Rumus Astronomi

Mathematical Formulae for Astronomy 1



Each of the following formulae is in this format:

Name of Formula: Mathematical Formula

Variable = name of variable (units in words, units abbreviation)

Variable of Physical Constant = name of physical constant = number (units)



CHAPTER 1

Conversions of Distances

1 Astronomical unit (AU) = 1.495979 x 1011 (meters, m)

1 light-year (ly) = 9.46053 x 1015 (meters, m)

1 parsec (pc) = 3.085678 x 1016 (meters, m)



Scientific Notation



CHAPTER 4

Kepler’s Third Law: P2 = a3

P = orbital period (years, y)

a = semi-major axis or average distance to Sun (Astronomical Units, AU)



Newton’s Second Law: F = ma

F = force (Newtons = kilograms meters per second per second, N = kg•m / s2)

m = mass (kilograms, kg)

a = acceleration (meters per second per second, m / s2)



Newton’s Law of Universal Gravitation: Fgrav = G(m1m2) / r2

Fgrav = force due to gravity (Newtons, N)

G = Gravitational constant = 6.67 x 10-11 (N•m2 / kg2)

m1 = mass of object 1 (kilograms, kg)

m2 = mass of object 2 (kilograms, kg)

r = radial distance between two object’s centers (meters, m)



Newton’s form of Kepler’s Third Law: P2 = [4π2 / G (m1+m2)] a3

P = orbital period (seconds, s)

π = 3.1415927….

G = Gravitational constant = 6.67 x 10-11 (N•m2 / kg2)

m1 = mass of object 1 (kilograms, kg)

m2 = mass of object 2 (kilograms, kg)

a = semi-major axis or average distance between m1 and m2 (meters, m)







CHAPTER 5

Wavelength – Frequency relationship: ln = c

l = wavelength (meters, m) (Greek letter lambda)

n = frequency (Hertz = 1 / seconds, Hz = 1 / s) (Greek letter nu not a “v”)

c = speed of all electromagnetic radiation = 299,792,458 (meters per second, m / s)



Wein’s Law: lmax = c / T

c = Wein’s constant = 0.0029 (meters × Kelvin = m•K)

lmax = wavelength of maximum emission (meters, m)

T = temperature (Kelvin, K)



Energy Flux: F = L / 4pR2

F = energy flux (joules / second / square meters = watts / square meters, W / m2)

L = luminosity (joules / second = watts, W)

π = 3.1415927….

R = radius (meters, m)



Stefan – Boltzmann’s Law: F = sT4

F = energy flux (joules / second / square meters, W / m2)

s = Stefan-Boltzmann’s constant = 5.67 x 10-8 (W / m2•K4)

T = temperature (Kelvin, K)



Photon Energy: E = hc / l = hn

E = energy (joules, J)

h = Planck’s constant = 6.625 x 10-34 (J•s)

l = wavelength (meters, m)

n = frequency (Hertz = 1 / seconds, Hz = 1 / s)



Bohr formula for Electron Energy Level transitions: 1 / l = R(1 / N2 – 1 / n2)

l = wavelength (meters, m)

R = Rydberg’s constant = 1.097 x 107 (1 / m)

N = energy level number of the inner (lower) orbit

n = energy level number of the outer (higher) orbit



Redshift / Doppler Effect: (l - l0) / l0 = vradial / c

z = redshift (+ numbers means away, - numbers means towards, no units)

l = wavelength of moving object (meters, m)

l0 = wavelength of non-moving object (meters, m)

vradial = radial velocity (meters / second, m / s)

c = speed of all electromagnetic radiation = 299,792,458 (meters / second, m / s)





CHAPTER 18

Energy – Mass conversion: E = mc2

E = energy (joules, J)

m = mass (kilograms, kg)

c = speed of all electromagnetic radiation = 299,792,458 (meters / second, m / s)



CHAPTER 19

Stellar Parallax: d = 1 / p

d = distance (parsecs, pc)

p = parallax angle (arcseconds, “)



Luminosity – Brightness relationship: b = L / 4πd2

b = apparent brightness (watts / square meters, W / m2)

L = luminosity (watts, W)

π = 3.1415927….

d = distance (meters, m)



Radial Velocity – Wavelength: vr / c = (l - l0) / l0

vr = radial velocity (meters / second, m / s)

c = speed of all electromagnetic radiation = 299,792,458 (meters / second, m / s)

l = wavelength of moving object (meters, m)

l0 = wavelength of non-moving object (meters, m)



Distance Modulus: m – M = 5log(d) – 5 OR d = 10[(m-M+5) / 5]

m = apparent magnitude (no units)

M = absolute magnitude (no units)

d = distance (meters, m)



Stefan-Boltzmann Law combined with Energy Flux: L / 4pR2 = sT4

L = luminosity (watts, W)

π = 3.1415927….

