topic badge

INVESTIGATION: Unusual timetables


Timetables are everywhere. In our day-to-day lives, we use basic calendars, diaries and schedules to stay organised and manage our time. They could be to keep track of our own daily tasks and events, or they could be for the public to know about important times such as when trains arrive or when sporting matches will be on. Businesses and hospitals also need timetables to keep track of the many tasks and people that make them run.

Most timetables are structured in a similar way, as a consecutive list of days and/or times. The following schedules from are the most common types you will encounter.

Nature's Timetable

There are particular patterns in nature that scientists can predict with a high level of accuracy, often years in advance. This is nature's timetable. It includes the motion of the stars and the planets, the variations of the tides, the phases of the moon, and the rising and setting of the sun.

What do all of these have in common? They are all to do with the movement of celestial bodies (things in space). Even the tides depend on where the sun, the moon and the earth are positioned.

Humans have been observing and tracking the motion of stars, planets and the moon since before Ancient times. The Egyptians, the Babylonians and Australian Aboriginals all wrote down early versions of star charts. Stars have determined spiritual practices and beliefs, and helped ships to navigate the ocean.

So how is the movement of celestial bodies different from, say, the changing of the seasons?

Well, even though we can predict when the seasons will occur, things like the weather are too complicated to predict well in advance with accuracy. The movement of celestial bodies, on the other hand, is one of the most predictable things in all of science.

For this reason, we have timetables for the tides, the phases of the moon, and sunrise/sunset.

However, these timetables often aren't formatted like the basic timetables above. Why might this be? What would it look like if we tried to use one of the above styles?

Well, one reason for using a different format is that these natural events are only occurring two or four times a day at most. Secondly, there is a lot of information associated with these events that we want to know, such as heights of the tides or time differences between sunrise and sunset. Thirdly, they are not occurring at nice half-hourly intervals. Sometimes, they aren't even occurring the same amount of times each day! For instance, most of the time, there are two high tides and two low tides each day. However, sometimes only three tide extremes can fit in a day, and not all days begin with a low tide.

We will now try to interpret some complex timetables such as these.


Worked example

Consider the following timetable.

  1. How many days begin with a high tide?
  2. Is the amount of daylight each day decreasing or increasing?
  3. On what day is the moon in the night sky for the least amount of time?
  4. What is the approximate amount of time between two moonrises?
  5. At what time on Thursday is the moon directly overhead?
  6. Saul wants to sail out of the bay for a day of fishing this weekend. However, he can not leave the bay in the dark and he can not enter or exit within two hours either side of low tide. Should he spend the day fishing on Saturday or Sunday to get the most out of the day?
  1. The extreme tides for each day are listed in order vertically. The table doesn't directly tell us if the tides are high or low. We have to read the water levels to figure that out ourselves.
    The tide information alternates between water levels above and below 1 m. Therefore, high tides are above 1 m and low tides are below 1 m.
    Hence, we can see from the table that Sunday through to Tuesday begin with high tides.
  2. We could explicitly calculate the amount of sunlight each day to figure this out. Or, we could notice that sunrise is getting later and sunset is getting earlier, so the amount of daylight must be decreasing.
    This is typical of March in Sydney, Australia, which is heading towards winter at this time of year as it is in the Southern Hemisphere.
  3. Let's take Wednesday as an example. The moon sets before the sun does, so it won't be in the night sky after sunset.
    However, the moon rises on Wednesday 1 hour and 12 minutes before sunrise, so this is the total amount of time the moon is in the night sky on Wednesday.
    We want to look for a day where the moon rises and sets almost with the sun. This will ensure that it is in the sky during the daytime and not during the night time.
    Thursday satisfies this condition. On Thursday, the moon is only in the night sky for 4 minutes before the sun rises, and it sets before the sun does, and no other day has a shorter time than this.
  4. We want to find the time between two moon rises. Choosing Wednesday and Thursday, we find the difference between 5:38 am and 6:47 am the next day to be 25 hours and 9 minutes.
  5. On Thursday, the moon rises at 6:47 am and sets at 7:09 pm. We want to find the time halfway between these two times.
    There are 12 hours and 22 minutes between the moonrise and moonset, so the moon will be overhead after half this time.
    So, we want to find the time 6 hours and 11 minutes after 6:47 am, which is 12:58 pm.
  6. Let's start with Saturday. Even though the sun rises at 6:52 am, Saul can't leave until 7:36 am because of the 5:36 am low tide.
    At the end of the day, if Saul waits two hours after the 5:58 pm low tide, it will be dark, so he has to return to the bay at 3:58 pm.
    This means he can fish for 8 hours and 22 minutes on Saturday.
    As for Sunday, Saul must wait until 8:34 am to leave due to the low tide, and must return at 4:45 pm due to the evening low tide.
    This means he can fish for 8 hours and 11 minutes on Sunday.
    Hence, Saturday is preferable for fishing.


Investigation part 1

Moon Phases

A good way to understand the phases of the moon is to view an animation. Further details, diagrams and selected animations can be found here.

One full revolution of the Earth is a day. One full revolution of the Earth around the Sun is a year.

