Astrophysics and General Relativity · BPhO 2013 #5
Physics
Problem
a) A particle of electromagnetic radiation is called a photon. A photon has an energy of hf where h is Planck's constant. Write down an expression for the wavelength of the photon if it is emitted from a body moving away from the observer at a speed of u where u is much less than c. However, Einstein's theory of general relativity predicts another effect. On leaving the star the photon gains potential energy due to the star's gravitational field.
Derive an expression that gives the change in wavelength due to this gravitational effect when light of frequency f leaves a star of mass M, radius R. For the purposes of this derivation you can assume that a photon has a fictional mass of m that will (should!) disappear from your final equation.
b) Among the animals that appear in the zoo of the Universe there are black holes and neutron stars. The mass of each of these is often the order of the mass of the Sun. The radius of a neutron star is about 10 km and a certain neutron star rotates at about 100π s⁻¹.
Calculate the ratio of the polar diameter to the equatorial diameter for a typical neutron star. Assume that liquid or solid neutron material is incompressible. How do we know that it is rotating at this frequency?
c) Why are space rockets launched from positions near the equator? In order to launch a space probe out of the solar system, it is decided to send the probe close to Jupiter. Explain why this route reduces the fuel needed.