Does cartesian velocity contribute to Lat Long conversion?

[k80sg]

We understand that Lat Long Alt can be derived from 3D Cartesian (X,Y,Z) but does a 5D Cartesian (X, Y, Z, Vx, Vy) does the extra mile to provide a more precise conversion to Lat Long Alt with the additional velocity data?

 

[Filip Larsen]

Welcome to PF.

Your question does not really make sense to me. The precision of the spherical coordinates of a point are determined by the precision of the corresponding Cartesian coordinates, speed does not enter the equation at all.

Perhaps you could explain the context of your problem and why you think the conversion is not precise enough for what you are trying to achieve. Sound a bit like there might be a moving object or vehicle involved?

 

[k80sg]

Welcome to PF.

Your question does not really make sense to me. The precision of the spherical coordinates of a point are determined by the precision of the corresponding Cartesian coordinates, speed does not enter the equation at all.

Perhaps you could explain the context of your problem and why you think the conversion is not precise enough for what you are trying to achieve. Sound a bit like there might be a moving object or vehicle involved?

Thanks for answering the query, yes a moving object is involved hence the velocity information given. I was told by someone who is convinced that the additional velocity information does make a difference when doing a conversion to Lat Long Alt. I couldn't really understand the theory behind hence I wanted to seek advice here.

 

[Filip Larsen]

In general, if you have the cartesian coordinates of a moving vehicle at any point in time you can, as I said earlier, convert to spherical (or more precisely, geodetic) coordinates without any particular loss of precision.

It is still not clear to me what precisely you (or your friend) are thinking about. Perhaps you are thinking of vehicles that are only slowly (or not at all) accelerating. If you know that the vehicle at time t₀ was at position r₀ moving with velocity v, then we can approximate the position of the vehicle for times t close to t₀ using an expression like r_t = r₀ + vt (with r and v being vectors). If you now would like a similar expression for the coordinates in spherical (or geodetic) coordinates, your friend is correct that you could transform the velocity as well to get a similar expression. However, since spherical and geodetic coordinates are "curved" while cartesian coordinates are "straight", spherical coordinates from such an expression, would in general be precise for a smaller period of time around t₀ compared to the expression in cartesian coordinates. You could also try to get a more precise expression, but again, most non-trivial motions that are simple to describe in straight coordinates are often complicated to describe in curved coordinates, and visa versa.

It may also be that you friend is thinking about the Coriolis force or something similar? If you still want to pursue the mater, I'm afraid you will need to elaborate a bit more.

 

[PJC01]

I can say that cartesian velocity does play a role in the conversion of coordinates from cartesian to latitude and longitude. The addition of velocity data in a 5D cartesian system (X, Y, Z, Vx, Vy) can provide more precise conversions to latitude, longitude, and altitude. This is because velocity is a crucial factor in determining the exact location of an object in space and time.

In a 3D cartesian system, the conversion to latitude and longitude is based solely on the X, Y, and Z coordinates. However, in a 5D cartesian system, the inclusion of velocity data (Vx, Vy) allows for the consideration of the object's movement in the conversion process. This can result in a more accurate determination of the object's location in terms of latitude, longitude, and altitude.

Furthermore, the use of velocity data in the conversion process can also account for any changes in altitude due to the object's movement. This is particularly important in scenarios where the object is moving at high speeds or undergoing changes in altitude, such as in the case of aircraft or satellites.

In conclusion, the inclusion of cartesian velocity in a 5D system can contribute to a more precise conversion to latitude, longitude, and altitude. This is because velocity is a crucial factor in accurately determining an object's location in space and time, and its consideration can improve the overall accuracy of the conversion process.