the Lenz-Runge-Laplace vector is stationary for the Newton-potential $\Phi\propto 1/r$. is that potential the only one with that property?

# 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, April 22, 2015

## Wednesday, April 15, 2015

### cosmic acceleration maxed out

what equation of state parameter and what density would a cosmic fluid need to have for producing a total deceleration larger than 1 or more negative than -1?

## Wednesday, April 8, 2015

### boosted electric and magnetic fields

electric and magnetic fields seem to transform into each other under Lorentz-transformation: is it possible to boost into a frame in which one type of field disappears completely?

## Wednesday, April 1, 2015

### Darwin-term in the Kepler-problem

planets are not pointlike objects and the total force in a gravitational field would need to be integrated over the planet's volume, i.e. the acceleration of the centre of gravity would need to be corrected by tidal forces. can you estimate how large that correction would be?

## Wednesday, March 25, 2015

### constant radius of the Hubble sphere

can you set up a FLRW-model in which the Hubble sphere has a constant comoving radius? what would be needed for such a construction?

bonus question: for which $n$ is the equality $\mathrm{i}^{n^2}=\pm\mathrm{i}^n$ with $\mathrm{i^2}=-1$ fulfilled?

bonus question: for which $n$ is the equality $\mathrm{i}^{n^2}=\pm\mathrm{i}^n$ with $\mathrm{i^2}=-1$ fulfilled?

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