R = radius (meters, m)

s = Stefan-Boltzmann’s constant = 5.67 x 10-8 (W / m2•K4)

T = temperature (Kelvin, K)



Kepler’s Third Law for Binary Star Systems: m1 + m2 = a3 / P2

m1 = mass of object 1 (Solar Masses, M8)

m2 = mass of object 2 (Solar Masses, M8)

P = orbital period (years, y)

a = semimajor axis (Astronomical units, AU)





CHAPTER 24

Schwarzschild Radius: RSch = 2GM / c2

RSch = Schwarzschild radius (meters, m)

G = Gravitational constant = 6.67 x 10-11 (N•m2 / kg2)

M = mass (kilograms, kg)

c = speed of all electromagnetic radiation = 299,792,458 (meters / second, m / s)



CHAPTER 26

Hubble Law: v = H0d

v = velocity (kilometers / second, km / s)

H0 = Hubble’s number = 71 (kilometers per second per Megaparsec, km / s / Mpc)

d = distance to galaxy (Megaparsecs, Mpc)



Redshift / Doppler Effect: z = (l - l0) / l0

z = redshift (+ numbers means away, - numbers means towards, no units)

l = wavelength of moving object (meters, m)

l0 = wavelength of non-moving object (meters, m)



CHAPTER 28

Age estimate of the Universe: T0 = d / v = 1 / H0

T0 = age estimate of the universe (seconds, s)

d = distance (meters, m)

v = velocity (meters / second, m / s)

H0 = Hubble’s number (kilometers per second per Megaparsec, km / s / Mpc)



CHAPTER 30

Frank Drake Equation: N = R* fp ne fl fi fc L

N = number of technologically advanced civilizations (no units)

R* = Rate of Sun-like stars forming (no units)

fp = fraction of stars with planets (no units, between 0 and 1)

ne = number of planets that are Earth-like (no units)

fl = fraction of Earth-like planets with life (no units, between 0 and 1)

fi = fraction of life that has become intelligent (no units, between 0 and 1)

fc = fraction of intelligent species technologically civilized (no units, between 0 and 1)

L = lifetime of a civilization (no units, between 0 and 1)

Bulan Terbelah

Allah SWT berfirman dalam QS. 54 Al-Qomar ayat 1:







1. telah dekat datangnya saat itu dan telah terbelah bulan[a].

[1] Yang dimaksud dengan saat di sini ialah terjadinya hari kiamat atau saat kehancuran kaum musyrikin, dan "terbelahnya bulan" ialah suatu mukjizat Nabi Muhammad SAW.

Selanjutnya Allah SWT berfirman dalam QS. 54 Al-Qomar ayat 2-5:

2. dan jika mereka (orang-orang musyrikin) melihat suatu tanda (mukjizat), mereka berpaling dan berkata: "(Ini adalah) sihir yang terus menerus".

3. dan mereka mendutakan (Nabi) dan mengikuti hawa nafsu mereka, sedang tiap-tiap urusan telah ada ketetapannya[2]

[2] Maksudnya bahwa segala urusan itu pasti berjalan sampai waktu yang telah ditetapkan terjadinya, seperti: urusan Rasulullah dalam meninggikan kalimat Allah pasti sampai pada akhirnya Yaitu kemenangan di dunia dan kebahagiaan di akhirat. sedang urusan orang yang mendustakannya pasti sampai pula pada akhirnya, Yaitu kekalahan di dunia dan siksaan di akhirat.

4. dan Sesungguhnya telah datang kepada mereka beberapa kisah yang di dalamnya terdapat cegahan (dari kekafiran).

5. Itulah suatu Hikmah yang sempurna Maka peringatan-peringatan itu tidak berguna (bagi mereka).







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