# "Semi" Synchronous coordinates

• merav
In summary, the question is whether a metric can be constructed with only $g_{0i}=0$ in all of spacetime, not just in a neighborhood of a point. The answer is yes, by using the equation $g'_{0i}=\frac{\partial x^{\alpha}}{\partial x'^{0}}\frac{\partial x^{\\beta}}{\partial x'^{i}}g_{\alpha\beta}=0$, which provides enough partial differential equations to construct such a metric.
merav
I understand that one can always construct a set Synchronous coordinates (or Gaussian normal coordinates) on a neighborhood of a point in spacetime.

My question is:
Does one can construct a metric with only $g_{0i}=0$ such that
$dS^2=g_{00}dt^2 + g_{ij}dx^{i} dx^{j}$ (where $i=1,,,,D$ and $j=1,,,,D$) not just in a neighborhood of a point but to all spacetime in general?

In this case one should use

Yes...
One can use

g'_{0i}=\frac{\partial x^{\alpha}}{\partial x'^{0}}\frac{\partial x^{\\beta}}{\partial x'^{i}}g_{\alpha\beta}=0

so it seems we have enough PDE...

## What are "Semi" Synchronous Coordinates?

"Semi" Synchronous Coordinates are a type of coordinate system used in satellite communication and navigation. It is a hybrid of synchronous and asynchronous coordinates, where the satellite orbits the Earth at a slightly lower altitude than traditional synchronous orbits.

## How are "Semi" Synchronous Coordinates different from traditional synchronous coordinates?

Unlike traditional synchronous coordinates, "Semi" Synchronous Coordinates allow for better coverage of polar regions and easier access to higher latitudes. They also have a shorter period of revolution, resulting in faster data transmission and more accurate positioning.

## What are the benefits of using "Semi" Synchronous Coordinates?

"Semi" Synchronous Coordinates offer a balance between the advantages of both synchronous and asynchronous orbits. They provide wider coverage of the Earth's surface, faster data transfer rates, and improved accuracy in positioning and navigation.

## How are "Semi" Synchronous Coordinates used in satellite communication?

"Semi" Synchronous Coordinates are used in satellite communication to transmit signals to and from ground stations. They are also used in satellite navigation systems, such as GPS, to accurately determine the location of receivers on Earth.

## Are there any limitations to using "Semi" Synchronous Coordinates?

One limitation of "Semi" Synchronous Coordinates is that they require more frequent adjustments to maintain the desired orbit, compared to traditional synchronous orbits. This can increase the operational costs of maintaining a satellite in this type of orbit.

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