Msun = 2x10^30 Lsun = 3.85 x 10^261LY = 9.5 x 10^12 km1 MPC = 3261636.26 LY c = 3 x 10^8

• a.

E = GM^2 / R

= G(2Msun)^2 / 10km = (6.67 x 10^-11)(2 x 10^30)(2 x 10^30) / (10000) = 2.668 x 10^46

b.

L = (1/4)(dM / dt)(c^2) L = dE / dt E = G(Mbh)(Mo) / 2Rs Rs = 2GMbh / c^2

E = (Mo)(C^2) / 4 L = (Mo)(C^2) / 4dt = (1/4)(dM / dt)(C^2)

Mo / dt = dM / dt Cancels out, same formula.

• 2
• 4 / 0.2 x 4.6 / 0.2 = 391

7200 x 76 x 391 x 30000000 = 6.42 x 10^15

• a.

L / d^2 = L / 100MLY^210^8 / d^2 = 10^4 / 10^16 LY^2 d^2 = (10^8 / 10^4) x (10^16) d = 10^10 LY

b.

• 6 BLY = 4.66 x 10^10

10^10 / 4.66 x 10^10 x 100% =21.46%

• a
• 6 / 656.3 -1

=5.03 x 10^-3

• 7 / 656.3 -1

=1.3 x 10^-2

• 2 / 656.3 -1

=3.5 x 10^-2

• 8 / 656.3 -1

=4.04 x 10^-2

• 03 x 10^-3 x c

= 1509000

• 3 x 10^-2

= 3900000

• 5 x 10^-2

= 10500000

• 04 x 10^-2

= 12120000

Fractions of speed of light will be same as part a of 4.

c.

1509 km/s / 75 =20.12 mpc

3900 km/s / 75 =52.0 mpc

10500 km/s / 75 =140.0 mpc

12120 km/s / 75 =161.6 mpc

• a.

7 = (f(x) / x) - 18 = f(x) / x The observed wavelength is 8x greater than the actual wavelength.

b. Z = V/C = ((lam)o / (lam)rest) - 1

Lor = 1 / (Root: 1-((beta)^2))

z +1 = (v/c +1)(lor) z+1 = (1+(beta))(lor) z+1 = 1+beta / (Root: 1+(beta^2))

c. z+1 = Root: ((1+V/C)/(1-V/C)) (7 + 1)^2 = 1 + V/C / 1 - V/C64 (1 - V/C) = 1 + V/C64 - 64V/C = 1 + V/C63 = V/C + 64V/C63 - V/C = 64V/C63C - V = 64V63C = 65V V = 63C/65 V = 2.91 x 10^8 m/s

d.

• 91 x 10^5 km/s / 75

= 3880 mpc = 1.27 x 10^10 LY

• 3 billion parsecs
• 13% of observable universe.
• a

14300 mpc x70 = 1001000 km/s

• 66 x 10^10 LY
• 427 x 10^23 km
• 427 x 10^23 / 1001000 = T (seconds)

= 4.42 x 10^17 s = 1.4 x 10^10 years