THE MISSING PLANET: A MYSTERIOUS NUMERICAL SEQUENCE aka TITIUS BODE LAW
Our solar system has always been an intriguing topic for humanity, probably because we consider
it as our home, our little place in the scaring immensity of the entire universe. Just think
about the names given to these eight bodies that together with us periodically revolve
around our bright star: except for the Earth, they all come from Roman Gods, arousing ancient
myths and adventurous stories. This is probably why during the Eighteenth
century the existence of a strange series of numbers which seemed to predict the positions
of our “neighbours planets” totally shocked the scientific community giving birth to hundreds
of different research works. And it doesn’t end here: these numbers also known as the
Titius Bode Law suggested the presence of a missing planet near us, a bit far away from
Mars. But wait a moment, what are we talking about?
What is this numerical sequence? And why is it linked with a possible new planet in our
system? Is this all true or it’s just a science fiction hoax? Stick with me and I’ll
tell you everything in a moment!
In order to answer all these questions we need to take a little step back moving directly
in the 18th century. At that time, scientists had only discovered five planets (different
from our earth) in the solar system: Mercury, Venus, Mars, Jupiter and Saturn.
At the same time, mathematicians were totally driven crazy by a strange sequence of numbers:
0,4-0,7-1-1,6-2,8-5,2-10-19,6. Apparently, it seems that there isn’t a
logic correlation between these numbers. However, we can make some little changes to discover
something very very interesting. Try to multiply the previous sequence for 10. We have: 4,
7, 10, 16, 28, 52, 100, 196. Now, let’s subtract 4. We obtain 0, 3, 6, 12, 24, 48,
96,192. Something can be surely said about this new
sequence. Have you noticed it? Except for the first two numbers, which seem to be randomly
chosen, all the other numbers are just twice the previous one.
This tricky sequence was studied by Johan Bode in 1772. Therefore, he wasn’t the first
one to deal with it. As a matter of fact, the same sequence was introduced by Johan
Titius in 1776. Consequently, these numbers are always mentioned as “the Titius-Bode
Law”. Even if it takes the name after these two scientists, the sequence was firstly discovered
at the beginning of the century by the Scottish mathematician David Grigory and re-elaborated
around the 20’s by the Polish philosopher Christian Wolff.
Wait a moment, we have understood how the Titius-Bode law originated, but what does
it state? What is it about? How is it linked to the possibility of a missing planet?
Let’s try to understand it step by step. Firstly, we must examine the original reasoning
of the scientists. Here are three different pieces that introduce the connection of the
sequence with planetary research. The first is taken by David Gregory’s “The
elements of astronomy” of 1915: "... supposing the distance of the Earth
from the Sun to be divided into ten equal Parts, of these the distance of Mercury will
be about four, of Venus seven, of Mars fifteen, of Jupiter fifty two, and that of Saturn ninety
five." This second one comes from Johan Titius:
“take notice of the distances of the planets from one another and recognize that almost
all are separated from one another in a proportion which matches their bodily magnitudes. Divide
the distance from the Sun to Saturn into 100 parts; then Mercury is separated by four such
parts from the Sun, Venus by 4+3=7 such parts, the Earth by 4+6=10, Mars by 4+12=16. But
notice that from Mars to Jupiter there comes a deviation from this so exact progression.
From Mars there follows a space of 4+24=28 such parts, but so far no planet was sighted
there. But should the Lord Architect have left that space empty? Not at all. Let us
therefore assume that this space without doubt belongs to the still undiscovered satellites
of Mars, let us also add that perhaps Jupiter still has around itself some smaller ones
which have not been sighted yet by any telescope. Next to this for us still unexplored space
there rises Jupiter's sphere of influence at 4+48=52 parts; and that of Saturn at 4+96=100
parts.” And finally, here’s the last one from Bode’s
"Manual for Knowing the Starry Sky" of 1772: “This latter point seems in particular to
follow from the astonishing relation which the known six planets observe in their distances
from the Sun. Let the distance from the Sun to Saturn be taken as 100, then Mercury is
separated by 4 such parts from the Sun. Venus is 4+3=7. The Earth 4+6=10. Mars 4+12=16.
Now comes a gap in this so orderly progression. After Mars there follows a space of 4+24=28
parts, in which no planet has yet been seen. Can one believe that the Founder of the universe
had left this space empty? Certainly not. From here we come to the distance of Jupiter
by 4+48=52 parts, and finally to that of Saturn by 4+96=100 parts.”
