## Wednesday, November 19, 2014

### a quantum of sunshine

the Planck-spectrum is dominated by Boltzmann-statistics at high energies and by Bose-statistics at low energies. could you estimate how much solar power we receive per unit area at Earth from the quantum-mechanical part of the Sun's spectrum?

## Wednesday, November 12, 2014

### tidal forces in the gravity train

earlier this year there was a question about the gravity train to New Zealand. a passenger would feel two kinds of tidal forces: firstly, there's a differential gravitational field between head and feet, and secondly, the shoulders would each follow trajectories pointing towards the Earth's centre. which of the two effects is larger?

## Wednesday, November 5, 2014

### anti-Earth

imagine there would be a planet identical in mass as our Earth circling the Sun in our orbit with a lag of exactly 6 months, i.e. it would always be behind the Sun and not directly visible for us. would there be nevertheless possibilities of detecting it?

## Wednesday, October 29, 2014

### correlation coefficient

can you provide a proof of the Cauchy-Schwarz inequality and show with it that the correlation coefficient

r = \frac{\langle xy\rangle}{\sqrt{\langle x^2\rangle\:\langle y^2\rangle}}

always ranges between $-1\leq r\leq +1$?

bonus question: can you compute the normalisation, variance and kurtosis of $p(x)\mathrm{d}x\propto\exp(-x^4)\mathrm{d}x$?

## Wednesday, October 22, 2014

### Eddington temperature

Astrophysical objects are limited in their luminosity by the Eddington luminosity, where radiation pressure exceeds gravity. Would it be sensible to define a limiting Eddington-temperature for Planckian spectra?