Physics · 6 Space physics

6.1.1 The Earth

Before you start

Speed = distance ÷ time, from 1.2.
The circumference of a circle of radius $r$ is $2 π r$ .
Converting hours and days into seconds: 1 hour = 3600 s.
Entering numbers in standard form, such as $1.5 \times 10^{11}$ , on your calculator.
You see an object that gives out no light because it reflects light into your eyes.

Syllabus objectives covered (4)

Know that the Earth is a planet that rotates on its axis, which is tilted, once in approximately 24 hours, and use this to explain observations of the apparent daily motion of the Sun and the periodic cycle of day and night
Know that the Earth orbits the Sun once in approximately 365 days and use this to explain the periodic nature of the seasons
Know that it takes approximately one month for the Moon to orbit the Earth and use this to explain the periodic nature of the Moon’s cycle of phases
Define average orbital speed from the equation v = 2πr / T where r is the average radius of the orbit and T is the orbital period; recall and use this equation

Part 1 of 6

A planet spinning on a tilted axis

The Earth is a planet. It does two separate things at the same time, and this whole lesson depends on keeping them apart: it spins on its own axis, and it travels round the Sun.
The axis is an imaginary line through the centre of the Earth, from the North Pole to the South Pole. Spinning about this line is called rotation.
The Earth rotates once in approximately 24 hours. That is one day.
The axis is not upright. It is tilted compared with a line at right angles to the Earth's path round the Sun. The tilt is about 23.5°, but the syllabus does not ask for the number. It asks you to know that the axis is tilted. You will see what the tilt does when you reach the seasons.
Keep the two words separate. Rotate means spin on an axis. Orbit means travel round another body. The Earth rotates once in about 24 hours and orbits the Sun once in about 365 days. If you write 'orbits' where you mean 'rotates', your answer gives the wrong cause, even when the idea in your head is right.

Part 2 of 6

Day, night and the Sun's path across the sky

The Sun lights only the half of the Earth that faces it. On that half it is day. On the half that faces away from the Sun it is night.
ray diagram — not drawn yet
The Earth seen from above the North Pole as a circle with a dot at its centre labelled 'North Pole'; parallel arrows labelled 'sunlight' arrive from the left; the left half of the circle is white and labelled 'day', the right half is shaded dark and labelled 'night'; a curved anticlockwise arrow round the circle is labelled 'rotation, once in about 24 hours'; the point at the top of the circle, where places move from the dark half into the lit half, is labelled 'sunrise' and the point at the bottom, where they move from the lit half into the dark half, is labelled 'sunset'.
Half of the Earth is always lit. Rotation carries each place from the dark half into the lit half (sunrise) and out again (sunset).
As the Earth rotates, every place on it is carried round with it. A place moves out of the dark half into the lit half, which is sunrise, and later out of the lit half into the dark half, which is sunset.
One rotation takes about 24 hours, so each place goes through one day and one night in about 24 hours. Then the same thing happens again. That is what periodic means: the cycle repeats once every rotation.
Now the Sun's movement across the sky. The Earth rotates from west to east. Seen from above the North Pole, it turns anticlockwise.
You do not feel the Earth turning, so the ground seems still and the Sun seems to move. You are carried towards the east, so the Sun appears to move the opposite way, from east to west. It appears to rise in the east, reach its highest point around midday, and set in the west.
Think of a passenger on a train. The train moves forward, but the trees outside appear to slide backwards. The Earth is the train and the Sun is the tree. The Sun does not travel round the Earth each day. The Earth turns.
That is why the syllabus calls it the apparent daily motion of the Sun: the Sun only appears to move. The same rotation makes the Moon and the stars appear to cross the sky from east to west.
You can put a number on it. The Earth turns through a full circle, 360°, in about 24 hours, so the Sun appears to move across the sky by about 15° every hour.
$\frac{360^{\circ}}{24 h} = 15^{\circ} per hour$

