The effect due to the ficticious centrifugal or centripetal force (however you choose to name it) is as follows.

$$\mathbf{F}_c = m(\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r}))$$

Where $$\mathbf{\omega}$$ and $$\mathbf{r}$$ are the angular velocity and radius of the Earth respectively.

 

[physics_lover]

thz very much, the obversed gravity g' is less than ture value of g =10ms^-2 .
But I can't find the equation of g' in term of g & "angle of a" & "r"
& angluar velocity W only,

help me again pls!

 

[Kurdt]

You need to resolve the centripetal acceleration into horizontal and vertical components (think about what would be the best definition of horizontal and vertical in this case).

 

[Charlie Costa]

The force of gravity is counteracted by the centrifugal force so the observed value of gravity is less than the true value. The effect due to the ficticious centrifugal or centripetal force (however you choose to name it) is as follows.

$$\mathbf{F}_c = m(\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r}))$$

Where $$\mathbf{\omega}$$ and $$\mathbf{r}$$ are the angular velocity and radius of the Earth respectively.

But at a latitude of $$\varphi$$, isn't the radius in the above expression not the radius of the earth, r, but rcos$$\varphi$$? Assuming of course a spherical earth, which is not really correct.

 

[ideasrule]

Yes.