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2

Of course, the metric $\eta_{\mu\nu}$ is not a unique solution for Einstein vacuum equations compatible with your given initial data. And yes, we can interpret the alternatives as arising from coordinate functions. Let us take the simplest of such function: redefine time by introducing new 'time' variable $\tau$ through a relation $t=f(\tau)$ (spacial ...

1

Both ecliptic and galactic coordinates are spherical coordinate systems that involve measuring angles on the celestial sphere. There are two equivalent ways to convert between such two coordinate systems: A transformation by deriving a general rotation matrix, for example using Euler angles; Finding an appropriate spherical triangle and calculating its ...

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Perhaps you're looking for something you can just punch into a spreadsheet instead of a generic matrix transformation? I've found it's easier to go from equatorial to other systems. So you can move it from ecliptic to equatorial (in degrees): $\alpha=tan^{-1}(\frac{sin(\lambda) *cos(\epsilon)-tan(\beta)*sin(\epsilon)}{cos(\lambda)})$ ...

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Elliptic coordinates are a general coordinate system while galactic coordinates are a set of 2-dimensional spherical coordinates with a heliocentric origin. Thus the conversion between the two would just be the conversion between elliptical and 2-dimensional spherical (i.e. polar) coordinates. This is easy to derive by writing each system in terms of ...

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