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mtc-slides.html
<!DOCTYPE html>
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<head>
<title>What Time Is It?</title>
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<textarea id="source">
class: middle, center
<img src="https://i.redd.it/tqhrj2o0vbz01.jpg" width="500px" />
---
class: center, middle
# Interplanetary Timezone Conversion
---
class: center, middle
# <strike>Interplanetary Timezone Conversion</strike>
---
class: center, middle
# Does anybody really know what time it is?
---
class: center, middle
# Does anybody really know what time it is?
## (Does anybody really care?)
---
# Let's review elementary school!
---
# Let's review elementary school!
- How long is a minute?
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
<img src="https://static1.squarespace.com/static/541bcb6be4b0ff8856437f90/t/5684a288df40f309608f2d62/1451533028048/party_emoji.png" width="200px" />
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
- How long is an hour?
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
- How long is an hour? *60 minutes!*
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
- How long is an hour? *60 minutes!*
<img src="https://static1.squarespace.com/static/541bcb6be4b0ff8856437f90/t/5684a288df40f309608f2d62/1451533028048/party_emoji.png" width="200px" />
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
- How long is an hour? *60 minutes!*
- How long is a day?
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
- How long is an hour? *60 minutes!*
- How long is a day? *24 hours!*
---
# Let's review elementary school!
- How long is a minute? *60 seconds!*
- How long is an hour? *60 minutes!*
- How long is a day? *24 hours!*
<img src="http://www.pngall.com/wp-content/uploads/2016/04/Red-Cross-Mark-PNG-Pic.png" width="200px" />
---
class: center, middle
# What kind of day?
---
class: center, middle
# What kind of _time_?
---
class: center, middle
So the earth rotates...
<img src="http://i926.photobucket.com/albums/ad101/iainn-cruise/Day_Sol_Eq21_RevolvingEarth.gif" width="400px" />
Which makes day and night. And stars that start overhead return to overhead
after one rotation.
---
class: center, middle
# So a rotation is a day, right?
---
class: center, middle
<img src="https://static1.squarespace.com/static/541bcb6be4b0ff8856437f90/t/5684a288df40f309608f2d62/1451533028048/party_emoji.png" width="300px" />
---
class: center, middle
# So one rotation of the earth is 24 hours?
---
class: center, middle
<img src="http://www.pngall.com/wp-content/uploads/2016/04/Red-Cross-Mark-PNG-Pic.png" width="300px" />
---
class: center, middle
# _Sidereal Day_ =
# 23 hours 56 minutes 4.0916 seconds
???
"sigh-deer-ee-uhl"
but the length of a sidereal day varies with the nutation ("wobble") of the earth
---
class: center, middle
# <strike>Sidereal Day</strike> _Mean_ Sidereal Day =
# 23 hours 56 minutes 4.0916 seconds
???
add up those 236 seconds 180 times and you lose about 12 hours
---
class: center, middle
# So why doesn't night swap with day every 180 days?
---
class: center, middle
So the Earth moves around the Sun...
<img src="https://community.dur.ac.uk/john.lucey/users/siderealsolarday.jpg" width="400px" />
---
class: center, middle
# So "high noon" to "high noon" is a day, right?
---
class: center, middle
<img src="https://static1.squarespace.com/static/541bcb6be4b0ff8856437f90/t/5684a288df40f309608f2d62/1451533028048/party_emoji.png" width="300px" />
---
class: center, middle
# So "high noon" to "high noon" is 24 hours?
---
class: center, middle
<img src="http://www.pngall.com/wp-content/uploads/2016/04/Red-Cross-Mark-PNG-Pic.png" width="300px" />
---
class: center, middle
# _Apparent Solar Day_ =
# 24 hours ± 30 seconds
???
apparent solar day varies with season
1. earth's orbit is an ellipse, so it covers a larger angle at perihelion vs at aphelion ("ap-hel...")
2. the earth's tilt
---
class: center, middle
# Well fine, let's just average it.
# (A solar year is constant, right?)
???
...close enough
---
class: center, middle
<img src="https://static1.squarespace.com/static/541bcb6be4b0ff8856437f90/t/5684a288df40f309608f2d62/1451533028048/party_emoji.png" width="300px" />
---
class: center, middle
# _Mean Solar Day_
---
class: center, middle
# So "mean solar noon" to "mean solar noon" is 24 hours?
---
class: center, middle
<img src="http://www.pngall.com/wp-content/uploads/2016/04/Red-Cross-Mark-PNG-Pic.png" width="300px" />
---
class: center, middle
# Mean Solar Day = 24 hours...
---
class: center, middle
# Mean Solar Day = 24 hours 0.002 seconds
???
where do those 2 milliseconds come from
obviously we chose the "wrong" size of second if we can't get it to add up to 24 hours...