Part 3 of 6

One orbit, one year

The Earth also orbits the Sun. Its path is very nearly a circle, and one complete orbit takes approximately 365 days. That is one year.
The Earth keeps rotating while it orbits, so each place has about 365 cycles of day and night in each orbit. That is why a year has about 365 days.
Here is the key fact for the seasons. As the Earth goes round the Sun, its tilted axis keeps pointing in the same direction in space. The axis does not swing round to keep facing the Sun.
So at one point in the orbit the North Pole leans towards the Sun. Half an orbit later the Earth is on the other side of the Sun. The axis still points the same way in space, so now the North Pole leans away from the Sun.
ray diagram — not drawn yet
The Sun at the centre of a near-circular orbit, seen from the side; the Earth drawn at the left and at the right of the orbit; at both positions the axis is a straight line through the Earth tilted by the same angle in the same direction, top end leaning to the right, with 'N' at the top end and the equator drawn across; the left-hand Earth, whose North Pole leans towards the Sun, is labelled 'June: northern hemisphere tilted towards the Sun'; the right-hand Earth, whose North Pole leans away from the Sun, is labelled 'December: northern hemisphere tilted away from the Sun'.
The axis points the same way in space at both positions. Half an orbit changes which hemisphere leans towards the Sun.
The equator divides the Earth into two halves: the northern hemisphere and the southern hemisphere. In June the northern hemisphere leans towards the Sun. In December the southern hemisphere does.

Part 4 of 6

Why the tilt makes seasons

Take a place away from the equator, in the hemisphere that is tilted towards the Sun. Two things are different for it from the time, half a year later, when its hemisphere is tilted away.
The Sun is higher in the sky at midday. The sunlight arrives more directly, so the same amount of sunlight falls on a smaller area of ground. Each square metre receives more energy, so it is heated more.
Shine a torch straight down at a table and you get a small, bright patch. Tilt the torch and the same light spreads into a larger, dimmer patch. A low winter Sun is the tilted torch.
The days are longer. More of that hemisphere is in the lit half of the Earth, so each place spends more of its 24-hour rotation in daylight than in darkness. More hours of sunlight means more hours of heating.
Higher Sun and longer days give summer. At the same time the other hemisphere is tilted away, with a lower Sun and shorter days. It has winter. The two hemispheres always have opposite seasons.
Half an orbit later, about six months, the Earth is on the other side of the Sun. The axis still points the same way in space, so the other hemisphere now leans towards the Sun and the seasons swap.
Between these two positions there are two points in the orbit where neither hemisphere leans towards the Sun. Spring and autumn fall around these points.
Why are the seasons periodic? The Earth comes back to the same point in its orbit, with its axis pointing the same way, once every orbit: about every 365 days. So the same hemisphere is tilted towards the Sun at the same time each year, and the seasons repeat every year.
The trap: distance from the Sun does not cause the seasons. The orbit is so nearly circular that the distance changes very little. And if distance were the cause, both hemispheres would have summer at the same time. They never do.

Part 5 of 6

The Moon and its cycle of phases

The Moon orbits the Earth. One orbit takes approximately one month. That is the value you need. If a question gives you a more exact period, use the value it gives.
The Moon gives out no light of its own. You see it only because it reflects sunlight.
At every moment the Sun lights half of the Moon: the half that faces the Sun. The other half is dark. This is true all month. The lit half never grows or shrinks.
What changes is how much of that lit half is turned towards the Earth. That depends on where the Moon is in its orbit. Each different shape you see is called a phase.
ray diagram — not drawn yet
The Earth at the centre, seen from above the North Pole, with parallel arrows labelled 'sunlight' arriving from the right; the Moon drawn at eight evenly spaced positions on a circular orbit round the Earth, each Moon with its right-hand half (the half facing the Sun) white and its left-hand half dark; an anticlockwise arrow on the orbit labelled 'Moon orbits in about one month'; next to each position a small disc shows how the Moon looks from the Earth (lit part on the right for the waxing phases and on the left for the waning phases, as seen from the northern hemisphere), labelled in anticlockwise order starting from the position between the Earth and the Sun: new moon (disc all dark), waxing crescent, first quarter (right half lit), waxing gibbous, full moon (opposite the Sun, disc all lit), waning gibbous, last quarter (left half lit), waning crescent.
The lit half of the Moon always faces the Sun. The phase you see depends on how much of that lit half faces the Earth.
New moon. The Moon is on the same side of the Earth as the Sun. Its lit half faces away from the Earth, so you face its dark half and see little or nothing of it.
Full moon. The Moon is on the opposite side of the Earth from the Sun. Its whole lit half faces the Earth, so you see a complete bright disc.
Quarter moons. A quarter of an orbit after new moon, you see half of the disc lit. This is called first quarter, which looks wrong because the shape is a half. The name means a quarter of the way round the orbit, not a quarter of the disc. A quarter of an orbit after full moon you see the other half of the disc lit: last quarter.
In between: when less than half the disc is lit, the Moon is a crescent. When more than half but not all of it is lit, it is gibbous. From new moon to full moon the lit part grows, which is called waxing. From full moon back to new moon it shrinks, which is called waning.
So the order is: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, waning crescent, then new moon again.
Why is the cycle periodic? The Moon returns to the same position compared with the Earth and the Sun once every orbit, about one month. So the whole sequence of phases repeats about once a month.
The trap: the phases are not caused by the Earth's shadow. At new moon the Moon is on the Sun's side of the Earth, and the Earth's shadow points away from the Sun, so the shadow is nowhere near the Moon. When the Earth's shadow does fall on the Moon, that is a lunar eclipse, which is a different event.

