Question 1: Define the Main Sequence in the context of stellar evolution.

Answer: The Main Sequence is the phase in a star's life during which it fuses hydrogen into helium in its core, maintaining a stable balance between gravity and pressure.

Question 2: Explain the primary mechanism that powers stars during the Main Sequence.

Answer: Nuclear fusion of hydrogen nuclei into helium in the star's core releases energy that powers the star and produces its luminosity.

Question 3: What is the relationship between a star's mass and its luminosity during the Main Sequence?

Answer: More massive stars have higher luminosities, approximately following the relation L ∝ M^3 to M^4.

Question 1: A star has a mass of 2 times that of the Sun. Using the relation L ∝ M^3, estimate its luminosity relative to the Sun's luminosity.

Answer: Luminosity ≈ 2^3 = 8 times the Sun's luminosity.

Question 2: Given that the Sun's surface temperature is approximately 5778 K and its radius is 6.96 × 10^8 m, calculate the Sun's approximate luminosity using the Stefan-Boltzmann law: L = 4πR^2σT^4. Use σ = 5.67 × 10^-8 W/m^2K^4.

Answer: L ≈ 3.83 × 10^26 watts (approximate value based on calculation).

Question 1: Describe a simple experiment or observation method that could be used to determine the surface temperature of a star.

Answer: Spectroscopic analysis of the star's light can be used to identify the absorption lines corresponding to specific elements, allowing determination of the star's surface temperature based on its spectral type.

Question 2: Identify two variables that affect the luminosity of a star during the Main Sequence and explain their roles.

Answer: Mass influences the amount of nuclear fuel available and thus the luminosity; surface temperature affects the energy output per unit area, impacting the overall brightness.

Question 1: A star observed to have a surface temperature of 7000 K and a radius twice that of the Sun. Using the Stefan-Boltzmann law, estimate its luminosity relative to the Sun.

Answer: Luminosity ≈ (2^2) × (7000/5778)^4 ≈ 4 × (1.21)^4 ≈ 4 × 2.15 ≈ 8.6 times the Sun's luminosity.

Question 1: Explain how the balance between gravitational collapse and nuclear fusion maintains a star in the Main Sequence phase. Include in your answer the roles of pressure, gravity, and energy production.

Answer: During the Main Sequence, gravitational force causes the star to contract, increasing pressure and temperature in the core. This triggers nuclear fusion of hydrogen into helium, releasing energy that creates outward pressure. The balance between inward gravity and outward pressure from fusion stabilises the star, keeping it in the Main Sequence for most of its life.

Question 1: Describe how knowledge of stellar properties during the Main Sequence is useful in determining the distances to stars using main sequence fitting methods.

Answer: By comparing the apparent brightness of a star to its known luminosity during the Main Sequence, astronomers can calculate its distance using the inverse-square law, aiding in mapping the scale of the universe.