Formula Sheet
Intensity Ratio:
= 2.512
−
Magnitude Difference:
= 2.5 log
=
Small Angle Formula:
Circular Velocity:
M = mass of central body (kg)
-11
3 2
G = 6.67 × 10 m /s kg
=
* Answer in m/s
D = diameter
* Answer in times (×)
=
Compare LGP:
Resolving Power:
=
Magnification:
=
.
(
D = diameter (cm)
* Answer in arcseconds
)
FO = focal length of objective
Fe = focal length of eyepiece
,
=
Wien’s Law:
=
=
,
* Answer in nm
.
× 10 Å
. ×
Å
Stefan-Boltzmann Law:
=
Doppler Formula:
=
Vr = radial velocity
c = 300,000 km/s
Δ = change in
= observed
Fusion Explained:
=
m = kg
c = 3×108 m/s
* Answer in Joules
Distance to Star:
F Ratio:
=
(/ /
T=K
= 5.67 ×10-8J/m2 s degree4
* Answer in J
)
,
p = parallax
(
)
(
)
* Answer in AU
−
Distance Modulus:
= −5 + 5 log
=
Luminosity of Star:
☉
+
Kepler’s 3rd Law:
=
Mass-Luminosity Relation:
=
Life Expectancy:
=
=
* Answer in times (×)
☉
Mass of Binary System:
= 10
☉
=
M = solar masses
p = orbital period (yrs) a = AU
p = orbital period (yrs) a = distance (AU)
.
M = star mass in MO * Answer in times (×)
M = star mass in MO
* Answer in O lifetimes × 10 billion = years
.
G = 6.67 × 10-11 m3/s2kg M = mass (kg)
Schwarzschild Radius:
=
Hubble Law:
= Hd
= velocity of recession of galaxy (km/s)
H = 20km/s/Mpc
d = distance (Mpc)
Redshift:
=
Δ = change in
Age of Universe:
Distance-Rate-Time:
Τ =
C = 3× 108 m/s
* Answer in m
O
= unshifted
H = 70 km/s/Mpc
* Answer in years
× 10
=
=
=
Newton’s Law of Gravity:
=
Kepler’s 1st Law (Eccentricity):
=
Ratio:
Frequency:
/
=
m3/s2kg
= masses of objects in kg
r = distance between the two masses (m)
F = the strength of the gravitational force (N)
G = 6.67 × 10
-11
Flux:
(
)=
(
=
Dispersion Distance:
)
Diameter of orbit: 300,000 km
* Answer in km
=
.
−
= 3.472 × 10
−
= 4.688 × 10
−
= 1.215 × 10
Constants
1
= 1.495979 × 10
1
= 206,265
= 3.085678 × 10
= 3.261633
1
,
,
ℎ
ℎ
= 9.46053 × 10
ℎ
ℎ = 2.997925 ×
= 6.67 × 10(
ℎ
⊕
10
)
+(
= 5.976 × 10
⊕
= 6,378.164
☉
= 1.989 × 10
☉
= 6.9599 × 10
☉
= 3.826 × 10
ℎ
= 7.350 × 10
ℎ
= 1738
= 1.67352 × 10
1
1
(1 ) =
1
60°
1
(1") =
1
60′
= 1,000,000
= 4.5 × 10
/
)/