ASTR 1P02 Lecture 11 Study Notes

ASTR 1P02 – Lecture 11: How Stars Shine

Overview of Topics

• Mass, energy, and their relationship

• Subatomic particles and fundamental interactions

• Nuclear fusion in stars

• Stars in the Milky Way Galaxy

• (Credits: NASA/JPL-Caltech/S. Stolovy (Spitzer Science Center/Caltech))

Mass and Energy

• Definition of Mass:

  • Denoted by 𝑚, mass intuitively measures "how much matter" is in an object.

  • Not a precise definition of mass.

• Newton's 2nd Law of Motion:

  • Equation: $F = ma$

  • In words: Force (𝐹) is the product of mass (𝑚) and acceleration (𝑎).

• Acceleration and Mass Relationship:

  • Rearranging gives: $a = \frac{F}{m}$

  • Implication: for constant force, as mass increases, acceleration decreases. Thus, greater mass indicates greater resistance to acceleration.

  • Conclusion: Resistance to acceleration can define mass (inertial mass).

• Gravitational Mass:

  • Newton's Law of Universal Gravitation:
    $F = \frac{G m<em>1 m</em>2}{r^2}$
    where:

  • 𝐺 is the gravitational constant.

  • 𝑚1 is the mass of the first object, and 𝑚2 is the second.

  • 𝑟 is the distance between the objects.

  • Description: Gravitational force relates to the product of masses divided by the square of the distance.

• Two Types of Mass:

  1. Inertial Mass: Resistance to acceleration.

  2. Gravitational Mass: Strength of gravitational force.

  • Equivalence principle ensures inertial mass equals gravitational mass.

Energy Concepts

• Definition of Energy:

  • Denoted by 𝐸; conceptualized as a “currency.”

  • Examples: You can trade equivalent energy values (like exchanging a table for chairs based on worth).

  • Total energy is conserved in exchanges.

• Types of Energy:

  • Kinetic Energy (KE): Energy of motion.

  • Gravitational Potential Energy (GPE): Energy due to an object's position in a gravitational field.

  • When an object falls, GPE converts into KE, leading to speed increase during the descent.

  • Simulated using a skater's movement (link to simulation provided).

• Energy Conservation:

  • There is no such thing as "pure energy"; energy exists in forms and is transformed (e.g., GPE to KE).

• Food Energy and Conversion:

  • Calories in food indicate its energy content.

  • Energy conversions in the body involve thermal, kinetic, etc.

Einstein’s Theory of Relativity

• Mass-Energy Equivalence:

  • Equation: $E = mc^2$
    where:

  • $E$ = energy (rest energy);

  • $m$ = mass;

  • $c ext{ (speed of light)} <br>ightarrow 3 imes 10^8 ext{ m/s}$.

  • Note: This does not suggest mass is "converted" into energy but rather relates mass to energy.

• Common Misconceptions:

  • Statement: “Matter can be converted into energy” is misleading.

  • It’s more accurate to say mass can transform into speed or kinetic energy and vice versa.

Atoms and Particles

• Composition of Matter:

  • Atoms form visible matter (stars, planets, humans).

  • Each atom contains a nucleus (protons + neutrons) surrounded by electrons.

• Atomic and Subatomic Sizes:

  • Size of an atom: $10^{-10} ext{ m}$

  • Size of nucleus: $10^{-15} ext{ m}$

  • Protons/neutrons are slightly smaller than nucleus.

• Common Atoms:

  • 118 known atoms (chemical elements), defined by the number of protons (atomic number).

  • Examples include Hydrogen (1 proton), Helium (2 protons).

Standard Model of Particle Physics

• Types of Subatomic Particles:

  • Fermions: Matter particles (e.g., electrons, quarks).

  • Bosons: Force carriers (e.g., photons, W/Z bosons).

• Fundamental Interactions:

  • Electromagnetic Interaction: Mediated by photons.

  • Strong Interaction: Holds protons and neutrons together, mediated by gluons.

  • Weak Interaction: Responsible for nuclear decay, mediated by W/Z bosons.

  • Gravity: Not part of the Standard Model but explained by general relativity.

• Energy Measurements:

  • Energy in particle physics measured in electron volts (eV) and converted: $1 eV <br>ightarrow 1.6 imes 10^{-19} ext{ J}$.

  • Mass measurable in eV/c², $1 eV/c² <br>ightarrow 1.8 imes 10^{-36} ext{ kg}$.

Antimatter

• Concept of Antimatter:

  • Corresponding antiparticles exist for every particle (e.g., electron vs. positron).

  • Matter is primarily made of regular matter; antimatter is rare and annihilates upon collision with matter, resulting in energy release.

  • Example reaction: e^- + e^+ → 2 ext{ }4 (2 photons).

Nuclear Fusion in Stars

• Process of Fusion:

  • Stars convert mass into speed through nuclear fusion (not just particle collisions).

  • For hydrogen to helium fusion, primarily involving the proton-proton chain process.

• Details of Proton-Proton Chain:

  1. First step: Two protons collide; one degrades into a neutron (beta-plus decay).

  2. Formation of deuterium (D): $p + p → D + e^+ + <br>u_e$.

  3. Formation of helium from three helium nuclei also occurs as energy is emitted in the form of photons during conversion.

• Energy Output from Fusion:

  • Stars generate immense light and energy through constant fusion.

  • The Sun produces approx. $10^{26} W$ (equivalent to 10 million times Canada’s yearly energy consumption) by fusing hydrogen into helium.

Conclusion

• Advanced concepts from relativity, particle physics, and nuclear fusion were introduced.

• Subatomic interactions are critical to understanding stellar processes and energy generation.

• Reading Assignment: OpenStax Astronomy, Chapter 16.

• Exercises: Practice questions will be posted on Teams.