---
class: center, middle
<img src="http://vignette1.wikia.nocookie.net/icarly/images/c/c3/Rage_table_flip.png/revision/latest?cb=20130324185425" width="500px" />
---
class: center, middle
# Before 1952...
## 1 Second =
## (Mean Solar Day) / 86400
---
class: center, middle
# Easy...
---
class: center, middle
# Easy... but variable
???
mean solar day is slowly getting longer
mostly because of tidal forces between the earth and the moon
---
class: center, middle
# From 1952 to 1967...
## Ephemeris Second =
## (100 Solar Years) / (36525 * 86400)
???
tidal forces between earth and sun _are_ also changing the solar year
but even at astronomical time scales it's nearly negligible
so close enough to constant
but it's still an _measured_ and drifting (if ever so slowly) value, not a _defined_ value
and standards bodies like immutable definitions
---
class: center, middle
# After 1967...
## SI Second =
"The duration of 9,192,631,770 periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of the Cesium
133 atom."
---
class: center
# I lied about the Mean Solar Day...
<img src="http://images.huffingtonpost.com/2015-02-04-Sorrypostitnote2.jpg" width="500px" />
???
talked about choosing the "wrong" size of a second...
---
class: center
# I lied about the Mean Solar Day...
## Mean Solar Day = 24h 0.002 _in SI seconds_
---
class: center
# I lied about the Mean Solar Day...
## Mean Solar Day = 24h 0.002 _in SI seconds_
## Mean Solar Day = 24h _in UT1 seconds_
---
class: center, middle
# UT1?
---
# GMT, UT1, UTC, and friends
---
# GMT, UT1, UTC, and friends
- GMT = Mean solar time _as angle_ at Greenwich
---
# GMT, UT1, UTC, and friends
- GMT = Mean solar time _as angle_ at Greenwich
- UT1 = Approximation of GMT using non-solar measurements
???
staring at the sun to make measurements is hard
staring at the fictitious "mean sun", which is right next to the actual sun but
not _exactly_ in the same spot, is also hard
---
# GMT, UT1, UTC, and friends
- GMT = Mean solar time _as angle_ at Greenwich
- UT1 = Approximation of GMT using non-solar measurements
- TAI = Number of SI seconds ticked since midnight GMT 1 January 1977
???
(I)nternational (A)tomic (T)ime
---
# GMT, UT1, UTC, and friends
- GMT = Mean solar time _as angle_ at Greenwich
- UT1 = Approximation of GMT using non-solar measurements
- TAI = Number of SI seconds ticked since midnight GMT 1 January 1977
- UTC = TAI + leap seconds to approximate UT1
---
class: middle, center
# Leap Seconds!
???
those 0.002 seconds difference per day add up
to about 1 second every 1.5 years
the actual period of adding a leap second is variable for many reasons, but
it's about that often and the 0.002 second discrepancy is the main contributor
idea of scale: if we moved the meridian to match UTC instead of correcting UTC
to match the meridian (which defines GMT), the meridian would drift about 300m
per year
---
class: middle, center
<img src="https://media.tenor.com/images/13fda09c48e6f5de5366b7a1147cca54/tenor.png" width="500px" />
---
class: center, middle
# One more!
---
class: center, middle
# TT (Terrestrial Time) = ...
---
class: center, middle
# TT (Terrestrial Time) = TAI ...
???
basically the same as TAI
uses SI seconds, doesn't have leap seconds
---
class: center, middle
# TT (Terrestrial Time) = TAI + 32.184s
---
class: middle, center
<img src="http://orig10.deviantart.net/a05b/f/2013/150/8/f/wut__by_djpavlusha-d678s0o.jpg" width="500px" />
---
class: middle, center
# TAI epoch = 1 January 1977 00:00:00 GMT
???
similar concept as unix epoch of 1 Jan 1970 00:00:00 UTC
---
class: middle, center
# Why?
???
but the SI second was defined back in 1967
why is the epoch in 1977?