Part 6 of 6

Average orbital speed

So far the orbits have been about timing. Now you put a number on how fast a body moves along its orbit.
Start from speed = distance ÷ time. In one complete orbit a body travels once round a circle of radius $r$ . The distance round a circle is its circumference, $2 π r$ . The time for one complete orbit is the orbital period, $T$ .
Put these into speed = distance ÷ time and you get the equation you must define, recall and use:
$v = \frac{2 π r}{T}$
Learn the definition in words as well: **average orbital speed is the distance travelled in one orbit, $2 π r$ , divided by the orbital period, $T$ **, where $r$ is the average radius of the orbit.
Why 'average'? Real orbits are not perfect circles, so the distance from the centre and the speed both change a little around the orbit. Using the average radius gives the average speed.
Units: with $r$ in metres and $T$ in seconds, $v$ comes out in m/s. Periods may be given in hours or days, so convert first. One hour is 3600 s, and one day is $24 \times 3600 = 86 400$ s.
The trap: $r$ is measured from the centre of the body being orbited, not from its surface. If a question gives a satellite's height above the Earth's surface, add the radius of the Earth to get $r$ .
$r = R_{Earth} + h$
forces diagram — not drawn yet
A circle labelled 'Earth' with its centre marked by a dot; a larger circle with the same centre showing a satellite's orbit, with a small satellite drawn on it; a straight line from the centre of the Earth to the satellite labelled 'r'; along that line, the section from the centre to the Earth's surface labelled 'R (radius of the Earth)' and the section from the surface to the satellite labelled 'h (height above the surface)'; an arrow at the satellite, tangent to the orbit, labelled 'v'.
The orbital radius is measured from the centre of the Earth, so $r = R + h$ .
To find $T$ or $r$ , rearrange before you substitute: $T = \frac{2 π r}{v}$ and $r = \frac{v T}{2 π}$ .
This equation is not given to you in Paper 4. You must recall it, like every other Physics equation.

Worked examples

Example 1. A student says: 'The Sun rises in the east and sets in the west because it travels round the Earth once a day.' (a) Explain what really causes the Sun's movement across the sky. (b) Calculate the angle through which the Earth rotates in $4.0$ hours.

Show the working

(a) Reject the wrong cause first. The Sun does not travel round the Earth. Its movement across the sky is only apparent.
Name the real motion and its period: the Earth rotates on its axis, once in about 24 hours.
Give the direction and its effect. The Earth turns from west to east and carries you with it, so the Sun appears to move the opposite way, from east to west.
(b) A full rotation is 360° in about 24 hours. Find the angle for one hour first.
$\frac{360^{\circ}}{24} = 15^{\circ} per hour$
Then multiply by the number of hours.
$15^{\circ} \times 4.0 = 60^{\circ}$

Answer: (a) The Earth rotates on its axis from west to east, about once every 24 hours, so the Sun appears to move across the sky from east to west. (b) 60°.

Example 2. In December the southern hemisphere is tilted towards the Sun. Explain why it is summer in Australia (southern hemisphere) and winter in Canada (northern hemisphere) in December, and why the same pattern returns every December.

Show the working

Use the tilt, not the distance. Australia and Canada are on the same planet, at practically the same distance from the Sun, so distance cannot make one warm and the other cold.
Australia is in the hemisphere tilted towards the Sun. There the Sun is higher in the sky at midday, so its energy falls on a smaller area and each square metre is heated more.
Australian days are also longer than its nights in December, so there are more hours of heating. Higher Sun and longer days: summer.
Canada is in the hemisphere tilted away from the Sun. The Sun is lower in the sky and the days are shorter: winter.
For 'every December', use the orbit. The Earth orbits the Sun once in about 365 days, and its axis keeps pointing the same way in space. So each December the Earth is back at the same point in its orbit, with the southern hemisphere tilted towards the Sun again.

