6. Space physics

At any moment, the hemisphere facing the Sun is illuminated and has daytime; the hemisphere facing away is in darkness and has night. As Earth rotates, each location moves into and then out of the illuminated half.

Earth rotates from west to east, so the Sun appears to move across the sky in the opposite direction, from east to west, rising in the east and setting in the west.

Because one rotation takes about 24 hours, the sequence of daylight and darkness and the Sun's apparent daily path repeat approximately every day.

Earth's axis remains tilted in a nearly fixed direction as Earth moves around the Sun. During part of the orbit, one hemisphere is tilted towards the Sun; about half an orbit later it is tilted away.

The same orientations recur each orbit, so the seasons form a periodic cycle that repeats approximately every 365 days. The two hemispheres experience opposite seasons.

The Sun always illuminates half of the Moon. As the Moon moves around Earth, the viewing angle changes, so observers see different fractions of the illuminated half.

The visible sequence repeats: new Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, last quarter and waning crescent, then new Moon again.

Because the Moon returns to approximately the same orbital arrangement after about one month, its cycle of phases is periodic with approximately a monthly timescale.

For an approximately circular orbit, the distance travelled in one orbit is 2πr, so v = 2πr/T, where r is the average orbital radius measured from the centre of the orbit and T is the time for one complete orbit.

For Earth, r ≈ 1.5 × 10¹¹ m and T ≈ 365 × 24 × 60 × 60 s. Therefore v ≈ 2π(1.5 × 10¹¹)/(3.15 × 10⁷) ≈ 3.0 × 10⁴ m/s.

The same relation can be rearranged: T = 2πr/v or r = vT/(2π).

The eight planets in order of increasing distance from the Sun are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

The accretion model begins with an interstellar cloud containing many elements in gas and dust. Gravity pulls the cloud material together.

As the cloud contracts, its rotation becomes more important and the material forms a rotating accretion disc around the developing Sun. Dust and other particles collide and stick, building larger bodies by accretion.

Near the hot young Sun, mainly heat-resistant rocky material could condense and accrete, producing smaller rocky planets. Farther out, cooler conditions allowed much more gas and icy material to collect, producing larger gaseous planets.

At a planet's surface, gravitational field strength depends on the planet's mass: a more massive planet generally produces a stronger gravitational field at its surface when making syllabus-level comparisons.

Around any one planet, gravitational field strength decreases as distance from the planet increases. A test mass farther away therefore experiences less gravitational force per kilogram.

The mean Sun–Earth distance is about 1.5 × 10¹¹ m, so light takes t = (1.5 × 10¹¹)/(3.0 × 10⁸) = 5.0 × 10² s, about 8.3 minutes, to travel from the Sun to Earth.

For a signal sent to an object and reflected back, the light travels twice the one-way separation, so use d = 2 × separation.

Because gravitational effects depend on mass, the Sun produces the dominant gravitational field across the Solar System. Each planet is gravitationally bound mainly to the Sun.

The planets therefore orbit the Sun rather than another planet or a small body. Their moons can still orbit them because the planet's gravity dominates close to that planet.

This gravitational force acts towards the Sun. It continually changes the direction of the object's velocity, providing the inward, or centripetal, force required for an orbit.

Without the inward gravitational force, the object would continue approximately along a straight-line tangent rather than follow its curved path.

In an ellipse, the Sun lies away from the geometric centre, at one focus. It is therefore not at the centre of the orbit.

When an orbit is approximately circular, its two focal positions are very close together, so the Sun is approximately at the centre.

The Sun–object distance changes around a visibly elliptical orbit. This is why a quoted orbital distance is often an average value.

To compare orbital positions, calculate the fraction of an orbit completed: elapsed time/orbital period. Multiply this fraction by 360° only when a circular-orbit angle model is appropriate.

Use counterexamples in the table to test a claim. A general increase does not prove direct proportionality; direct proportionality requires a constant ratio and a straight line through the origin.

The orbital speeds of the planets also decrease as their distance from the Sun increases: nearer planets orbit faster and farther planets orbit more slowly.

A nearer planet experiences a stronger solar gravitational field and needs a higher speed for its tighter orbit. A farther planet experiences weaker solar gravity and follows a larger orbit at a lower orbital speed.

As the object moves towards the Sun, its gravitational potential energy decreases. Gravity transfers energy to its kinetic store, so kinetic energy and speed increase.

As the object moves away from the Sun, kinetic energy is transferred to its gravitational potential store, so kinetic energy and speed decrease.

Ignoring resistive effects, the total of kinetic energy and gravitational potential energy remains constant. Energy changes store; it is not created near the Sun or destroyed farther away.

The Sun consists mostly of the elements hydrogen and helium. Other elements are present in much smaller amounts.

The Sun radiates most of its energy in three neighbouring regions of the electromagnetic spectrum: infrared, visible light and ultraviolet.

