# The mysteries of the wibbly-wobbly star

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OK, so we've decided it might be time for a different approach to getting away. If we're able to, and that's a big if, get the interstellar drive of our crashed ship working, we could try locating a neighbouring star with one of our colonies on it, and use that to get home. Seeing as our people have been busy building colonies for the last millennia or so, just finding a planet around a neighbouring star should be enough.

To this end, we've decided to analyse the radial velocity of a reasonably bright star we see clearly every night. What we're going to try is to calculate the mass of this planet by it's pull on the star the Doppler-shift caused by the stars wiggling back and forth from the gravitational pull of it's planets. If it has a sufficiently large planet orbiting it, we might be able to contact a colony from there.

What we start by doing is observing the planets light throughout one night in all wavelengths. From this we found out that our calculation robots had the ability to automatically get a radial velocity curve from this, so hey presto: ready made RV-plot.

In our library we found a formula that should allow us to easily calculate the mass of our star given a few more parameters. The formula says that \(m_p \sin i = \frac{m_*^\frac{2}{3} v_{* r} P^\frac{1}{3}}{(2 \pi G)^\frac{1}{3}}\), so what we'll need to know is the angle between our line of sight and the normal of the orbital plane \(i\), the orbital period of a given planet that's affecting our star \(P\), and the mass of the star \(m_*\). This can all be determined for some spectroscopic analysis of the star, which again it turns out our robots can do. Seems like somebody spared no expense when kitting out these things. They even included the Advanced Spectroscopy and Happy Birthday in 763 languages package (yes, they're bundle. No, nobody knows why. Probably to charge more.) Anyway, this means we've got all the necessary data from just feeding our observations to the robots. This showed us that we're looking at a star of 3.98 solar masses with period of about 12.5 solar years. They also discovered that we're looking essentially dead on to the plane of orbit, so \(i\) is \(\frac{\pi}{2}\) and the entire sin expression becomes one, and can be removed. We also see from our plot that the radial velocity peaks at about \(17.5 \frac{m}{s}\), leading us the get a mass of about \(1.08 \times 10^{-5}\)solar masses. That sound pretty reasonable, being in the same order of magnitude as our own systems most massive planet, and seems reasonable as a place to find colonists who can save us.

Now, we just have to be able to travel the 12 or so light years our robots tell us it is to this planet...

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