Factors to consider when determining the Matariki holiday

[kumkee]

Factors to consider when determining the Matariki holiday

Friday

The holiday is always on a Friday. How to determine the day of the week depends on the language you use. In JavaScript, for example, it is the getDate() function of the Date class.

Moon Phase

The holiday is ideally a Tangaroa night. There are normally 4 Tangaroa nights in a Māori lunar month, Tangaroa-ā-mua, Tangaroa-ā-roto, Tangaroa whakapau, and Tangaroa whāriki kiokio. In a 30-night month, these are the 23th to 26th nights. However, Tangaroa are the 23th to 25th nights in a 29-night months. As in Traditional Chinese Calendar, a Māori month starts at new moon.

The Tangaroa nights won't always include a Friday. In that case, the Friday after the starting of Tangaroa period will be the holiday if it is a weekday, and the Friday before if it is a weekend.

NZST

We will use midnight in New Zealand Standard Time (UTC+12) to determine the date where the new moon falls. For those trying to use the Traditional Chinese Calendar (TCC), please be mineful that TCC is based on the Chinese Standard Time (UTC+8).

Apparent position of Matariki cluster to the Sun

The Matariki cluster must be visible at dawn. This turns out to be the easiest factor. Since the Georgian calendar is a solar calendar, we can always predict the Matariki cluster becomes visible at dawn on and after 19 June every year. If you want to be even more precise, please see the Bonus Point at the end of this document.

Summary

The Matariki holiday is a Friday during or after the first Tangaroa Luna period after 19 June.

How to Find the Moon Phase

JPL Horizons

The most accurate way to calculate the moon phase is through Horizons System from NASA's Jet Propulsion Laboratory. For a quick check, you can use their web app. However, to do arbitrary predictions, you will need to use their API or a third party API wrapper for your language. More on that later.

Moon Phase from JPL Horizons

To predict the moon phase, you may use the following setting:

• Ephemeris Type: Observer Table
• Target body: Moon
• Observer Location: Geocentric
• Table Settings: Sun-Target-Observer ~PHASE angle (S-T-O)

There is a Wikipedia page about the S-T-O phase angle.

A new moon happens when the S-T-O climbs to a local maximum (should be just below 180°, while 180° is a solar eclipse), and full moon when it declines to a local minimum (just above 0°, while 0° is a lunar eclipse).

************************************************
 Date__(UT)__HR:MN        S-T-O    
************************************************
 2022-May-30 11:06     178.5031
 2022-May-30 11:07     178.5033
 2022-May-30 11:08     178.5035
 2022-May-30 11:09     178.5036
 2022-May-30 11:10     178.5037
 2022-May-30 11:11     178.5037 <-- local maximum = new moon
 2022-May-30 11:12     178.5037
 2022-May-30 11:13     178.5037
 2022-May-30 11:14     178.5036
 2022-May-30 11:15     178.5035
 2022-May-30 11:16     178.5033
 2022-May-30 11:17     178.5031
...
 2022-Jun-14 11:24       2.6851
 2022-Jun-14 11:25       2.6849
 2022-Jun-14 11:26       2.6848
 2022-Jun-14 11:27       2.6847
 2022-Jun-14 11:28       2.6846
 2022-Jun-14 11:29       2.6846  <-- local minimum = full moon
 2022-Jun-14 11:30       2.6846
 2022-Jun-14 11:31       2.6847
 2022-Jun-14 11:32       2.6848
 2022-Jun-14 11:33       2.6849
 2022-Jun-14 11:34       2.6850

In the example above, a new moon occurs at around 2022-May-30 11:11 UTC, and a full moon at around 2022-Jun-14 11:29.

JPL Horizons API Wrappers

• Python wrapper - Using this wrapper, I've written a python programme to predict the 24 Chinese Solar Terms. You may use that as an example.
• JavaScript wrapper - I haven't tested this.
• Other languages - you will need to find the wrapper for your language, if it is other than Python or JavaScript.
• Direct API call - as an alternative, you can directly call their API

Other Ways of Calculating Moon Phase

If you are using other method, you may want to compare your results with the one from JPL Horizons.

Bonus Point - determining when Matariki can be visible by its coordinates

Instead of using the rule of thumb of 19 June to predict the rise of Matariki, you can calculate the locations of the sun and Matariki cluster and see when the cluster is visible at dawn.
To do this you will need to find out horizontal coordinates (AZ/EL) for both objects. The AZ/EL for the sun can be retrieved from JPL Horizons. For the Matariki cluster, you will need to convert its equatorial coordinate (RA/DEC) (which can be safely assumed to be constants) to its AZ/EL. This conversion can be done for example using Astropy in python.

