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?

Wednesday, March 18, 2015

charge asymmetry

if the Earth was electrically charged its orbit would decay due to energy loss by electromagnetic radiation. can you construct an upper limit on the charge asymmetry, i.e. the ratio between electron and proton charge, from the observation that the solar system is very long lived? which planet would provide the best bound?

bonus question: can you show that $(-1)^{n^2}=(-1)^n$?

Wednesday, March 11, 2015

mass content of the Universe

can you estimate and quote an error on the estimate of the total mass inside the Hubble-volume? what assumptions do you make and which measurements are needed?

Wednesday, March 4, 2015

oscillations in the expansion history

the age of the Universe is estimated from the inverse Hubble constant, i.e. from the current expansion speed. imagine now that the Universe underwent a series of expansion and contraction phases such that we would underestimate the Universe's true age from the Hubble constant. would there still be ways of figuring out the true age?