AstroNotes September 2019

Editor’s Message . Ottawa Skies . Johannes Kepler . Estelle's Pick of the Month . Monthly Challenge Objects . Carp Star Parties . FLO Star Parties . Next Meeting . Centre Information .

Volume: 

58

Number: 

8

Pages: 

43

Download PDF version: 

AstroNotes

The Newsletter of the Ottawa Centre, RASC

Volume 58 – No. 8 – September 2019

Editor’s Message

I would like to open this issue with a very special message. On behalf of the
Ottawa Centre, I would like to congratulate Oscar and his wife Katherine on the
arrival of their daughter, Isabella, who was born August 14 th . I am told all are
doing well. Welcome to the world Isabella. We look forward to seeing you at a
meeting very soon. Oscar and Katherine, we are very happy for you.

This month’s issue is a little bit longer than most. We were able to convince Bob
Olson to share his presentation on Kepler with us. As well as being a very
interesting and well written article, it has, appropriately, an astronomical number
of photos and images with it. And of course, we have all our regular features.

Over the Labour Day weekend, we held what I hope will become an annual event. In conjunction with
the members star party at the FLO, we had a Family Day/BBQ. We had a good turn out and everyone
enjoyed the socializing. Although the afternoon had been cloudy and didn’t look promising, Attilla had
assured us on the Clear Sky Chart that the sky would clear in the early evening and it did. The sky for
the star party was (mostly) very nice and a good time was had by all.
One thing that is missing from this issue is Submitted Images. Please remember that we love to publish
your images, sketches or photographs. We want to see what you are observing. It is always nice to have
images of the previous Challenge Objects as well. I hope to see lots of submissions over the coming
months. We also welcome Letters to the Editor and full-blown articles. If there is an article you would
like to see, send us your idea even if you don’t feel up to writing it. We will see what we can do.

Clear Skies,
Gordon
astronotes@ottawa.rasc.caAstroNotes


Ottawa Skies

By Dave Chisholm

Full moon on September 14

Mercury
Not Visible
Rise/Set 06:09/19:41 -> 08:45/19:15

Venus
Visible just before sunset.
Rise/Set 06:51/19:54 -> 08:08/19:12

Mars
Not Visible
Rise/Set 06:27/19:42-> 06:11/18:26

Jupiter
Visible first part of evening.
Rise/Set 14:53/23:35 -> 13:14/21:52

Saturn
Visible through the evening.
Rise/Set 19:06/03:52 -> 15:05/23:45

Uranus
Visible late evening to sunrise.
Rise/Set 21:41/11:31 -> 19:45/09:33

Neptune
Visible late evening to sunrise.
Rise/Set 19:59/07:12 -> 18:03/05:14


Johannes Kepler

by Bob Olson

When I was teaching physics, Kepler’s work was an obvious and important part of my courses as he was
one of the giants that physics was based on. But I must admit that I tended to trivialize his work as he
seemed to pull his theories out of thin air. He had great theories, but I doubted that he actually knew
what they meant.

Then a friend of mine loaned me two books that he had bought while visiting the Royal Museum in
London England. The author, Nicolas Mee, received his PhD in theoretical particle physics from the
University of Cambridge and is a fellow of the Royal Astronomical Society. The books, “Higgs Force”
and “Gravity”, treated Kepler in a much more complementary way. This rekindled my interest in Kepler
and I did some more reading about him .

It is impossible to talk about Kepler without starting by mentioning a few other scientists first.
Nicholas Copernicus was a Polish astronomer and cleric born in 1473.

The model of the solar system that was in general use at that time was developed by Ptolemy. The earth
was at the centre and everything rotated around it. Thus, the name geocentric. As you can see, it sure
was a mess and many scientists and astronomers were suspicious that anything this complicated was
probably incorrect.

