Variation of gravity with latitude

In summary, the observed value of gravity at a latitude with an angle "a" is affected by the motion of rotation, resulting in a decreased value due to the counteracting centrifugal force. This force can be represented by the equation \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. However, at a latitude of \varphi, the radius used in this expression would be rcos\varphi, assuming a spherical Earth.
  • #1
physics_lover
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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?
 
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  • #2
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.

[tex] \mathbf{F}_c = m(\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r}))[/tex]

Where [tex]\mathbf{\omega}[/tex] and [tex] \mathbf{r}[/tex] are the angular velocity and radius of the Earth respectively.
 
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  • #3
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!
 
  • #4
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).
 
  • #5


Kurdt said:
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.

[tex] \mathbf{F}_c = m(\mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r}))[/tex]

Where [tex]\mathbf{\omega}[/tex] and [tex] \mathbf{r}[/tex] are the angular velocity and radius of the Earth respectively.

But at a latitude of [tex]\varphi[/tex], isn't the radius in the above expression not the radius of the earth, r, but rcos[tex]\varphi[/tex]? Assuming of course a spherical earth, which is not really correct.
 
  • #6


Yes.
 

1. What is the variation of gravity with latitude?

The variation of gravity with latitude refers to the change in the strength of the Earth's gravitational pull at different latitudes. This is due to the oblate shape of the Earth, which causes the gravitational force to be slightly stronger at the poles and weaker at the equator.

2. Why does gravity vary with latitude?

Gravity varies with latitude because the Earth is not a perfect sphere. It is slightly flattened at the poles and bulging at the equator, which affects the distribution of mass and therefore the strength of the gravitational pull.

3. How is the variation of gravity with latitude measured?

The variation of gravity with latitude is measured using a device called a gravimeter, which can detect small changes in gravitational force. Scientists also use data from satellites and mathematical models to map the distribution of gravity around the Earth.

4. What is the impact of variation of gravity with latitude?

The variation of gravity with latitude has several impacts on Earth. It affects the shape of the Earth, the ocean tides, and the motion of celestial bodies. It also has implications for geodesy, which is the science of measuring and mapping the Earth's surface.

5. How does the variation of gravity with latitude affect us?

The variation of gravity with latitude has a very small effect on our daily lives. However, it is important for precise navigation and surveying, as well as for understanding the Earth's structure and evolution. It also plays a role in the development and maintenance of our planet's ecosystems.

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