3.2-3

Question 1

Central Pressure of the Sun (P_c)

Answer 1

• P_c ≈ 6 · 10¹⁴ Nm^-2 (6 billion atmospheres)
• Derived from assumptions and basic equations about the Sun’s properties

Question 2

Central Temperature of the Sun (T_c)

Answer 2

• Using ideal gas assumptions for fully ionized hydrogen
• T_c ≈ 10⁷ K

Question 3

Kelvin-Helmholtz Timescale (τ_KH)

Answer 3

Estimate of the Sun’s lifetime based on gravitational energy and luminosity:

𝛕_KH ≈ 1/2 |E_G| / L_⊙

𝛕_KH ≈ 10⁷ years

Question 4

Scaling Relation for Pressure (P)

Answer 4

P ∝ M² / R⁴

Question 5

Scaling Relation for Temperature (T)

Answer 5

T ∝ M / R

Question 6

Scaling Relation for Luminosity (L)

Answer 6

More massive stars are significantly more luminous.

L ∝ M³

Question 7

Relation between Mass and Effective Temperature (M and T_eff)

Answer 7

M ∝ T²_eff

Question 8

Relation between Luminosity and Effective Temperature (L and T_eff)

Answer 8

L ∝ T⁶_eff

Question 9

Lifetime of a Star (τ)

proportionaly relation

Answer 9

More massive stars have shorter lifespans.

𝛕 ∝ M^-2

Question 10

The Opacity Term (α_R)

Answer 10

Opacity of stellar matter, averaged over all frequencies.

α_R = 𝛒𝛘