In a stable star, hydrogen nuclei join together to form helium nuclei. Joining small nuclei to make a larger nucleus is nuclear fusion.

Fusion releases energy. This energy moves through the star and is radiated from its surface as electromagnetic radiation.

The Sun is much closer to Earth than every other star in the Milky Way. Even the nearest stars beyond the Sun are so far away that astronomical distance units are useful.

If a star is four light-years away, its light takes about four years to reach us. We therefore observe that star as it was about four years earlier.

Light travels at about 3.0 × 10⁸ m/s and one year is about 365 × 24 × 60 × 60 = 3.15 × 10⁷ s. Therefore d = ct ≈ (3.0 × 10⁸)(3.15 × 10⁷) ≈ 9.5 × 10¹⁵ m.

A distance of 6.6 × 10²⁰ m corresponds to (6.6 × 10²⁰)/(9.5 × 10¹⁵) ≈ 6.9 × 10⁴ light-years.

A star begins in an interstellar cloud of gas and dust containing hydrogen. Internal gravitational attraction makes part of the cloud collapse; as it contracts, its temperature rises and it becomes a protostar.

A protostar becomes a stable star when the inward force of gravitational attraction is balanced by an outward force due to the high temperature at its centre. Hydrogen fusion supplies the energy that maintains this hot stable state.

Eventually every star runs short of hydrogen fuel in its centre because much of that hydrogen has been converted to helium. The star expands: most stars become red giants, while more massive stars become red supergiants.

Material in the nebula from a supernova can later be pulled together by gravity to form new stars. Accretion discs around those forming stars may also produce orbiting planets, so stellar material is recycled into later systems.

Shared beginning: hydrogen-rich gas and dust → protostar → stable star → hydrogen fuel runs low. Initial mass then controls which end branch the star follows.

The Milky Way itself contains many billions of stars and has an approximate diameter of 100 000 light-years.

Light therefore takes about 100 000 years to travel a distance equal to the Milky Way's diameter. This is a galactic scale, far larger than the Solar System.

Astronomers compare identifiable spectral lines in received starlight with the wavelengths of the same lines measured in a laboratory. A shift to longer wavelengths is a redshift.

For a receding source, successive wavefronts arrive more spread out, so the observed wavelength is longer than the emitted or laboratory wavelength.

If a hydrogen line has wavelength 656 nm in a laboratory but is observed at 667 nm from a galaxy, the observed wavelength has increased: 667 − 656 = 11 nm. The galaxy's light is redshifted.

The known laboratory spectrum acts as the reference. Matching the pattern of lines identifies the element; their displacement to longer wavelength identifies redshift.

When light from galaxies in all directions is generally redshifted, the large-scale separations between galaxies are increasing. This is evidence that the Universe is expanding.

Running the expansion model backwards implies that matter was closer together in the past. Redshift therefore supports the Big Bang Theory.

More distant galaxies generally show greater redshift and recession speed, strengthening the expansion interpretation.

Detectors receive this faint microwave background from every direction rather than from one local star, planet or galaxy.

Its all-sky presence is why it is described as a cosmic background: it is a property observed throughout the surrounding Universe.

As the Universe expanded, the wavelength of this radiation was stretched to longer wavelengths.

That expansion shifted the radiation into the microwave region of the electromagnetic spectrum, where it is observed today from all directions.

The CMBR's ancient origin, stretched wavelength and all-sky distribution support the model of a hot early Universe that has expanded.

A larger wavelength increase means a larger redshift and, under the syllabus model, a greater speed away from Earth.

A supernova of known intrinsic brightness appears dimmer when it is farther away. Comparing its observed brightness with the expected intrinsic brightness provides the distance.

Astronomers can therefore obtain the two quantities needed for Hubble analysis in different ways: supernova brightness gives distance, while redshift gives recession speed.

If H₀ is treated as constant, v = H₀d, so recession speed is directly proportional to distance. A graph of v against d has gradient H₀ when units are consistent.

If v is in m/s and d is in m, the metres cancel and H₀ has unit s⁻¹. Convert kilometres and light-years before substitution when required.

The s⁻¹ unit follows from H₀ = v/d: (m/s)/m = 1/s.

The very small value is expected because cosmic expansion is measured over extremely large distances and timescales.

Using H₀ = 2.2 × 10⁻¹⁸ s⁻¹ gives age ≈ 1/H₀ ≈ 4.5 × 10¹⁷ s. Dividing by about 3.2 × 10⁷ s/year gives approximately 1.4 × 10¹⁰ years.

Galaxies are now receding, and more distant galaxies generally recede faster. Extrapolating their separations backwards implies that matter was closer together and supports the idea that all matter was once concentrated at a single point.

This is an estimate based on using the current expansion relation over cosmic history; it is not a direct stopwatch measurement.