Sometime around 1514 Copernicus published a model of the solar system that had the planets rotating
around the sun. This manuscript was circulated amongst Europe’s leading intellectuals, but Copernicus
was hesitant about publishing it. Sometime about 20 years later, he developed a manuscript that more
completely described his model. Despite encouragement from his friends, he did not publish this
manuscript until he was on his deathbed in 1543, 11 years later.

The Lutheran preacher who had taken over the task of supervising the printing and publication in an
effort to reduce the controversial impact of the book added his own unsigned note which stated that
Copernicus' system was mathematics intended to aid computation and not an attempt to declare literal
truth.

The Copernicus model did not accurately predict the motion of the planets but putting the sun at the
centre was a giant stride ahead. This system is called heliocentric or sun centered.

Giordana Bruno (1548-1600)

Copernicus’ caution was not unwarranted. Our friend here, Bruno, took Copernicus’ ideas to their
obvious conclusion and declared that the sun was just one of many stars and that the other stars had their
own planetary systems which were probably the homes of other civilizations. He travelled all over
Europe promoting these ideas and on his return to Venice in 1592 he was arrested and turned over to the
Roman Inquisition. In 1600, after an 8-year trial, he was burned at the stake. To be clear, he was not
burnt for proclaiming the earth rotated around the sun, but that there were many other civilizations.
Tycho was Danish royalty born in 1546. His father and other close relatives were in the tier of
government just below King Frederick. When Tycho was one year old he was kidnapped by his uncle
and raised as his own child. Apparently, he had a deal with Tycho’s father that he would adopt Tycho as
soon as a second child was born. Tycho’s uncle Jorgen was a great sea captain and Vice Admiral of the
Danish Navy. Jorgen once saved the King from drowning when the King fell from his horse into the
water after a night of drinking. This might explain the enormous generosity that he later showed to
Tycho.

At age 16, Tycho observed a conjunction of Jupiter and Saturn and when he checked the almanacs, they
were out by a whole month. He realized that astronomy needed an overhaul and that systematic
measurements taken over a long period would be required to do this. At age 19 when his uncle died,
Tycho inherited enough money to provide him the funds to undertake this immense task.

Tycho could be cranky and unpleasant. He was also a heavy drinker. When he was a young man, he
fought a drunken duel with his cousin. His cousin lopped off Tycho’s nose so Tycho had a fake nose
made which he attached to his face with glue. It was reported that for special occasions the nose was
gold and for ordinary use, it was a silver one. We now have evidence that it was in fact made of bronze.
When talking to my students about Tycho, I called him the man with the tin nose. Tycho and his cousin
made up and were friends for the rest of their lives.

In 1576, when Tycho was 20 years old, the king granted him the island of Hven which he could use for
an observatory and as a source of income. At this time Denmark had possession of Southern Sweden so
this island is now in Sweden. My ancestors were from Sweden, so I must assume that I am related to
Tycho.

This is a wider angle so you can see the location compared to other countries.
Notice Prague which is where Tycho ended up.

This was the house that Tycho built on his island. He entertained many famous people here including
King James VI before he was king of England. James had married a Danish Princess and was visiting
Denmark when he took shelter from a storm on the island. Shakespeare’s play, The Tempest, was
reportedly about this visit.

This is his observatory on the island.

Tycho carefully studied all possible errors and tried to eliminate them. He decided that he could get
more consistent measurements if his observatory was underground out of the wind and away from
vibrations.

This is a painting of Tycho in front of a painting of Tycho! The background mural shows Tycho
pointing at the slot in the observatory wall where the target would be in the sky and the foreground
painting is Tycho sighting the target while his assistants report the time and record the results. His
measurements were accurate to within 1 or 2 minutes. His average error was 1/30 to 1/60 of a degree.

In 1597 Tycho left Denmark and headed to Prague. The king had died, and the new king was not a fan
of Tycho. Tycho was hired to be the Imperial Mathematician for the Holy Roman Emperor.

His planetary model made the earth the center, but the planets rotated around the sun. This would have
made calculating orbits a nightmare.

