PHYA3709: Latex assignment
Letlhogonolo Khenisa
19 February 2026
1
Initial Questions
1.1
Question 2
Figure 1: Heart of Phantom Galaxy
1.2
Question 3
Kepler’s third law is described by the equation,
T2 =
4π 2 3
a ,
GM
(1)
where T is the orbital period,G = 6.6743 × 10−11 N.m2 .kg−2 , is the gravitational
constant, M is the mass of the system and a is the semi-major axis of the orbit.
The most important equation in fluid dynamics is the Navier-Stokes equation
which is given by equation 2 below.
∂U
+ ∇ · T(U) = S(U),
∂t
where,
1
(2)


T
ρΓ
ρΓv
U =  ρΓ2 hv  , T(U) = ρΓ2 hvv + P I , S(U) = 0,
ρΓ2 h − P
ρΓ2 hv

where ρ is the proper density, P is the pressure, h is the specific enthalpy, Γ
is the bulk flow Lorentz factor, I is a 3x3 unit matrix and v is the three velocity.
1.3
Question 4
Table 1: Characteristics of main sequence stars by spectral type.
Spectral Class temperature(◦ C ) Approximate size (R∗ ) Population fraction (%)
O
> 30000
> 6.6
≈ 3 × 10−5
B
9700 − 30000
1.5 6.6
0.13
A
7200 − 9700
1.4 1.8
0.6
F
5700 −7200
1.1 1.4
3
K
4900 −5700
0.9 1.1
7.6
G
3400 − 4900
0.7 0.9
12.1
M
2100 − 3400
< 0.7
76.5
2