1.a:

• Alpha Centari A:
  • 4.4LY
  • 2.7x(10^-8) W/(m^2).
  • 2.7x(10^-8) = L / (4.4^2)
  • L = (2.7 x 10^-8)(4.4^2)
  • L = (5.2272 x 10^-7) W/(LY^2)
  • LY -> M: 9.46(10^15)
  • L = 4.95 x 10^9 w.

1.b:

• 100w Lightbulb
  • 2.7 x 10^-8 AB.
  • D^2 = 100w / (2.7 x 10^-8)
  • D = 60858.06m

2.a:

• Magnitude 7 -> magnitude 2
  • (10^0.4)^(7-2)
  • (10^0.4)^5
  • 100x brighter

2.b:

• 4 star is brighter than +6 star.
  • (10^0.4)^(6-(-4)).
  • (10^0.4)^10.
  • 10000x brighter

3.a:

• Radius of particle: 10^-7
• Mass of particle: 10^-14
  • 1500Msun cloud, 2% particles.
  • 1500 x 2 x 10^30 x 1000 x 0.02 / 10^-14
  • 6 x 10^48

3.b:

• SA of particle: (pi)(r^2)
  • (pi)((10^-7)^2)
  • (pi)(10^-14)
  • 6 x 10^48 particles
  • (1.89)(10^35)m^2
  • (4.34)(10^17)m
  • m -> LY: x((1.06)(10^-16))
  • 46.02 LY
  • 2117.94LY^2

3.c:

• Density = 10^21
  • Mass/V = 10^21
  • 1500x2x10^30x1000 / V = 10^21
  • V = 3 x 10^15
  • V = (4/3)(pi)r^3
  • r = 89470.02cm
  • cm -> LY: 1.06x(10^-18)
  • r = 9.48 x 10^-14 LY
  • SA = 4(pi)r^2
  • SA = 1.13 x 10^-25 LY^2

3.d:

• Cloud: 1.13 x 10^-25 LY^2
• Particles: 2117.94 LY^2
• 5.33 x 10^-27 %

4.a:

• Mbalance = (18)(Msun)(Root: T^3/n)
• Msun = 2 x 10^30 (kg)
• Tsun =
• Average particle mass: 10^-24 g
• Vsun: 1.412 x 10^18
  • Particle density: Number of particles / Vsun
  • Number of particles: Msun / Mparticle
  • 2 x 10^30 / 10^-24
  • 2 x 10^54
  • 2 x 10^54 / 1.412 x 10^18
  • D = 1.42 x 10^36 (particles / km3)
  • D = 1.42 x 10^36 x 10^15 (particles/cm3)
  • D = 1.42 x 10^51 (particles / cm3)

4.b:

• Mbalance = 18 x 2 x 10^30 x (Root: (T^3 / (1.42 x 10^51)))
• T = CubeRoot: (((MBalance / 18Msun)^2)(n))
• T = 4.38 x 10^48 K

4.c:

• IT doesn't really lololololol

5.:

• BetelGeuse D: 427 LY
• BetelGeuse SN-L: 10^10 Lsun
• Sirius D: 8.6 LY
• Sirius L: 26 Lsun
  • Betelgeuse AB: 10^10 / 427^2
  • 54845.91
  • Sirius AB: 26 / 8.6^2
  • 0.351541373
  • 156015.52 x brighter

6.:

• year observed: 1054
  • 100 / 0.11
  • 909.1
  • 2011 - 909 = 1102
  • They're close, I blame the expansion of the universe.

7.a:

• M1 + M2 = A^3 / P^2
  • 10500000 km -> 0.07 AU
  • 4 days = 0.011 years
  • Mtotal = 0.07^3 / 0.011^2
  • Mtotal = 2.84 Msun
  • 4.96 x 10^30 kg

7.b:

• Mass of Main sequence B2 star: Spica - 10.5 Msun

8.a:

• Rs = 2GM / c^2 = 3 x M/Msun km.
  • 3 x (10^8 Msun) / Msun km
  • 3 x 10^7 km.

8.b:

• 3 x (10^5 Msun) / Msun km
• 3 x 10^4 km.

8.c:

• Mass of moon?

8.d:

• (2)(6.67x10^-11)(60) / (3 x 10^8)^2
• 8.89 x 10^-29 km

9.:

• Age = p / 2r
  • p = 30 / second = 0.033 seconds.
  • r = -4.2 x 10^-13
  • 0.033 / 2 (4.2 x 10^-13)
  • 3.93 x 10^10 s
  • 1074.23 years
  • Close enough to the given age.