quiz
a)
From the diagram, we get when
R1 = 2kpc, v1 = 200km/s
R2 = 5kpc, v2 = 220km/s
R3 = 10kpc, v3 = 225km/s
R4= 15kpc, v4 = 220km/s
R5 = 20kpc, v5 = 222km/s
R6 = 25kpc, v6 = 223km/s
v2 = GMR/R
MR = v2R/G
M1 = (2000002*2000*3.09*1016)/(6.67*10-11) = 3.706*1040kg
M2 = (2200002*5000*3.09*1016)/(6.67*10-11) = 1.12*1041 kg
M3 = (2250002*10000*3.09*1016)/(6.67*10-11) = 2.35*1041kg
M4 = (2200002*15000*3.09*1016)/(6.67*10-11) = 3.36*1041kg
M5 = (2220002*20000*3.09*1016)/(6.67*10-11) = 4.57*1041kg
M6 = (2230002*25000*3.09*1016)/(6.67*10-11) = 5.76*1041kg
b)Six plots
(logR, logM)
(0.3, 40.6); (0.7, 41); (1, 41.4); (1.2, 41.5); (1.3, 41.7); (1.4,41.8)
c) logMR = (3-α) logR+k
3-α = (41.8 - 40.6)/(1.4-0.3)
3-α = 1.1 α = 1.9
2.
Larger galaxy: v = H0d d = v/H0 = 5000/71 = 70.4 Mpc = 70.4 * 3.09 * 1022m = 2.18 * 1024 m
34 arcminutes = pi/10800 * 34 = 9.89 * 10-3 radians
Linear separation = 2.18 * 1024 * 9.89 * 10-3 = 2.16 * 1022m
Since
F = mv2/r and F = GMm/r2
So mv2/r = GMm/r2 vm = 5200-5000 = 200000m/s
M = rv2/G = 2.16 * 1022 * 2000002 / (6.67 * 10-11) = 1.3 * 1043kg
So the larger galaxy has 1.3 * 1043kg.
a)
From the diagram, we get when
R1 = 2kpc, v1 = 200km/s
R2 = 5kpc, v2 = 220km/s
R3 = 10kpc, v3 = 225km/s
R4= 15kpc, v4 = 220km/s
R5 = 20kpc, v5 = 222km/s
R6 = 25kpc, v6 = 223km/s
v2 = GMR/R
MR = v2R/G
M1 = (2000002*2000*3.09*1016)/(6.67*10-11) = 3.706*1040kg
M2 = (2200002*5000*3.09*1016)/(6.67*10-11) = 1.12*1041 kg
M3 = (2250002*10000*3.09*1016)/(6.67*10-11) = 2.35*1041kg
M4 = (2200002*15000*3.09*1016)/(6.67*10-11) = 3.36*1041kg
M5 = (2220002*20000*3.09*1016)/(6.67*10-11) = 4.57*1041kg
M6 = (2230002*25000*3.09*1016)/(6.67*10-11) = 5.76*1041kg
b)Six plots
(logR, logM)
(0.3, 40.6); (0.7, 41); (1, 41.4); (1.2, 41.5); (1.3, 41.7); (1.4,41.8)
c) logMR = (3-α) logR+k
3-α = (41.8 - 40.6)/(1.4-0.3)
3-α = 1.1 α = 1.9
2.
Larger galaxy: v = H0d d = v/H0 = 5000/71 = 70.4 Mpc = 70.4 *
From the diagram, we get when
R1 = 2kpc, v1 = 200km/s
R2 = 5kpc, v2 = 220km/s
R3 = 10kpc, v3 = 225km/s
R4= 15kpc, v4 = 220km/s
R5 = 20kpc, v5 = 222km/s
R6 = 25kpc, v6 = 223km/s
v2 = GMR/R
MR = v2R/G
M1 = (2000002*2000*3.09*1016)/(6.67*10-11) = 3.706*1040kg
M2 = (2200002*5000*3.09*1016)/(6.67*10-11) = 1.12*1041 kg
M3 = (2250002*10000*3.09*1016)/(6.67*10-11) = 2.35*1041kg
M4 = (2200002*15000*3.09*1016)/(6.67*10-11) = 3.36*1041kg
M5 = (2220002*20000*3.09*1016)/(6.67*10-11) = 4.57*1041kg
M6 = (2230002*25000*3.09*1016)/(6.67*10-11) = 5.76*1041kg
b)Six plots
(logR, logM)
(0.3, 40.6); (0.7, 41); (1, 41.4); (1.2, 41.5); (1.3, 41.7); (1.4,41.8)
c) logMR = (3-α) logR+k
3-α = (41.8 - 40.6)/(1.4-0.3)
3-α = 1.1 α = 1.9
2.
Larger galaxy: v = H0d d = v/H0 = 5000/71 = 70.4 Mpc = 70.4 * 3.09 * 1022m = 2.18 * 1024 m
34 arcminutes = pi/10800 * 34 = 9.89 * 10-3 radians
Linear separation = 2.18 * 1024 * 9.89 * 10-3 = 2.16 * 1022m
Since
F = mv2/r and F = GMm/r2
So mv2/r = GMm/r2 vm = 5200-5000 = 200000m/s
M = rv2/G = 2.16 * 1022 * 2000002 / (6.67 * 10-11) = 1.3 * 1043kg
So the larger galaxy has 1.3 * 1043kg.
a)
From the diagram, we get when
R1 = 2kpc, v1 = 200km/s
R2 = 5kpc, v2 = 220km/s
R3 = 10kpc, v3 = 225km/s
R4= 15kpc, v4 = 220km/s
R5 = 20kpc, v5 = 222km/s
R6 = 25kpc, v6 = 223km/s
v2 = GMR/R
MR = v2R/G
M1 = (2000002*2000*3.09*1016)/(6.67*10-11) = 3.706*1040kg
M2 = (2200002*5000*3.09*1016)/(6.67*10-11) = 1.12*1041 kg
M3 = (2250002*10000*3.09*1016)/(6.67*10-11) = 2.35*1041kg
M4 = (2200002*15000*3.09*1016)/(6.67*10-11) = 3.36*1041kg
M5 = (2220002*20000*3.09*1016)/(6.67*10-11) = 4.57*1041kg
M6 = (2230002*25000*3.09*1016)/(6.67*10-11) = 5.76*1041kg
b)Six plots
(logR, logM)
(0.3, 40.6); (0.7, 41); (1, 41.4); (1.2, 41.5); (1.3, 41.7); (1.4,41.8)
c) logMR = (3-α) logR+k
3-α = (41.8 - 40.6)/(1.4-0.3)
3-α = 1.1 α = 1.9
2.
Larger galaxy: v = H0d d = v/H0 = 5000/71 = 70.4 Mpc = 70.4 *