1.1: 45.71 parsecs
1.2: 1644371.7 parsecs
1.3: -1.77
1.4: -11.87
2.1: 4417.68 K
2.2: 2503.46 Angstroms
2.3: 0.323 nm
2.4: 2.53 x 10^17 K
2.5: 4858.7 K
2.6: 4 solar luminosities
3.1: 1 AU (T^2/a^3 = 4 pi^2/(GM))
3.2: USE T^2/a^3 = 1/M, T in years, a in AU, M in SOLAR MASSES (NOT kg)
T = 2.24 x 10^-26 years
3.3: USE T^2/a^3 = 1/M_total (T in yeras, a in AU) (M_total = M_planet + M_star, everything in
solar masses)
The numbers don’t work out, but you get the mass of the planet is -0.75 solar masses
(do M_tot-M_star, M_star is 2 solar masses)
4.1: -0.00757575 (negative is important)
4.2: It’s moving at 0.67 c, use this formula:
Z = 1.25
4.3: -2272727.27 m/s (negative is important)
4.4: Hubble’s law, v = Hd; v in km/s NOT m/s; H = 70 km/s/Mpc; d = distance in Mpc
d = 32.47 Mpc (distance always positive)
5.1: By simple trigonometry, angular diameter (in radians) = actual diameter/distance (actual
diameter and distance have to have the same units, but the actual unit doesn’t matter)
1 arcsecond = 1/3600 of a degree, then convert to radians
Make sure to double the star’s radius to get diameter
Distance = 5.78 x 10^15 m
5.2: d=1/p, d in parsecs and p in arcseconds
Make sure to convert to light years
D = 1.63 x 10^8 light years
5.3: Two step problem: First calculate the distance using the formula in 5.1, then use d=1/p
Don’t forget to convert distance from meters to parsecs
Parallax angle = 5.35 arcseconds
6.1: IMPORTANT FORMULA: Lifetime of a star = 10^10 years/(M^2.5), M in solar masses
Lifetime = 10^10 years (10 billion years)
6.2: E=hf, h is planck’s constant and f is frequency. E = 3.313 x 10^-31 J
6.3: c = wavelength times frequency, make sure units are good (1 THz = 10^12 Hz)
Wavelength = 3 x 10^-5 meters
6.4: Same formula as 6.3, frequency = 4.05 x 10^14 Hz (405 THz)