- #1

Hak

- 709

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The planet's atmosphere is such that clouds form at a height [tex]h[/tex] above the ground. The clouds create rain that falls in a rarefied atmosphere with negligible friction. We can also assume for simplicity that [tex]h[/tex] is very small and negligible compared to the radius of the planet. Let us assume that the clouds and rain are at a [tex]\theta[/tex] colatitude.

Now, this problem serves as an example to extrapolate some really interesting physics-related information. The question posed by the problem (which I do not report) has been solved by me, but I would like some difficult implications explained. I would like to understand a little if and why the data that is given is realistic and how it is found. Meaning: how do you measure the ratio of the planet's radius to the star, the distance between the two, how do you measure the temperature of a star and a planet, the planet's rotational speed, etc...

For the temperature of the star, I think it is possible to obtain it from Wien's law if it is possible to receive the radiation emitted by the star and measure its wavelength; on the other hand, I don't think there are many other ways of obtaining information about distant celestial bodies. I had thought that the same procedure could be applied to obtain the temperature of the planet, but I don't think it is possible. Planets emit very little, that you can capture and recognise the light coming from the planet seems difficult to me. I can't think of anything.

For the planet's rotational velocity, I am reminded of the question in this year's second level competition, where it was required to apply the Doppler effect to obtain the Sun's rotational velocity. This assumes, as with temperature, that we are able to measure the radiation emitted by the celestial body with sufficient precision. However, this method does not convince me very much; in the problem we were talking about hydrogen stripes, so it may be inapplicable to a rocky planet. Alternatively, if the planet has an atmosphere, we could deduce something about its rotation by observing the motions of any clouds (assuming we have a powerful enough telescope).

For the distance between the two bodies I have thought of two possibilities: the first, simply, is that we are in a position to measure it by observing for at least one period the planet's motion of revolution (the maximum distance observed would correspond to the one sought); the second, much more improbable, is that it can be deduced from Kepler's law by knowing the planet's period of revolution (which I think is measurable) and the mass of the star. I don't really have a decent idea of how the latter could be measured in general (perhaps there is some relationship between the surface temperature and the mass of a star?), but I thought that, in the case where several planets orbit the same star, its Kepler constant (and thus its mass) can be derived by measuring the periods of revolution of the planets and the ratios of their distances from the star (I think at least the ratio can be determined by telescope).

For the ratio of planet and star radii, I throw up my hands. The only idea I have is to compare them when the planet passes exactly in front of the star (i.e. they are aligned with our view), but this only makes sense if the distance between the two is much smaller than the distance between us and that star system (which I think is true enough for every system except the Solar system) and if it is possible to obtain such high resolutions (and I already had my doubts about the distance between the two, which should be much greater than their radii anyway).

Thanks for any reply.