Astronomical Masses

Question 1

What is the

Centre of Mass relation of 2 stars

Answer 1

M1r1 = M2r2

M = mass, r = radius of orbit

Question 2

What is the equation for

Angular velocity

Answer 2

ω =2π/P

ω = angular velocity, P = orbital period

Question 3

What is the equation for

Angular acceleration

Answer 3

a = rω^2

ω =angular velocity, a = angular acceleration, r = orbital radius

Question 4

Kepler’s Third Law

Answer 4

ω^2 = G(m1 + m2)/(R^3)

ω =angular velocity, m = mass, R = distance between the 2 stars

Both stars have same period

Question 5

What is the equation for

Doppler Effect

Used to resolve binary stars that have short periods

Answer 5

λ = λ0(1 + v/c)

λ = apparent wavelength, λ0 = lab wavelength, v = radial velocity

Question 6

How do we

Find the radial velocity of binary stars

Answer 6

• Measure the velocity over the star’s period (Sine wave)
• Maximum gives radial velocity because the star is moving away/towards to us

Question 7

What is the equation linking

Radial velocity, Radius and Period

Answer 7

v = 2πr/P

r = radius of orbit

Question 8

What is

Gravitational Lensing

Answer 8

• Due to General Relativity, light will bend around heavy objects
• The heavy object will act as a lens
• Observer sees a ring of light (Einstein Ring)

Question 9

What is the equation for

Angle of deflection due to Gravitation Lensing

Answer 9

∆α = 4GM/(rc^2)

M = mass of lens (Heavy object), r = radius of Einstein ring

Question 10

How do you calculate

Einstein Ring Radius

Answer 10

Θ^2 = 4GM/Dc^2

Θ = Einstein Ring Radius, D = Distance from lens to observer

D = distance from source to lens = distance from lens to observer