Preview
IB DP Physics — Unit E: Nuclear and Quantum Physics | SL & HL | E.5 Fusion and Stars
📋 What You Will Learn
- Observe how stars differ in luminosity, temperature, and colour, and understand what these differences reveal about stellar structure and evolution
- Define luminosity, apparent brightness, parallax angle, and stellar radius, and understand the units and scales used in stellar astronomy
- Derive the relationship between luminosity, radius, and surface temperature using the Stefan–Boltzmann law
- Use the parallax method to calculate stellar distances and understand its limitations
- Interpret the Hertzsprung–Russell (HR) diagram to classify stars and trace stellar evolutionary pathways
- Apply the inverse square law of light and the Stefan–Boltzmann law to solve figure-based and calculation problems in the style of IB Paper 2
🌍 Real-World Context On a clear night, the stars appear as points of light — some brilliant white, others faint and reddish, a few intensely blue. Yet these are not just aesthetic differences. The colour of a star encodes its surface temperature, and its apparent brightness depends on both how much energy it radiates and how far away it is. Astronomers have used these clues — colour, brightness, and the tiny shift in a star's apparent position as Earth orbits the Sun — to map the universe and classify billions of stars into a surprisingly orderly pattern. That pattern, the Hertzsprung–Russell diagram, is one of the most powerful tools in all of astrophysics.
🔍 Guiding Question How can astronomers determine the distance, size, temperature, and evolutionary stage of a star from observations made entirely from Earth?
Part 1 — Measuring Stellar Distance: Stellar Parallax
Before we can say anything meaningful about a star's true brightness or size, we must first know how far away it is. The most direct method available to astronomers for nearby stars is stellar parallax — a geometric technique that exploits Earth's annual orbit around the Sun as a baseline for triangulation.
As Earth moves from one side of its orbit to the other over six months, a nearby star appears to shift its position slightly against the backdrop of much more distant stars. This apparent shift is the parallax effect. The total angular shift observed over six months is twice the parallax angle \( p \). The closer the star, the larger the parallax angle — and vice versa.
📖 Key Definition — Parallax Angle The parallax angle \( p \) is defined as half the total angular displacement of a star observed from Earth at six-month intervals. It is the angle subtended at the star by the Earth–Sun distance (1 AU). The parallax angle is measured in arcseconds (symbol: ″ or arcsec), where 1 arcsecond = \( \frac{1}{3600} \) of one degree.
📖 Key Definition — The Parsec One parsec (pc) is the distance at which a star would have a parallax angle of exactly 1 arcsecond. It is defined geometrically from the parallax method and equals approximately \( 3.086 \times 10^{16} \) m, or about 3.26 light-years.
Notation Summary — Stellar Parallax
\( p \) = parallax angle (arcseconds, ″); \( d \) = distance to the star (parsecs, pc); 1 AU = \( 1.496 \times 10^{11} \) m (Earth–Sun distance); 1 pc = \( 3.086 \times 10^{16} \) m.
Derivation — The