Distances, Magnitudes and Spectral Classes Equations

m = -2.5 log I + constant

d = R / tan θ_p   (d = Distance (m))

θ_p = (t / 3600)°

θ = 2θ_p = W / d   (d = Distance (m))

m_b - m_a = 2.5 log (L_a / L_b)

m - M = 5 log (d / 10)      (d = Distance (parsecs))

R (Radius of Earth Orbit and 1 Astronomical Unit (AU)) = 1.5x10¹¹ m

W (Width of Earth Orbit) = 3x10¹¹ m

1 pc = 3.09x10¹⁶ m

1 Mpc = 3.09x10²²m

m, m_a, m_b (Apparent Magnitude)

I (Intensity) = W m^-2

θ_p (Angle of Parallax) = degrees

t (Time of Parallax) = s

L_a, L_b (Luminosity) = W

M (Absolute Magnitude)

©2011 Grant Dwyer

Lenses and Telescopes Equations

P = 1 / f 

1 / f = 1 / u + 1 / v   (Convex Lens)

1 / f = 1 / v - 1 / u   (Concave Lens)

M = θ_i / θ_o = f_o / f_e = β / α 

α = h / f_o

β = h / f_e

θ ≈ λ / D

f = f_o + f_e

s = r θ

P (Power) = D (Dioptres)

f (Focal Length) = cm

u (Object Distance) = cm

v (Image Distance) = cm

M (Magnification)

θ_i (Image Angle) = Degrees

θ_o (Object Angle) = Degrees

f_o (Objective Lens Focal Length) = cm

f_e (Eyepiece Lens Focal Length) = cm

β (Angle Subtended at Eye Using Instrument) = Radians

α (Angle Subtended at Unaided Eye) = Radians

h (Height of Object) = cm

θ (Angular Resolution) = Radians

λ (Wavelength) = m

D (Aperture) = m

r (Radius) = m

s (Distance) = m

©2011 Grant Dwyer