Answer: Australia's hemisphere is tilted towards the Sun, so the Sun is higher (more energy per square metre) and days are longer: summer. Canada's is tilted away, with a lower Sun and shorter days: winter. The Earth returns to the same point in its orbit every 365 days with its axis pointing the same way, so the pattern repeats each December.

Example 3. Tonight the Moon is full. (a) Describe where the Moon is compared with the Earth and the Sun. (b) Predict the phase seen about one week later and about two weeks later. (c) State roughly when the next full moon will be.

Show the working

(a) Full moon means the whole lit half faces the Earth. The lit half always faces the Sun, so the Moon must be on the opposite side of the Earth from the Sun.
(b) One orbit takes about one month, roughly four weeks. So one week is about a quarter of an orbit.
A quarter of an orbit after full moon, you see half of the disc lit, and the lit part is shrinking. That is last quarter.
Two weeks is about half an orbit. The Moon is now on the same side of the Earth as the Sun, with its lit half facing away from you. That is new moon.
(c) The phases repeat once every orbit, so the next full moon comes about one month after this one.

Answer: (a) On the opposite side of the Earth from the Sun. (b) After about one week: last quarter (half the disc lit). After about two weeks: new moon. (c) About one month later.

Example 4. A satellite orbits the Earth at a height of $2.02 \times 10^{7}$ m above the Earth's surface. Its orbital period is $12.0$ hours. The radius of the Earth is $6.4 \times 10^{6}$ m. Calculate the average orbital speed of the satellite.

Show the working

Recall the equation $v = \frac{2 π r}{T}$ . It is not given on the paper.
Find $r$ . The height is measured from the surface, but $r$ is measured from the centre of the Earth, so add the Earth's radius.
$r = 6.4 \times 10^{6} + 2.02 \times 10^{7} = 2.66 \times 10^{7} m$
Convert the period to seconds, so that the speed comes out in m/s.
$T = 12.0 \times 3600 = 43 200 s$
Substitute.
$v = \frac{2 π \times 2.66 \times 10^{7}}{43 200} = 3870 m/s$
Notice what the trap would have cost. With the height alone as $r$ , you would get about 2940 m/s, a wrong answer from a correct equation.

Answer: $v = 3.87 \times 10^{3}$ m/s (3870 m/s).

Where people go wrong

Mistake: Saying it is summer because the Earth is closer to the Sun.

Instead: The seasons are caused by the tilt of the Earth's axis. The hemisphere tilted towards the Sun has a higher Sun and longer days.

The two hemispheres have opposite seasons at the same moment, and distance cannot explain that, because both are at practically the same distance from the Sun. In fact the Earth is nearest the Sun in early January, during the northern winter.

Mistake: Saying day and night happen because the Earth orbits the Sun.

Instead: Day and night come from the Earth rotating on its axis, once in about 24 hours. The orbit takes about 365 days and gives the year and the seasons.

Rotate and orbit are different motions with different periods. The wrong word gives the wrong cause.

Mistake: Saying the Sun moves across the sky because it travels round the Earth.

Instead: The Sun only appears to move. The Earth rotates from west to east, so the Sun appears to move from east to west.

You turn with the Earth and cannot feel it, so the motion you see is your own motion, in reverse.

Mistake: Saying the phases of the Moon are caused by the Earth's shadow.

Instead: The phases are caused by how much of the Moon's sunlit half faces the Earth as the Moon orbits.

At new moon the Moon is on the Sun's side of the Earth, nowhere near the Earth's shadow. The Earth's shadow falling on the Moon is a lunar eclipse, a separate event.

Mistake: Using a satellite's height above the surface as $r$ , or leaving $T$ in hours or days.

Instead: Add the Earth's radius to the height to get $r$ , and convert $T$ to seconds before you use $v = \frac{2 π r}{T}$ .

$r$ is the radius of the circle the satellite travels round, and that circle is centred on the centre of the Earth. A speed in m/s needs a time in seconds.