---
class: middle, center
<img src="http://torahtimes.org/articles/starlight/grav-time-dialation.gif" width="500px" />
???
the definition for the SI seconds is _not_ invariant!
after making the definition, they had multiple atomic clocks keeping time with it -- and they started to drift apart
altitude affects gravity affects time
corrected SI second definition to be same definition but at mean sea level ("on the geoid")
this correction was applied starting at the new epoch 1977
---
class: middle
# Astronomers want TT = ET, so at:
- TAI = 1 January 1977 00:00:00
---
class: middle
# Astronomers want TT = ET, so at:
- TAI = 1 January 1977 00:00:00
- ET = 1 January 1977 00:00:32.184
???
figured "while we're at it, making a new time, might as well make it match ET at the epoch. provide a cleaner transition away from ET"
---
class: middle
# Astronomers want TT = ET, so at:
- TAI = 1 January 1977 00:00:00
- ET = 1 January 1977 00:00:32.184
- TT = 1 January 1977 00:00:32.184 = TAI + 32.184s
---
class: middle
# What does any of this have to do with "Interplanetary Time"?
---
class: middle, center
<img src="https://pics.onsizzle.com/this-was-all-a-trick-i-deceived-you-haha-you-3205445.png" width="500px" />
---
class: middle, center
# Mean Martian Solar Day = ...
???
let's use Mars as an example
---
class: middle, center
# Mean Martian Solar Day =
# k * Mean Solar Day
---
class: middle, center
# Martian Second = k * SI Second
---
class: middle, center
# k = 1.0274912517
???
or: mean martian solar day is longer than an mean earth solar day by about 40 earth minutes
---
class: middle
# The apparent Martian solar time...
???
let's find a "reference point" to connect martian time and earth time
similar to how 32ºF = 0ºC is a reference point to connect fahrenheit and celsius
32<->0 comes from a "coincidence" of water's freezing point
so let's look for a earth/mars solar time-based "coincidence"
---
class: middle
# The apparent Martian solar time...
# at the center of the Airy-0 crater on Mars...
---
class: middle
# The apparent Martian solar time...
# at the center of the Airy-0 crater on Mars...
# at January 5, 2000 23:59:05.816 UTC...
???
why that weird time?
---
class: middle
# The apparent Martian solar time...
# at the center of the Airy-0 crater on Mars...
# at January 6, 2000 00:00:00 TT...
???
difference between UTC and TT
32.184 seconds TT to TAI + 22 leap seconds in 2000
---
class: middle
# The apparent Martian solar time...
# at the center of the Airy-0 crater on Mars...
# at January 6, 2000 00:00:00 TT...
# was high noon!
---
class: middle
# The apparent Martian solar time...
# at the center of the Airy-0 crater on Mars...
# at January 6, 2000 00:00:00 TT...
# was 11:58:36.831!
???
well, close enough
difference is because the middle of the crater wasn't as precisely mapped
the couple minutes off is due to the shift in the measured center of the crater with later better measurements
---
class: middle, center
### Martian prime meridian = Center of Airy-0 crater
### Common Epoch = January 6, 2000 00:00:00 TT
### MJD Epoch = December 29, 1873 00:00:00 TT
???
definitions to parallel greenwich
as far as I can tell, 1873 was an arbitrary epoch, couldn't find any significance
---
class: middle, center
# Coordinated Mars Time (MTC)
---
class: middle, center
# Coordinated Mars Time (MTC)
# aka Airy Mean Time (AMT)
---
# Calculating Coordinated Mars Time (MTC)
Start with current UTC date and time...
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | **2021-03-23T20:30:00 UTC**
???
Aside: almost exactly 2 years since last time I gave this presentation.
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | **2021-03-23T20:31:09.184 TT**
???
currently at 37 leap seconds
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | 2021-03-23T20:31:09.184 TT
Convert to TT Julian date | **2459297.35497**
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | 2021-03-23T20:31:09.184 TT
Convert to TT Julian date | 2459297.35497
Subtract 2451549.5 (JD of common epoch) | **7747.85497**
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | 2021-03-23T20:31:09.184 TT
Convert to TT Julian date | 2459297.35497
Subtract 2451549.5 (JD of common epoch) | 7747.85497
Divide by 1.0274912517 | **7540.555656**
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | 2021-03-23T20:31:09.184 TT
Convert to TT Julian date | 2459297.35497
Subtract 2451549.5 (JD of common epoch) | 7747.85497
Divide by 1.0274912517 | 7540.555656
Add 44796 (MJD of common epoch) | **52336.555656**
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | 2021-03-23T20:31:09.184 TT
Convert to TT Julian date | 2459297.35497
Subtract 2451549.5 (JD of common epoch) | 7747.85497
Divide by 1.0274912517 | 7540.55565
Add 44796 (MJD of common epoch) | 52336.55565
Subtract 0.0009626 (83.169s correction) | **52336.55469**
---
# Calculating Coordinated Mars Time (MTC)
Step | Example
:--- | --:
Current UTC datetime | 2021-03-23T20:30:00 UTC
Convert to TT datetime | 2021-03-23T20:31:09.184 TT
Convert to TT Julian date | 2459297.35497
Subtract 2451549.5 (JD of common epoch) | 7747.85497
Divide by 1.0274912517 | 7540.55565
Add 44796 (MJD of common epoch) | 52336.55565
Subtract 0.0009626 (83.169s correction) | 52336.55469
Convert MJD to datetime | **Sol 52337, 01:18:45 MTC**
---
class: center, middle
# 1:19am MTC!
---
class: center, middle
<img src="https://static1.squarespace.com/static/541bcb6be4b0ff8856437f90/t/5684a288df40f309608f2d62/1451533028048/party_emoji.png" width="300px" />
---
class: center, middle
# Ares Time Zone System
###http://www.aresastro.com/2016/03/ares-time-zone-system/
???
