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3

If all you need is a quick and free tool to visualize orbits around earth, websites such as the following might be enough: First, the very simple orbitalmechanics.info, where you can just ignore the "add launch" option: And then, the more artsy Harmony-of-the-Spheres, which can also visualize some other systems. Maybe that already helps.


2

Kepler's Third Law including the constants of proportionality is: $$GM T^2 = 4\pi^2 a^3$$ Substituting $\mu = GM$, this can be rearranged to give: $$\frac{2\pi}{T} = \sqrt{\frac{\mu}{a^3}}$$ Which lets you rewrite your first formula as your second one and vice-versa. Note that in the first formula the reference epoch $t_0$ is assumed to be the time of ...


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