Check yourself

Explain why a place on the Earth has day and night.
Answer
The Sun lights the half of the Earth that faces it. As the Earth rotates on its axis, about once every 24 hours, the place is carried into the lit half (day) and then out of it into the dark half (night).
Through what angle does the Earth rotate in $6.0$ hours?
Answer
$360^{\circ} \div 24 = 15^{\circ}$ per hour, so $15^{\circ} \times 6.0 = 90^{\circ}$ .
It is summer in New Zealand, which is in the southern hemisphere. Which hemisphere is tilted towards the Sun, and what season is it in the northern hemisphere?
Answer
The southern hemisphere is tilted towards the Sun. It is winter in the northern hemisphere.
State two reasons why the hemisphere tilted towards the Sun is warmer.
Answer
The Sun is higher in the sky, so its energy is spread over a smaller area (more energy per square metre). The days are longer, so there are more hours of heating.
Why do the seasons repeat about every 365 days?
Answer
The Earth orbits the Sun once in about 365 days with its axis pointing the same way in space, so each hemisphere is tilted towards the Sun at the same point in every orbit.
The Moon is on the opposite side of the Earth from the Sun. Which phase is seen, and roughly how long is it until the same phase is seen again?
Answer
Full moon. The same phase returns after one orbit, about one month.
Define average orbital speed, then rearrange the equation to make $T$ the subject.
Answer
Average orbital speed is the distance travelled in one orbit, $2 π r$ , divided by the orbital period $T$ : $v = \frac{2 π r}{T}$ , where $r$ is the average radius of the orbit. Rearranged: $T = \frac{2 π r}{v}$ .
The Moon orbits the Earth at an average radius of $3.84 \times 10^{8}$ m with an orbital period of $27.3$ days. Calculate its average orbital speed.
Answer
$T = 27.3 \times 86 400 = 2.36 \times 10^{6}$ s, so $v = \frac{2 π \times 3.84 \times 10^{8}}{2.36 \times 10^{6}} = 1.02 \times 10^{3}$ m/s.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. The Earth rotates on a tilted axis and orbits the Sun.

(a) State the time taken for the Earth to rotate once on its axis. 1 mark No calculator

Mark scheme

B1 approximately 24 hours (accept: 1 day; accept 23 h 56 min)

(b) A person in a field watches the Sun rise, cross the sky and set. Explain why the Sun appears to move across the sky. 2 marks No calculator

Mark scheme

B1 the Earth rotates / spins on its axis (insufficient: 'the Earth moves'; 'the Earth orbits the Sun' does not score)
B1 the Sun does not move round the Earth; the person is carried round by the rotation, so the Sun appears to move (from east to west), owtte

(c) In June the northern hemisphere is tilted towards the Sun. Explain why it is summer in the northern hemisphere in June and winter there in December. 3 marks No calculator

Mark scheme

B1 in June the Sun is higher in the sky (in the northern hemisphere) / sunlight more concentrated / more energy per unit area; ORA for December (Sun lower / energy spread over a larger area)
B1 in June the days are longer than the nights / more hours of daylight; ORA for December (shorter days / fewer hours of daylight)
B1 in December the northern hemisphere is tilted away from the Sun (accept: the Earth is on the opposite side of its orbit / half an orbit later, with the axis pointing the same way in space); do not credit 'the Earth is closer to the Sun in summer'

Question 2. The Moon orbits the Earth.

(a) State why the Moon can be seen from the Earth. 1 mark No calculator

Mark scheme

B1 it reflects light from the Sun / reflects sunlight (it gives out no light of its own)

(b) Explain why the Moon goes through a cycle of phases that repeats about once a month. 3 marks No calculator

Mark scheme

B1 half of the Moon is always lit by the Sun
B1 as the Moon orbits the Earth, the amount of the lit half that faces the Earth changes / we see different amounts of the lit half
B1 the Moon orbits the Earth once in about one month, so the cycle repeats every month; do not credit 'the Earth's shadow covers the Moon'

(c) One night the Moon is on the same side of the Earth as the Sun. Predict the phase seen about two weeks later, and give a reason. 2 marks No calculator

Mark scheme

B1 full moon
B1 the Moon has moved about half an orbit / is now on the opposite side of the Earth from the Sun, so all of the lit half faces the Earth

Question 3. Take the average radius of the Earth's orbit round the Sun to be $1.5 \times 10^{11}$ m, and the radius of the Earth to be $6.4 \times 10^{6}$ m.

