Astroparticle Physics

340 17 SolutionsWithµ = 1.67 × 10 −27 kg , ε = 1eV= 1.6 × 10 −19 J ,G = 6.67 × 10 −11 m 3 kg −1 s −2 , A = 50one gets the conditionM>4.58 × 10 22 kg .This means that our moon is gravitationally bound, while the moons of Mars (Phobosand Deimos) being much smaller are bound by solid-state effects, i.e., essentially byelectromagnetic forces.6. In special relativity the redshift is given byz = λ − λ 0λ 0=√1 + β1 − β − 1 .Let us assume that this relation can be applied even for the young universe, where atreatment on the basis of general relativity would be more appropriate.Solve z(β) for β or v:β = (z + 1)2 − 1(z + 1) 2 + 1⇒ v = (z + 1)2 − 1(z + 1) 2 + 1 c = Hd,t = d c = 1 (z + 1) 2 − 1H (z + 1) 2 + 1 ≈ 0.967H .SinceH 1 is the age of the universe, we see the distant quasar when it was ≈ 3.3% of itspresent age.17.2 Chapter 21. a) lepton-number conservation is violated: not allowed,b) possible,c) possible, a so-called Dalitz decay of the π 0 ,d) both charge and lepton-number conservation violated, not allowed,e) kinematically not allowed (m K − + m p >m Λ ),f) possible,g) possible,h) possible.