Tycho was a great experimenter but not such a great theorist or mathematician. He needed help putting
his data into tables for publication and he wanted to calculate the orbit of Mars.
This worked out perfectly for both Kepler (shown here) and Tycho. Tycho needed a mathematician and

Kepler’s father was a mercenary and headed off when Kepler was 5 and never returned. It is believed
that he was killed in the 80-years war in the Netherlands. His Mother was a healer and herbalist. Kepler
was born prematurely and was weak and sickly but showed an aptitude for math as a child. They lived in
a tavern owned by his grandfather. He attended seminary school at age 13 and went to university at age
17. At age 26, in 1596 he was hired to teach mathematics in Graz. This same year he published
Cosmographic Mystery which was a defense of the Copernican system. (Which was Sun centered)
In 1596, when he was 25-years old, he was introduced to Barbara Muller, a 23-year-old twice widowed
woman. She was heiress to her late husband’s estates and her father was a wealthy mill owner. Her
father objected but Kepler’s nobility (inherited from his grandfather who was a mayor) and the
publication of Cosmographic Mystery changed his mind. Barbara and Johannes were married in 1597.
This map shows the locations that Kepler ended up in during his life. He was born in Wurttemberg in
1571 and died in Regensburg 61 years later in 1630. In between, he moved for education, employment,
and to avoid religious persecution. Kepler was Lutheran and Germany was Catholic and Lutheran.
During the last 12 years of his life Germany was embroiled in the 30 years War which managed to kill 8
million people in Europe.

He seemed to get fixated on shapes and sizes and how they related to the heavens. This cup with weird
shapes inside of it was supposed to represent the orbits of the planets.
These are random attempts at finding relationships between earthly things and the heavens. This was a
very Kepler thing to do.

Kepler was a teacher, a mathematician, and an astronomer. But he earned a significant part of his
income as an astrologer. I have such a bias against astrology that it coloured my opinion of Kepler. He
drew up over 800 horoscopes for the rich and famous. He also published annual almanacs for 30 years.
These were similar to today’s Farmer’s Almanacs. I think he honestly felt that the position of the planets
when a baby was born could affect that baby’s future.
Astrology clearly paid well as his job at this time was teacher of mathematics.

When he lived here, he was District mathematician for the city.
Two years earlier, his wife, Barbara, died of Hungarian spotted fever. And his son died of smallpox. In
1613, he remarried.
In his late 20s, Kepler realized that he needed better data if he wanted any hope of figuring out what the
planets were doing. This meant heading to the man with the tin nose. In 1600 Kepler headed to Prague
where he was employed by Tycho to calculate the orbit of Mars.

This statue of Tycho and Kepler demonstrates how these two men are forever tied together in history.
21AstroNotes

When he was hired, Kepler bragged that he could calculate the orbit in eight days. One of the least
endearing characteristics of Tycho was that he hoarded his data. He released it on an as needed basis.
Kepler found this very frustrating.
And then everything changed. After a little more than a year of working for Tycho, Tycho died.
And even in death Tycho was dramatic. He attended a banquet hosted by Baron Rosenberg. As was
usual, Tycho consumed large quantities of food and drink but etiquette at the time meant he could not

leave to use the toilet while his host was still at the table. By the time he reached home, he couldn’t
urinate at all. He died 11 days later.

His death was so unusual that there was a suspicion that he had been murdered. He was a rather mean-
spirited man so there were many suspects, Kepler being one of them. In 1901, exactly 300 years after
Tycho’s death, his tomb in Prague was opened and his bones examined. The skull showed the wound
from the dueling sword and the greenish tinge on his skin from the copper nose. In 1990s, some of his
beard was examined and the hair was found to contain mercury. But Tycho dabbled in alchemy so
exposure to mercury was to be expected. In 2010, his body was re-exhumed and examined using modern
techniques. It was decided that the probable cause of death was obesity, diabetes and alcoholism.
Almost immediately Kepler was named the new imperial mathematician by Emperor Rudolf. Kepler
grabbed Tycho’s chest of data and started work on trying to decipher it.