(a) Define average orbital speed. 2 marks No calculator

Mark scheme

B1 distance travelled in one (complete) orbit / circumference of the orbit / 2πr
B1 divided by the time taken for one orbit / the orbital period (T); v = 2πr / T with r named as the (average) orbital radius and T as the orbital period scores both marks

(b) The Earth takes $365$ days to orbit the Sun once. Calculate the average orbital speed of the Earth. 3 marks

Mark scheme

C1 T = 365 × 24 × 3600 = 3.15 × 10⁷ s
C1 v = 2πr / T used, or distance 9.4 × 10¹¹ m seen
A1 3.0 × 10⁴ m/s (accept 2.99 × 10⁴ m/s, 29 900 m/s or 30 km/s); unit required

(c) A space station orbits the Earth at a height of $4.0 \times 10^{5}$ m above the Earth's surface, with an average orbital speed of $7.7 \times 10^{3}$ m/s. Calculate its orbital period. 3 marks

Mark scheme

C1 r = 6.4 × 10⁶ + 4.0 × 10⁵ = 6.8 × 10⁶ m
C1 T = 2πr / v used; ecf for r
A1 5.5 × 10³ s (accept 5550 s or 92 minutes); unit required

How this is examined

Working out an orbital speed or period with $v = \frac{2 π r}{T}$ when the time is in hours or days: a three-mark Calculate; the radius may be given as a height above the Earth's surface instead The period converted to seconds (for example $365 \times 24 \times 3600 = 3.15 \times 10^{7}$ s); $r$ measured from the centre ( $r = R + h$ when a height is given); $v = \frac{2 π r}{T}$ or its rearrangement seen; the final answer with its unit, such as $3.0 \times 10^{4}$ m/s.
Explaining the seasons with the tilt of the axis, not the distance from the Sun: a two- or three-mark Explain about one hemisphere at a named time of year 'That hemisphere is tilted towards the Sun'; 'the Sun is higher in the sky, so the energy is spread over a smaller area / more energy per square metre'; 'the days are longer than the nights'. For the repeat: 'the Earth orbits the Sun once in about 365 days with its axis pointing the same way in space'. A distance-from-the-Sun reason earns nothing.
Explaining why the Moon shows a cycle of phases: a two- or three-mark Explain, or a Predict about the phase after part of an orbit 'Half the Moon is always lit by the Sun'; 'as the Moon orbits the Earth, we see different amounts of the lit half'; 'one orbit takes about a month, so the cycle repeats every month'. For a Predict: about half an orbit (two weeks) turns new moon into full moon, and full moon into new moon.
Explaining day, night and the Sun's movement across the sky: a one- or two-mark Explain 'The Earth rotates (spins) on its axis'; 'once in about 24 hours'; 'the half facing the Sun has day, the half facing away has night'; 'the Earth turns from west to east, so the Sun appears to move from east to west'. 'The Earth orbits the Sun' is a different motion and does not explain day and night.
Defining average orbital speed: a one- or two-mark Define, or a State that asks for the equation 'The distance travelled in one orbit ( $2 π r$ ) divided by the time for one orbit (the orbital period $T$ )', or $v = \frac{2 π r}{T}$ with $r$ named as the average radius of the orbit and $T$ as the orbital period.
The three periods, each with the right motion: one-mark State parts The Earth rotates once in about 24 hours. The Earth orbits the Sun once in about 365 days. The Moon orbits the Earth once in about one month. The motion must match the period: rotate for 24 hours, orbit for 365 days.

Words to know

Axis: The imaginary line through the North and South Poles about which the Earth rotates. The Earth's axis is tilted.
Rotation: Spinning about an axis. The Earth rotates once in approximately 24 hours.
Orbit: The path of one body around another, such as the Earth around the Sun or the Moon around the Earth.
Orbital period ( $T$ ): The time taken for one complete orbit.
Periodic: Repeating after a fixed interval of time, such as day and night every 24 hours.
Apparent motion: Movement that a body only seems to have because the observer is moving, such as the Sun crossing the sky as the Earth rotates.
Hemisphere: Half of the Earth: the northern hemisphere is north of the equator and the southern hemisphere is south of it.
Phase (of the Moon): The shape of the lit part of the Moon as seen from the Earth.
Waxing / waning: Growing / shrinking. The lit part seen from the Earth waxes from new moon to full moon and wanes from full moon to new moon.
Average orbital speed: The distance travelled in one orbit divided by the orbital period: $v = \frac{2 π r}{T}$ , where $r$ is the average radius of the orbit.

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