but of course, you can't talk about time without timezones
---
# What time is it for Curiosity?
<img src="https://www.spaceanswers.com/wp-content/uploads/2013/01/Curiosity-Power.jpg" width="500px" />
---
# What time is it for Curiosity?
- Landed: 4.6°S 137.4°E
---
# What time is it for Curiosity?
- Landed: 4.6°S 137.4°E
- AMT+9: Eastern Amenthean Time (EMT)
---
class: center, middle
<img src="https://www.spaceanswers.com/wp-content/uploads/2013/01/Curiosity-Power.jpg" width="500px" />
# 10:19am EMT
---
class: center, middle
<img src="https://www.spaceanswers.com/wp-content/uploads/2013/01/Curiosity-Power.jpg" width="500px" />
# 10:19am EMT
# 9:47am apparent solar time
???
but "sol 52337" is a bit unwieldy
what season is it even?
how about a calendar
---
class: center, middle
# Darian Calendar
### https://en.wikipedia.org/wiki/Darian_calendar
---
# Darian Calendar
- Epoch (day 1 of year 0) on March 11, 1609
???
in 1609:
kepler's published his work on planetary motion ("kepler's laws"); it used tycho brahe's observations of mars as an example
galileo made his first observations through telescopes, including of mars
---
# Darian Calendar
- Epoch (day 1 of year 0) on March 11, 1609
- Epoch is 94131 sols before MJD epoch
---
# Darian Calendar
- Epoch (day 1 of year 0) on March 11, 1609
- Epoch is 94131 sols before MJD epoch
- Epoch is on Martian vernal equinox
---
# Darian Calendar
- Epoch (day 1 of year 0) on March 11, 1609
- Epoch is 94131 sols before MJD epoch
- Epoch is on Martian vernal equinox
- 668 or 669 sols per year
---
# Darian Calendar
- Epoch (day 1 of year 0) on March 11, 1609
- Epoch is 94131 sols before MJD epoch
- Epoch is on Martian vernal equinox
- 668 or 669 sols per year
- Leap year mostly every other year
---
# Darian Calendar
- Epoch (day 1 of year 0) on March 11, 1609
- Epoch is 94131 sols before MJD epoch
- Epoch is on Martian vernal equinox
- 668 or 669 sols per year
- Leap year mostly every other year
- 24 months of about 28 days / month
---
# Current Darian Date
- 94131 + 52337 = 146468 sols since Darian epoch
---
# Current Darian Date
- 94131 + 52337 = 146468 sols since Darian epoch
- 66859 sols per century = 2 centuries 12750 sols
---
# Current Darian Date
- 94131 + 52337 = 146468 sols since Darian epoch
- 66859 sols per century = 2 centuries 12750 sols
- 6686 sols per decade = 21 decades 6064 sols
---
# Current Darian Date
- 94131 + 52337 = 146468 sols since Darian epoch
- 66859 sols per century = 2 centuries 12750 sols
- 6686 sols per decade = 21 decades 6064 sols
- 1337 sols per 2 years = 218 years 716 sols
---
# Current Darian Date
- 94131 + 52337 = 146468 sols since Darian epoch
- 66859 sols per century = 2 centuries 12750 sols
- 6686 sols per decade = 21 decades 6064 sols
- 1337 sols per 2 years = 218 years 716 sols
- 668 sols per non-leap year = 219 years 48 sols
---
# Current Darian Date
- 94131 + 52337 = 146468 sols since Darian epoch
- 66859 sols per century = 2 centuries 12750 sols
- 6686 sols per decade = 21 decades 6064 sols
- 1337 sols per 2 years = 218 years 716 sols
- 668 sols in non-leap year = 219 years 48 sols
- 28 sols per month = 219 years 1 month 20 sols
- 20th day of the 1st month of year 219
---
class: center, middle
# Sol Veneris, Sagittarius 20, 219 AE
<img src="http://ops-alaska.com/time/gangale_mst/month2a.gif" width="500px" />
???
a lovely early spring day
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