Space Physics: Orbits, Stars and the Expanding Universe

Introduction

Yo! Quick-fire space physics. Why do we get day and night, why does the Moon never fall on us, why are summer and winter a thing, and how do we know the Universe started with a bang? Same toolkit every time: things go round in orbits, gravity does the pulling, and light carries the evidence across billions of years.

This is your fast refresh, not the full textbook. One key formula per concept, one quick worked example, and the exact sentence the marker wants. Skim it the night before, lock in `v = 2πr/T` and `v = H₀d`, walk in calm. Let's launch! 🚀

The Earth, the Moon and Orbital SpeedE6.1.1

The Earth spins once a day (giving day and night) and orbits the Sun once a year, with its axis tilted, which is what gives us seasons. The Moon orbits the Earth roughly once a month, and the changing slice of its sunlit half that we see is the cycle of phases. Anything in a circular orbit moves at a steady speed set by how big the orbit is and how long one lap takes.

> 🔑 Key formula: orbital speed $v = \dfrac{2\pi r}{T}$ — circumference of the orbit ($2\pi r$) divided by the time for one lap ($T$). Keep $r$ in metres and $T$ in seconds for m/s. 🎯

Worked Example: How Fast Is the Moon Moving?E6.1.1

Problem The Moon orbits the Earth at a radius of $3.8 \times 10^8$ m, taking $27.3$ days for one lap. Find its orbital speed.

Step 1 Convert the period to seconds: $T = 27.3 \times 24 \times 3600 = 2.36 \times 10^6$ s. Always work in seconds before using the formula.

Step 2 Apply $v = \dfrac{2\pi r}{T}$:

The Moon looks like it's drifting lazily across the sky, but it's actually screaming around us at about a kilometre every second. It doesn't fall on us because that sideways motion keeps "missing" the Earth as gravity bends its path into a circle.

$$v = \frac{2\pi \times 3.8 \times 10^8}{2.36 \times 10^6} = 1.0 \times 10^3 \text{ m/s} \approx 1 \text{ km/s}.$$

The Solar System and OrbitsE6.1.2

Our Solar System is one star (the Sun) plus eight planets, their moons, plus asteroids and comets, all held in orbit by the Sun's gravity. The four inner planets are small and rocky; the four outer ones are large and gassy. Orbits are slightly elliptical (squashed circles), not perfect circles, so a planet (or a comet) speeds up when it is closer to the Sun and slows down when it is farther away. The closer a planet's orbit, the stronger the Sun's pull and the faster it must travel.

> 🔑 Key idea: orbits are ellipses; a body moves fastest at its closest point to the Sun and slowest at its farthest. Inner planets orbit faster than outer ones.

Worked Example: Mars vs Jupiter — Which Orbits Faster?E6.1.2

Problem Mars orbits closer to the Sun than Jupiter. Without any numbers, state which planet has the greater orbital speed and why.

Step 1 Mars is closer, so the Sun's gravitational pull on it is stronger, and a stronger pull is needed to bend a faster body into orbit, so Mars orbits faster than Jupiter. The rule to remember: closer to the Sun always means a higher orbital speed.

The Sun, Stars and the Life CycleE6.2.1, E6.2.2

The Sun is an average-sized star powered by nuclear fusion of hydrogen into helium in its core, releasing the energy that lights and warms the Solar System. Stars are grouped into galaxies (ours is the Milky Way), and distances are so vast we measure them in light-years (the distance light travels in one year). A star forms from a cloud of gas and dust (a nebula) pulled together by gravity, lives a long stable life, then dies. How it dies depends on its mass: a star like the Sun swells to a red giant then shrinks to a white dwarf; a much heavier star becomes a red supergiant, explodes as a supernova, and leaves a neutron star or black hole.

> 🔑 Key idea: the Sun fuses hydrogen → helium. A star's death depends on its mass: Sun-like → red giant → white dwarf; massive → red supergiant → supernova → neutron star or black hole.

Worked Example: Order a Star's Life CycleE6.2.1, E6.2.2

Problem Put these stages of a massive star (much heavier than the Sun) in order: supernova, nebula, red supergiant, main-sequence star, black hole.

Step 1 Follow the lower (massive-star) path: nebula → main-sequence star → red supergiant → supernova → black hole. The trick for full marks is to read the word "massive": a Sun-mass star would end as a white dwarf instead, so the mass tells you which branch to take.

The Expanding Universe and Hubble's LawE6.2.3

Light from distant galaxies is stretched to longer (redder) wavelengths: redshift. The further away a galaxy is, the bigger its redshift, which means the faster it is moving away from us. That is Hubble's law, and it tells us the whole Universe is expanding from an initial hot, dense state: the Big Bang. The faint microwave glow filling all of space (cosmic microwave background radiation, CMBR) is the leftover heat of that beginning. Running the expansion backwards with the Hubble constant $H_0$ even estimates the age of the Universe as about $1/H_0$.

> 🔑 Key formula: Hubble's law $v = H_0 d$ — recession speed equals the Hubble constant times distance. Redshift is the evidence; the CMBR confirms the Big Bang; age of Universe $\approx 1/H_0$.

Worked Example: How Fast Is That Galaxy Receding?E6.2.3

Problem A galaxy is $8.0 \times 10^{24}$ m away. Taking the Hubble constant as $H_0 = 2.2 \times 10^{-18}$ s$^{-1}$, find how fast it is moving away from us.

Step 1 State Hubble's law and substitute. Units already match (metres and per-second), so no conversion is needed: $$v = H_0 d = (2.2 \times 10^{-18})(8.0 \times 10^{24}) = 1.8 \times 10^7 \text{ m/s}.$$

Step 2 Sanity-check the size: that's about $6\%$ of the speed of light ($3 \times 10^8$ m/s), which is huge but believable for a galaxy this far away. The further out you look, the faster things recede, which is exactly why a bigger distance means a bigger redshift.

Key Points to Remember

• The Earth spins (day/night) and orbits the tilted Sun (seasons); the Moon orbits Earth, giving phases. Orbital speed $v = 2\pi r / T$ with $r$ in m and $T$ in s.
• The Solar System is the Sun plus eight planets (rocky inner, gassy outer) held by gravity. Orbits are ellipses, so bodies move fastest when closest to the Sun.
• The Sun is a star fusing hydrogen into helium. A star's fate depends on mass: Sun-like → red giant → white dwarf; massive → red supergiant → supernova → neutron star or black hole.
• Galaxies show redshift; the further away, the faster they recede. Hubble's law $v = H_0 d$ shows the Universe is expanding from the Big Bang, confirmed by the CMBR; age $\approx 1/H_0$.