the globular cluster Palomar 5 orbits the Milky Way and is stretched by tidal forces. on what time-scale would the tidal arms reach all around the Milky Way?

# cosmology question of the week

CQW is an educational resource for theoretical astrophysics and cosmology. we post a new question every week for students to get and for teachers to stay in shape.

## Wednesday, November 26, 2014

## 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

\begin{equation}

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

\end{equation}

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

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

\begin{equation}

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

\end{equation}

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

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

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