Firstly, notice just how slowly the Moon moves around us. Even though we talk of sunrises, sunsets, moonrises and moonsets, in reality, it is the earth that is doing the moving.

Secondly, notice that the Moon is almost always lit. It does not matter what phase the Moon is in, half of the moon is always lit by the Sun. The Earth's position relative to the Moon and Sun is the reason why we don't always see a Moon which is half lit and the phases of the Moon which we see is the determined by the potion of the lit Moon we can see from the Earth's position relative to the position of the Sun and the Moon.

The Moon does not appear lit during a lunar eclipse, which only happens a small number of times a year at most. This is when the Moon passes directly behind the Earth and into its shadow, with the Sun, Earth and Moon closely aligned,

Thirdly, notice also that on any particular night, the moon is in a different position in relation to the Earth and the Sun. Sometimes it is between the two, sometimes it is to the side of the Earth, and sometimes it is behind the Earth. This determines what part of the lit moon we can see at night, called the moon phase.


Investigation task:

  1. Go to your local bureau of meteorology website, or an equivalent website, and find a calendar showing the moon phases in your area for the next two months.

(a) When is the next Full Moon? Where will the Moon be in relation to the Earth and the Sun on that night?

(b) When is the next New Moon? Where will the Moon be in relation to the Earth and the Sun on that night?

(c) When is the next Crescent Moon? Where will the Moon be in relation to the Earth and the Sun on that night?

(d) Approximately how many days are there between Full Moons? This is called a Lunar Month.

(e) Approximately how many Lunar Months are there in a year?

2. Another name for a Lunar Month is a Synodic Month, the amount of time between Full Moons. On the other hand, a Sidereal Month is the amount of time it takes the Moon to orbit 360 \deg around the Earth. These are not the same. A Sidereal Month is about two days shorter than a Synodic Month. Why do you think this is? Discuss with your classmates and your teacher.

Did you know?

The words Moon and Month come from the same Latin word.

Moon phases, the changing of the seasons, and later the calculation of the Earth's orbit around the Sun, are the ways humans have historically used to define the calendar year.


Investigation part 2

Indigenous Australian seasons


Indigenous Australian calendars

Most people are used to having four seasons- Summer, Autumn, Winter and Spring. However, some indigenous calendars divide the year up differently based on subtle changes in the natural environment. For example, the Yarwuru tribe has seven seasons, while the Miriwoong tribe only has three.

Indigenous Australians observed the relationship between changes in the astronomy and corresponding changes in flora and fauna. Stories about the rising and setting stars and constellations, as well as movements of the sun, moon and planets were passed on to teach people when it was time to move on and find a new source of food.

For example:

  • The Boorong people in Victoria know that when the Malleefowl constellation disappears from the sky in

    A malleefowl on her nest.

    October, it was time to start gathering the birds' eggs on the Earth.
  • When the Scorpius constellation appeared, the Yolngu know that the Macassan fisherman would soon arrive to fish for trepang.
  • To the people of D'harawal Country during Marrai'gang (when the weather is wet and becoming cooler), the cries of the Marrai'gang (quoll) seeking his mate can be heard, is the time when the lilly-pilly fruit begins to ripen on trees and would be a good source of food.

Investigation task:

  1. Go the the Australian Bureau of Meteorology Indigenous Weather page and research an Aboriginal tribe.
  2. Write a report about the different seasons within this tribe, and what changes happen in each of these seasons.
  3. What other countries/cultures use different seasons other than Summer, Autumn, Winter and Spring? What are they?
  4. Why might countries experience different seasons?


Did you know?

There is evidence Aboriginal Australians may actually have been some of the first astronomers. For example, according to oral tradition, the rock engravings by the Nganguraku people at Ngaut Ngaut (shown at the top of the page) represent lunar cycles. Lunar cycles influences the tides. Tides are caused by the gravitational pull of the sun and moon, which can be used to tell the time.



Fishing and surfing trip

Ben and his friends are planning a surfing and fishing holiday for the coming week near Triggs Beach in Western Australia. Ben checks the surf forecast for a beach where they are staying to help plan for the week ahead.

Ben knows that a falling tide, which is about two hours before a low tide, are the best conditions for fishing. Ben and his friends don’t mind fishing in the rain. For surfing at this spot, high tide, above about 0.5 m, tends to be the best and surfers usually prefer to surf when the weather is clear and at dawn and dusk.

Investigation task:

  1. Collect detailed information about wind, rain, tide, wave height, sunrise and sunset information for the Triggs Beach area. You can use the following site for a detailed surf report or use the web and search for conditions in this area. Search for similar surf report websites or use a combination of information from the Bureau of Meteorology and other weather sites. 
  2. Help Ben prepare a detailed description on the conditions which have been forecast each day so that along with his friends, they can plan when they will go fishing and when they will go surfing.
  3. What are the best wind conditions for surfing and fishing?
  4. Where is the closest good fishing or surfing sport near you? What are the optimum conditions for good surfing/fishing for the spot?
  5. How do the conditions for the upcoming week at the surfing/fishing spot near you compare to the conditions Ben and his friends will experienced on their trip?



interpret complex timetables, such as tide charts, sunrise charts and moon phases

What is Mathspace

About Mathspace