[6xtvo]

What parameter do we use to get the S-T-O from the JPL Horizons API? (since I get several columns, and it'd be easier to deal with less columns)

[kumkee]

What parameter do we use to get the S-T-O from the JPL Horizons API? (since I get several columns, and it'd be easier to deal with less columns)

To predict the moon phase, you may use the following setting:

Ephemeris Type: Observer Table
Target body: Moon
Observer Location: Geocentric
Table Settings: Sun-Target-Observer ~PHASE angle (S-T-O)

[kumkee]

(since I get several columns, and it'd be easier to deal with less columns)

You'll need to restrict the ephemerides output.
In astroquery.jplhorizons in Python, this is done by specifying the quantities argument of the ephemerides function to 24 (which represents the S-T-O angle.
If you are using a JS wrapper, you'll need to figure it out from their documentation.

[6xtvo]

Alright, thanks. I'm not using any wrapper, I'm just directly fetching from the API

[kumkee]

Alright, thanks. I'm not using any wrapper, I'm just directly fetching from the API

For direct API call, you need QUANTITIES='24' among your parameters.

[jyee4187]

In the summary for the Factors to consider for the moon dates, it states "The Matariki holiday is a Friday during or after the first Tangaroa Luna period after 19 June.", whereas in the governments report (https://www.mbie.govt.nz/assets/matariki-dates-2022-to-2052-matariki-advisory-group.pdf), it states "The Matariki holiday date falls on the closest Friday to the Tangaroa lunar calendar period of the correct lunar calendar month.

As a result in some of their dates, the Matariki Holiday occurs before the Tangaroa period. Which condition do we take as true?

[kumkee]

There is an exception in 2040. 1st July is a Sunday but they chose the following Friday instead. Is there some reasoning behind this?

Tangaroa should be starting on the 3rd July instead of the 1st.

[sttaseen]

I am confused. Why is Tangaroa on 3rd July?

[6xtvo]

There's another exception with 2044, where the Tangaroa period is 19 - 22 June and the holiday is 24 June but 19 June is a Sunday

[kumkee]

There's another exception with 2044, where the Tangaroa period is 19 - 22 June and the holiday is 24 June but 19 June is a Sunday

Matariki can't be before 19th June.

[6xtvo]

Oh right, didn't notice that.

[sttaseen]

For 2037, by looking at the STO, it appears that the Tangaroa period starts on the 5th of July but in their document, they mentioned it starts on the 6th of July. Because of this, I am choosing the wrong Friday. Is this some kind of error or am I missing something?

[kumkee]

How to find the new moon for the specific month of Matariki? I know that by using STO you can find the new moon, but would that new moon be before or after 19th June? Sometimes 19th June is the 23rd day of the Maori month

The new moon can be before 19 June, but the Matariki holiday has to be on of after 19 June.
The star cluster can only be visible on or after 19 June.

[6xtvo]

How to find the new moon for the specific month of Matariki? I know that by using STO you can find the new moon, but would that new moon be before or after 19th June? Sometimes 19th June is the 23rd day of the Maori month

The new moon can be before 19 June, but the Matariki holiday has to be on of after 19 June.
The star cluster can only be visible on or after 19 June.

How do we determine the start date to start searching the API if the new moon could occur during or before June?

[6xtvo]

For 2037, by looking at the STO, it appears that the Tangaroa period starts on the 5th of July but in their document, they mentioned it starts on the 6th of July. Because of this, I am choosing the wrong Friday. Is this some kind of error or am I missing something?

You shouldn't look for STO being 90 degree. It is not how Tangaroa is defined. It's about the 23rd night of a Maori month or 22 days after the new moon.

The Matariki dates PDF quotes

The Tangaroa lunar period is situated in the last quarter of the lunar cycle, when the moon is waning. In this period the moon goes from a quarter to completely dark (New Moon).

Wouldn't this mean the S-T-O should be just under 90 degrees?

[kumkee]

The Matariki dates PDF quotes

The Tangaroa lunar period is situated in the last quarter of the lunar cycle, when the moon is waning. In this period the moon goes from a quarter to completely dark (New Moon).

Wouldn't this mean the S-T-O should be just under 90 degrees?

"In the last quarter" ≠ "at the beginning of the last quarter"

[kumkee]

How to find the new moon for the specific month of Matariki? I know that by using STO you can find the new moon, but would that new moon be before or after 19th June? Sometimes 19th June is the 23rd day of the Maori month

The new moon can be before 19 June, but the Matariki holiday has to be on of after 19 June.
The star cluster can only be visible on or after 19 June.

How do we determine the start date to start searching the API if the new moon could occur during or before June?

One way (among many) of doing that is to list the STOs for the 30 days before and after 19 June (step=1d for efficiency).

[kumkee]

Hello teams,
One of the 30 government announced Matariki dates might be wrong (I won't tell you which one yet). If your codes produce that single wrong date but still agree with the definition, it will still be regarded as 100% correct.

[6xtvo]

What value do I put for the CENTER parameter for Auckland?

[6xtvo]

Found it, it's 467

[sttaseen]

Why is the 19th June rule always true? I didn't quite get the reasoning.

[kumkee]

Why is the 19th June rule always true? I didn't quite get the reasoning.

Since the Georgian calendar is a solar calendar, we can always predict the Matariki cluster becomes visible at dawn on and after 19 June every year. If you want to be even more precise, please see the Bonus Point at the end of this document.