1.1-3

Question 1

Kepler’s 1st Law

Answer 1

• Planetary orbits are ellipses
• around the sun as one focal point

Question 2

Kepler’s 2nd Law

Answer 2

• Equal areas are swept out in equal times
• (Angular Momentum Conservation).

Formula:
(r × v dt) ^. 0.5 = constant
→ L = constant

Question 3

Kepler’s 3rd Law

Answer 3

• square of the orbital period P is proportional to cube of the major axis a: P² ∝ a³
• For circular orbits:
  Centrifugal force = Gravitational force.

Formulas:
v² = GM/r
r³/P² = G/(4 π²) M

Question 4

Doppler Effect

Answer 4

Radial velocity measurement:
Δλ/λ0 = v/c for v << c.

Question 5

Equatorial System

Answer 5

Earth orientation:

• Right Ascension α (h:min:sec) [0^h, 24^h]
• Declination δ (deg:min:sec) [-90°, +90°].

Question 6

Alt-Azimuth Coordinates

Answer 6

For telescope operations.

Question 7

Ecliptic Coordinates

Answer 7

Earth’s orbit around the sun:

tilt of 23.5 degrees relative to equatorial system

Question 8

Galactic Coordinates

Answer 8

Objects with respect to Milky Way:

• Galactic longitude ℓ degr [0°, 360°]
• Galactic latitude b degr [-90°, +90°]
• zero point towards galactic center.

Question 9

Astronomical Mass Unit

Answer 9

kg, g for particles.
Solar Mass M_⊙ = 1.99 x 10³⁰ kg.

Question 10

Astronomical Length Unit

Answer 10

m, km for small bodies.
- Solar Radius R_⊙ = 6.96 x 10⁸ m.
- Astronomical Unit (AU): 1.50 x 10¹¹ m.
- Parsec (pc): 3.09 x 10¹⁶ m.

Question 11

Astronomical Luminosity Unit

Answer 11

• Solar Luminosity L_⊙ = 3.84 x 10²⁶ W
• Flux: [W/m^2]
• Solar irradiance: 1.36 kW/m².

Question 12

Apparent Magnitude (m)

Answer 12

brightness difference Δm = 5^m
→ equals a factor of 100.
Formulas:
m₁ - m₂ = -2.5 ^. log (F₁/F₂)

Question 13

Absolute Magnitude (M)

Answer 13

M: Apparent magnitude at 10 pc.
Distance modulus:
m - M = 5 log d[pc] - 5.