You have to understand the enormity of this task. We are standing on a spinning planet that is flying
around the sun on some unknown path. And the math to do the work has not been yet developed.
Algebra was in its infancy. Coordinate geometry was not yet invented, and calculus did not exist.
Kepler did have basic arithmetic, a little trigonometry and classical geometry.
The first problem that Kepler had to deal with was the position of the sun. The sun does not go overhead
at the same speed every day. Sometimes the earth is closer to the sun and goes faster. The spin of the
earth on its axis is very regular. This fact was known by the ancients, so they created something called
the mean sun. Copernicus had placed the mean sun at the centre of the solar system. Kepler replaced it
with the true sun. This was a big step.

This drawing shows a ridiculous exaggeration of the effect. There are many ways to think of this, but
one is that as the earth falls closer to the sun it gains speed. Another is to realize that gravity is greater
closer to the sun so if you don’t go faster, you will fall into the sun.
Kepler also realized that the orbits were slightly tipped and that the sun was in the plane of each one of
them. This is called Kepler’s zero law.

Kepler needed some way to simplify the problem. He decided to only use the position of Mars when it
was in opposition to earth. That is a line from the sun through Earth hits Mars. Or when the sun sets,
Mars rises. He was able to find 10 examples in Tycho’s data and 2 more taken after Tycho’s death for a
total of 12. He started with 4 and when he got a circular orbit that fit these 4, he then added in the next 8.
He kept at this until he got an orbit that fit all 12 within 2 minutes of error. He did this without the
benefit of computers or calculators. It must have been a brutal task. He was successful on his 70 th try.

Then he plugged in the positions of Mars when not in opposition to check the orbit. Now the error
jumped to 8 minutes. Kepler knew that Tycho would never have made an error this big. He had to start
all over .

I mentioned earlier that Tycho was standing on a spinning earth as it raced around the sun while making
these observations. The problem that Kepler had was that he didn’t actually know the path of the earth
around the sun. So, he had to calculate that first.

Imagine that you are in a car driving in the fog at night. You come to a telephone pole. You know the
location of the pole relative to the car but still have no idea where the pole is on the earth. That was the
problem that Kepler had with the Earth and Mars.
Again, he needed to simplify the problem.

It takes Mars 687 days to circle the sun. If Kepler could find measurements of the sun and Mars made at
intervals of exactly 687 days, he could find the angle between the sun and Mars and calculate the orbit
of Earth. Lucky that Tycho had spent 36 years doing just that. This was just like calculating the aspects
for an astrological chart and this was what Kepler did for money! I guess being an astrologer can pay
off.

Once he had the orbit of Earth figured he used that to correct his earlier calculations and realized the
orbit of Mars was egg shaped.
It took Kepler a while to realize that is egg shaped orbit was actually an ellipse. Once he had that, the
rest was pretty easy. At least, relatively easy.
That the planets follow an elliptical orbit with the sun at one of the focuses is Kepler’s first law.
Once you know this, it is easy to figure out an orbit with just a few sightings as we know the formula of
an ellipse.

All those of you who did not sleep through high school algebra will remember that circles, ellipses,
parabolas and hyperbolas are conics.
Do you know why the focus of the ellipse is called a focus? It is because a candle held at one focus of an
ellipse shaped mirror will focus the light at the other focus.

Kepler realized that the planets were travelling faster nearer the sun and he was able to figure a method
to calculate this using the area swept out by a radius. On the picture the blue areas are the same size and
each takes one month. This is a consequence of conservation of angular momentum. Kind of like when a
whirling figure skater pulls their arms in and spins faster.
I’m not sure if it’s a fluke that Kepler chose Mars, but it’s lucky he did.

Lucky Mars
Mercury too close to sun (No Data)
Venus is almost a circle
Jupiter and Saturn take too long to orbit Sun
And would take several lifetimes to collect enough data.

