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Formula Sheet For Astronomy 1 - Paper 1 and Stars & Planets

This document provides formulas for various astrophysical concepts related to astronomy 1 and stars/planets. It includes formulas for: 1) Planck distribution, Wien's law, and Stefan's law which relate to blackbody radiation. 2) Energy levels of hydrogen-like atoms and ions. 3) Kepler's third law and other orbital mechanics formulas. 4) Stellar magnitudes and formulas relating luminosity and temperature. 3) Formulas for gas properties, degeneracy pressure, and magnetic field energy density which are relevant to stars.

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prashin
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297 views2 pages

Formula Sheet For Astronomy 1 - Paper 1 and Stars & Planets

This document provides formulas for various astrophysical concepts related to astronomy 1 and stars/planets. It includes formulas for: 1) Planck distribution, Wien's law, and Stefan's law which relate to blackbody radiation. 2) Energy levels of hydrogen-like atoms and ions. 3) Kepler's third law and other orbital mechanics formulas. 4) Stellar magnitudes and formulas relating luminosity and temperature. 3) Formulas for gas properties, degeneracy pressure, and magnetic field energy density which are relevant to stars.

Uploaded by

prashin
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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Formula Sheet for Astronomy 1 - Paper 1

and Stars & Planets

Astrophysical Concepts and Solar System


2hc 2 1
I     
Planck distribution: 5  exp hc   1
 
  kT  

Wien’s law:  max T  2.898x 10  3 m.K

Stefan’s law: F = T4

 C1Z 2  1 1 
or h = C1Z 
2
Energy levels for Hydrogen-like atom or ion: E n  
n2  n1
2
n 22 

C1 = 13.6 eV

 v
1  
   v
  o 
c
Doppler effect: For v << c,  
v2 o o c
1 2
c

3
Average thermal energy of atom in gas: E kT
2

a (1  e 2 )
Equation of ellipse in polar co-ordinates: r
1  e cos 

1/ 2
 b 2 
eccentricity: e  1 
 a 2 

perihelion distance: rp  a (1  e)

1 1 1
Synodic period of planet, Ts, given by:  
Ts TE Tp

2
 T  a3
Kepler’s Third Law:   
 2  GM

2mab
Angular momentum: J=
T

 2 1
Vis-viva equation: v 2  GM  
r a
1/ 3
 9M 
Roche limit: r   
 4 

dP  GM ( r )( r )
Hydrostatic equilibrium: 
dr r2

Barometer equation: P = Ps exp(-mgh/kT)

1/ 4
 (1  A)L o 
Thermodynamic equilibrium: T=  
 16r 2 
Stars

F 
m A  m B  2.5 log10  A 
Magnitudes:  FB 
m  M  5 log10 r (pc)  5

4 2 1
Binary star orbits: M1     r1  r2  2 r2
G T2

k
Ideal gas equation: P    T
m

Degeneracy pressure: P = A5/3

B2
Energy density in a magnetic field: UB 
2 o

2GM
Schwarzschild radius of a black hole: RS 
c2

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