8 Astrophysics

Selection method: identify the physical quantity first, then copy the matching unit symbol after the value. The words in the quantity are decisive: orbital speed uses m/s, orbital radius uses m, time period uses s, and gravitational field strength uses N/kg.

Read the containment chain from small to large: Earth is a planet in the Solar System; the Solar System is in the Milky Way galaxy; the Milky Way is one of the billions of galaxies in the universe.

At Earth's surface, $g$ is about 10 N/kg; at the Moon's surface it is about 1.7 N/kg. The Moon's much smaller mass is the main reason its surface gravitational field is weaker.

$v$ is orbital speed, $r$ is orbital radius measured from the centre of the orbit, and $T$ is the time period for one orbit. Rearrangements are $T=2\pi r/v$ and $r=vT/(2\pi)$. Use compatible units: metres with m/s, kilometres with km/s, and convert the period to seconds when speed is per second.

Example: a satellite has orbital radius 7100 km and period 5800 s. $v=(2\pi\times7100)/5800=7.69$ km/s, so its orbital speed is about 7.7 km/s.

Use the colour itself as the classification evidence: common groups include red, orange, yellow, white and blue-white. For example, two red stars share a colour classification even if they differ in size, brightness or evolutionary stage.

The Sun appears yellow, while Betelgeuse appears red. The colour relationship therefore shows that the Sun has a higher surface temperature than Betelgeuse. Likewise, a blue-white star has a higher surface temperature than a yellow star.

1. In a nebula, gravity pulls gas and dust together. The collapsing material heats and forms a protostar. When nuclear fusion begins, it becomes a main sequence star.

2. During the main sequence, hydrogen fusion releases energy. When the core hydrogen supply is depleted, the star expands and its surface cools, forming a red giant. The outer layers are then lost; the hot, dense remaining core is a white dwarf, where fusion no longer occurs.

The ordered sequence is: nebula → protostar → high-mass main sequence star → red supergiant → supernova → neutron star or black hole. After leaving the main sequence, the star expands into a red supergiant; its core then collapses and the outer layers explode as a supernova.

The magnitude scale runs backwards: a lower or more negative absolute magnitude means a brighter star. For example, a star with absolute magnitude −4 is brighter at the standard distance than one with absolute magnitude +6.

Draw the horizontal axis with hot blue or white stars on the left and cool red stars on the right, so temperature decreases from left to right. Draw absolute magnitude with bright, low or negative values at the top and dim, high positive values at the bottom; a typical scale runs from −5 at the top to +15 at the bottom.

Drawing method: label both axes and their directions first; add the main-sequence diagonal; then place and label the red-giant region above and to the right, and the white-dwarf region below and to the left. The Sun lies on the main sequence.

Past-to-present sequence: an early hot, dense universe → continuing expansion → increasing size and falling average temperature → the cooler, much larger universe observed today. The theory describes the expansion of the universe itself, not matter exploding from one location into an already existing universe.

The evidence is stronger as a pair: red-shift describes continuing large-scale expansion, while CMBR is a surviving signal of the universe's hotter past. Both are consequences expected from the same expanding-universe history.

$\lambda_0$ is the reference wavelength measured for the same spectral line at rest, $\lambda$ is the wavelength observed from the galaxy, $\Delta\lambda$ is the change, $v$ is galaxy velocity and $c$ is the speed of light. For red-shift, $\lambda>\lambda_0$, so $\Delta\lambda$ is positive. Use the same units for both wavelengths and the same speed units for $v$ and $c$.

Example: a hydrogen line has $\lambda_0=605$ nm and is observed at $\lambda=683$ nm. $\Delta\lambda=683-605=78$ nm, so $v=3.0\times10^8\times(78/605)=3.9\times10^7$ m/s.

For the same reference spectral line, if galaxy Q is twice as far away as galaxy P and follows the observed distance–speed relationship, Q recedes about twice as fast and has about twice the wavelength change. Its detected line is therefore shifted farther towards longer wavelengths.

Reasoning chain: most distant galaxies show red-shift → their light has longer wavelength → they are moving away → more distant galaxies generally show greater red-shift and higher recession speed → distances between galaxies are increasing as the universe expands.