Astroparticle Physics

1.5 Problems 191.5 Problems1. Work out thea) velocity of an Earth satellite in a low-altitude orbit,b) the escape velocity from Earth,c) the altitude of a geostationary satellite above groundlevel. Where can such a geostationary satellite bepositioned?2. What is the bending radius of a solar particle (proton,1 MeV kinetic energy) in the Earth’s magnetic field(0.5 Gauss) for vertical incidence with respect to thefield? Use the relation between the centrifugal force andthe Lorentz force (6.1), and argue whether a classicalcalculation or a relativistic calculation is appropriate.3. Estimate the average energy loss of a muon in the atmosphere(production altitude 20 km, muon energy ≈10 GeV; check with Fig. 4.2).4. What is the ratio of intensities of two stars which differby one unit in magnitude only (for the definition of themagnitude see the Glossary)?5. Small astronomical objects like meteorites and asteroidsare bound by solid-state effects while planets are boundby gravitation. Estimate the minimum mass from whereon gravitational binding starts to dominate as bindingforce. Gravitational binding dominates if the potentialgravitational energy exceeds the total binding energy ofthe solid material, where the latter is taken to be proportionalto the number of atoms in the object. The averageatomic number is A, from which together with the Bohrradius r B the average density can be estimated.6. There is a statement in this chapter that a quasar at aredshift of z = 6.68 gives us information on the universewhen it was only about 3% of its present age. Can youconvert the redshift into the age of the universe?