Kepler was obsessed with finding a relationship that would explain the motion of the planets. He knew
the motion but what was the relationship? He attempted different answers for 10 years before he came
up with his third law. Apparently, he was working on music theory when this idea popped into his head.

The Period squared is proportional to Radius cubed can be written as an equality if you insert a constant.
If the units that you use are years and the radius is the distance between the earth and the sun (which we
call an astronomical unit), k becomes 1. If you rearrange the equation to solve for radius, you can easily
find the orbit distance of anything circling the sun in astronomical units. Unfortunately, Kepler did not
know the distance between the sun and the earth.

Before I go to the next section I need to talk about mass. Let’s take this brick as an example. It has mass.
What exactly does that mean? It turns out that mass has 2 important properties. First, it is attracted to
other masses. As an example, this brick is attracted by the earth and, if it had twice the mass, it would be
attracted two times as much. This is called gravitational mass.

Another property of mass is that is it doesn’t like to change motion. That is, it has inertia. If this brick is
flying through the air, it will keep flying in a straight line until you push on it.
In this case with my head. What would happen if we were in outer space, far away from any other big
mass? This brick would weigh less than a feather, less than a balloon. If a feather or a balloon hit your
head, you might not even notice it. So, what would happen in outer space if this brick hit your head? Its
mass has not changed so you would have to apply exactly the same force to the brick to stop it or change
its direction. The brick would hurt exactly the same in space as on earth. This is called inertial mass.

We don’t have a good fix on the connection between inertial and gravitational mass but they seem to be
exactly the same. In fact, Einstein said that every time we measure inertial and gravitational mass, they
are the same, so thus they must be the same. He used this in his theory of relativity.
Inertial and gravitational mass are calculated differently so we can equate them to solve problems.
I often get asked why the moon does not fall on us. The real question is why does the moon not fly off.
Here is a picture of a planet circling the sun. The planet actually wants to travel in a straight line heading
into outer space. For it to travel in a circle, we need to apply a force to it and since we know its inertial
mass, we can calculate the force using the formula shown. This is the force we need to apply to a planet
to bend its path. But what is applying that force? We know that it is gravity, but nobody else did until
Isaac Newton.

This is the formula that Isaac Newton came up with that describes the effect of gravity on planets and
the sun. It is the universal law of gravitation. If we equate the force needed to overcome inertia to the
force of gravity which is bending the path, we get this formula. As you can see, it leads to Kepler’s third
law. But this was derived using physics not pulled out of a hat.

Does Kepler’s third law work? It was a spectacular success. Here is a chart showing the value of k for
objects orbiting the earth, the sun and Jupiter. If you read the last column, you can see that ratio is the
same for each central object. The Earth row only shows the moon, but we would get the same value for
anything orbiting the earth.

This is a statue of Kepler’s mother Kathrina. In 1620, at the age of 73, she was accused of being a witch.
This was no trivial matter as something around 50,000 people were executed for being witches. 25,000
of those were German. One of the problems Kepler’s family had was that if she was convicted, it would
taint all of their reputations. Kepler took a leave of absence from work to defend his mother. His pointed
and scientific defense resulted in her being acquitted in 1621. But the ordeal was so traumatic that she
died six months later. Kepler never told his employers nor his friends where he had been during this
time.

Kepler was born in an era where there was no clear difference between astronomy, mathematics and
astrology, but physics was different! Kepler brought astronomy into physics. He called it celestial
physics.

Isaac Newton was probably the greatest scientist who ever lived. Every problem that he attacked, he
solved. However, the laws of planetary motion that Kepler discovered would play a decisive role in
enabling Newton to discover his laws of motion and his universal law of gravitation.
Kepler managed to get his Rudolphine Tables published in 1627, but by now he was unemployed and
the new Emperor wouldn’t pay him his back wages. Kepler died in Regensburg in 1630. This is his
epitaph. His gravesite was lost when it was destroyed by rampaging Swedish soldiers two years later. As
I mentioned earlier, my heritage is Swedish. But seriously, when you attack a city, why would you
pillage a graveyard?


