Calculating gravity in rotating frame(ECR)

[Banjo]

In reading through URL=ftp://164.214.2.65/pub/gig/tr8350.2/wgs84fin.pdf]this[/URL] pdf I came across the potential described on pg 51. I have no problem with the spherical harmonic expansion of the gravitational force, however I'm a bit confused about the phi potential added to account for the Earth's rotation. I think this only gives the the "centrifugal" force. Assuming the gravity vector that results is in ECR (Earth Centered Rotating, if I was going to rotate the acceleration given by this formula into ECI (Earth Centered Inertial)(from ECR), wouldn't I also need to add a coriolis term? or at least not add the coriolis term when doing the rotation? I have been told otherwise which is why I ask. BTW the position must be in ECR as the formula for V, the gravitational potential, is in terms of geodetic lattitude and longitude.

 

[member 553083]

The phi potential as defined in the paper you linked to is related to the Coriolis force, as it contains contributions from the centrifugal force and Coriolis acceleration. The difference between the two is that the Coriolis component of the phi potential is constant (i.e. it does not depend on the position of the body), while the centrifugal component depends on the position. Therefore, when performing a rotation from ECR to ECI, you would need to add a Coriolis term, as this term is not included in the phi potential.

 

[M98Ranger]

The calculation of gravity in a rotating frame is a complex topic and can be confusing, so it's understandable that you have some questions about it. Let's break down the different components and clarify their roles.

First, we have the spherical harmonic expansion of the gravitational force. This is a mathematical representation of the Earth's gravitational field, which takes into account the varying density of the Earth's mass distribution. This is necessary because the Earth is not a perfect sphere and the gravitational force varies slightly depending on your location on its surface.

Next, we have the phi potential, which is added to account for the Earth's rotation. This potential accounts for the centrifugal force, which is the perceived outward force due to the Earth's rotation. This is necessary because in a rotating frame, objects appear to be pushed outward, and this needs to be accounted for in the calculation of gravity.

Now, you are correct in saying that if you were to rotate the acceleration given by this formula into the Earth Centered Inertial (ECI) frame, you would also need to add a Coriolis term. The Coriolis force is a result of the Earth's rotation and is responsible for the apparent deflection of objects moving in a rotating frame. So, if you were to rotate the acceleration into the ECI frame, you would need to add the Coriolis term to account for this deflection.

However, if you are already working in the Earth Centered Rotating (ECR) frame, the Coriolis term is not necessary. The formula for V, the gravitational potential, is in terms of geodetic latitude and longitude, which are coordinates in the ECR frame. So, if you are using these coordinates, you do not need to add the Coriolis term.

In summary, the phi potential accounts for the centrifugal force in the ECR frame, and if you were to rotate the acceleration into the ECI frame, you would also need to add the Coriolis term. But if you are already working in the ECR frame, the Coriolis term is not necessary. I hope this helps clarify things for you.