We saw earlier (Chapter 19) that the rate energy reaches the Earth from the Sun (the “solar constant”) is about 1.3 x 10³ W/m². What is (a) the apparent brightness b of the Sun, and (b) the intrinsic luminosity L of the Sun?

If a galaxy is traveling away from us at 2.2% of the speed of light, roughly how far away is it?

Starting from Eq. 44–3, show that the Doppler shift in wavelength is ∆λ/λᵣₑₛₜ ≈ v/c (Eq. 44–6) for v ≪ c. [Hint: Use the binomial expansion.]

Calculate the peak wavelength of the CMB at 1.0 s after the birth of the universe. In what part of the EM spectrum is this radiation?

At approximately what time had the universe cooled below the threshold temperature for producing (a) kaons (M ≈ 500 MeV/ c²), (b) Y (M ≈ 9500 MeV/c²), and (c) muons (M ≈ 100 MeV/c²)?

(a) In order to measure distances with parallax at 100 ly, what minimum angular resolution (in degrees) is needed?

(b) What diameter mirror or lens would be needed?

Use special relativity and Newton’s law of gravitation to show that a photon of mass m = E/c² just grazing the Sun will be deflected by an angle ∆θ given by ∆θ = 2GM/c²R, where G is the gravitational constant, R and M are the radius and mass of the Sun, and c is the speed of light. Put in values and show ∆θ = 0.87". (General Relativity predicts an angle twice as large, 1.74".)

Determine the radius of a neutron star using the same argument as in Problem 65 but for N neutrons only. Show that the radius of a neutron star, of 1.5 solar masses, is about 11 km.