Estelle’s Pick of the Month


Monthly Challenge Objects


Announcements

Carp Star Parties

Paul Sadler and his team continue to work hard to be sure the Public Star Parties run smoothly. They
have been doing a great job and getting good turn outs. If you haven’t been to one lately, grab your
scope and join them. You are bound to have a good time. As always, these are weather dependent and
subject to change.

Saturday May 25 th – Star Party at the Carp Public Library / Diefenbunker
Rain Date - Friday May 31 st
Saturday June 22 nd – Star Party at the Carp Public Library / Diefenbunker
Rain Date - Friday June 28 th A Success!
Saturday July 27 th – Star Party at the Carp Public Library / Diefenbunker - Yes but...
Rain Date - Friday August 2 nd - Much better night
Saturday August 24 th – Star Party at the Carp Public Library / Diefenbunker
Rain Date - Friday August 30 th Another success!
Saturday September 21 st – Star Party at the Carp Public Library / Diefenbunker
Rain Date - Friday September 27 th
Saturday September 28 th – Star Party at the Astropontiac site in Luskville
No Rain Date
Friday October 18 th – Star Party at the Carp Public Library / Diefenbunker
No Rain Date
Other Dates of Interest
Saturday October 5 th – International Astronomy Day (Fall) at the Canada Aviation and Space
Museum, part of World Space Week.

FLO Star Party Dates for 2019

Our Ottawa Centre’s Members’ Star Parties at the FLO will continue this summer. If you
haven’t attended before, be sure to mark at least one of these dates on your calendar. You are
welcome to bring family members or a guest.

SUMMER & FALL DATES

May 4 – New Moon
Good turn-out, great night
June 1 – Waning Crescent Moon, 3.8% illumination No Go
July 6 – Waxing Crescent Moon, 19.7% illumination, sets 11:53P.M. NO GO
August 3 – Waxing Crescent Moon, 2 days old, sets 9:51 P.M. – moved to August 4 th Good
turnout
August 31 – Waxing Crescent Moon, 2.4% illumination - Family Day BBQ, Great turn out
Sept 28 – New Moon
October 26 – Waning Crescent Moon, 3.5% illumination

Next Meeting

7:30 PM Friday September 6, 2019 at the Canada Aviation and Space Museum (directions). Note
there is a $4.00 parking fee for museum parking. The meeting runs until 9:30 pm
PLUS: all our regular meeting features: Ottawa Skies, 10-minute Astronomy News Update, Observation
Reports and, of course, the beloved Door Prizes!

All RASC monthly meetings are free and open to members and non-members alike. Refreshments will
be available and this will be a wonderful opportunity to meet new friends who share a common interest
and chat in a relaxed, stimulating and fun environment. Please join us!


Centre Information

To subscribe (or unsubscribe) to our members-only discussion list (rascottawa@googlegroups.com )
please contact secretary@ottawa.rasc.ca .

The Ottawa Centre 2018 Council

President: Mike Moghadam (president@ottawa.rasc.ca)
Vice President: Stephen Nourse
Secretary: Chris Teron (secretary@ottawa.rasc.ca)
Treasurer: Oscar Echeverri (treasurer@ottawa.rasc.ca)
Centre Meeting Chair: Oscar Echeverri (meetingchair@ottawa.rasc.ca)
Councillors: Carmen Rush, Gerry Shewan, Jim Sofia
National Council Representatives: Karen Finstad, Ingrid de Buda
Past President: Tim Cole

2018 Appointed Positions

Membership: Art Fraser
Star Parties: Paul Sadler
Fred Lossing Observatory: Rick Scholes (flo@ottawa.rasc.ca)
Light Pollution Abatement: OPEN
Public Outreach Coordinator: OPEN
Hospitality: Art & Anne Fraser
Stan Mott Astronomy Library: Estelle Rother
Ted Bean Telescope Library: Darren Weatherall
Webmaster: Mick Wilson (webmaster@ottawa.rasc.ca)