We can easily understand that the sequence was like a representation of the astronomical
distances between the sun and the planets of our Solar System.
Therefore, something doesn’t seem to be right, since the distances of the six known
objects from our Star, measured in Kilometers, were very different from the first sequence
I mentioned. How can we show the relation between this mysterious law and our planets?
It’s quite easy, we just need to change units of measure. In Astronomy it’s very
common to talk about distances relatively to the Astronomical Unit A.U. or U.A. (the
distance between sun and earth), which is nearly 150 million km or 8 minutes at the
speed of light. If we show the distance of planets from the sun expressed in A.U. we
can surprisingly find an almost perfect correlation with the Titius Bode Law (all measures are
obviously approximated) Mercury 0,4 AU
Venus 0,7 AU Earth 1 AU
Mars 1.5/1.6 AU Jupiter 5.2 AU
Saturn 10 AU They align on the first sequence we mentioned,
but something seems to be wrong. There isn’t correspondence for the 2,8 AU distance. What
was scientists’ first question? Is there any missing planet between Mars and Jupiter?
Or is the law just wrong? "Before finding out more about this, be sure
to like or dislike the video so that we can continue to improve and make these videos
better for you the viewer. Plus, be sure to subscribe to the channel clicking the bell
so that you don't miss ANY of our weekly videos." Surely, the scientific community started to
point its telescopes in that region in the sky, but surprisingly in 1781 William Herschel
discovered Uranus at a totally different (but not random) distance: 19,6 AU. This is the
next number of the sequence we are dealing with: the possibility of the law to be correct
quickly grew and everyone started searching for the “missing planet”.
In the February of 1801 Giuseppe Piazzi, an Italian astronomer working in Palermo, observed
a planet precisely at 2.8 AU from the Sun. He gave it the name Ceres, the ancient goddess
of Sicily. All the scientific community was extremely excited due to this discovery.
During 1802, while observing the eighth planet of the solar system Ceres, the astronomer
Heinrich Olbers underwent a strange and unpredictable event: he observed anther object passing in
front of Ceres and he gave it the name Pallas. He was initially shocked by this coincidence,
but then he tried to furnish a proper explanation of the phenomenon.
Olbers proposed that these Ceres and Pallas were the fragments of a disrupted planet that
had formerly orbited the Sun, and predicted that more of these pieces would be found.
The discovery of the asteroid Juno by Karl Ludwig Harding and Vesta by Olbers, buttressed
his hypothesis. Thoughts regarding the formation of the asteroid belt from the destruction
of a hypothetical fifth planet are today collectively referred to as "the disruption
theory". This hypothesis states that there was once a major planetary member of the Solar
System circulating in the present gap between Mars and Jupiter, which was destroyed by one
or more of the following hypothetical processes: (1) it was struck by another large celestial
body,(2) it was destroyed by a hypothetical brown dwarf, (3) it veered too close to Jupiter
and was torn apart by its powerful tides or (4)it was shattered by some internal catastrophe.
This hypothetical destroyed planet took the name “Phaeton”, but this theory was superseded
by more advanced models. Later on in time, more and more objects were
observed in the region of 2.8 AU: Hebe, Iris, Flora, Metis and Igea. What were all these
rocks orbiting in the area of the famous “missing planet”? Before trying to state whether
the Titius Bode Law had a rigorous scientific foundation or not, scientists started to catalogue
all these objects. The majority of them took the name from Herschel’s definition “asteroid”,
which literally means “an object that can easily be confused with a star”.
What is an asteroid made of? Its composition is nearly the same of the Earth, but the size
is very small. For an example, imagine that the average diameter of an asteroid (which
is only rarely spherical) is less than one kilometer. Nowadays, the general belief is
that asteroids are the parts of a protoplanetary disk (a structure that often occurs in the
formation of a planet) that have failed to be attracted to the major body of the object.
As a matter of fact, this theory explains why the composition of an asteroid is really
similar to that of a planet and why we can see volcanic phenomena or water on asteroids.
This definition turned to be important in further astronomic researches and observations;
imagine that we have observed and catalogued more than 600000 different asteroids just
in our solar system and the actual predictions say that more than one million are to be discovered.
However, not all the objects discovered at the beginning of 19th century were catalogued
as asteroids. As a matter of fact, the first one, Ceres, is actually known as a dwarf planet
similarly to Pluto, considered for 76 years as the ninth planet of the solar system. Dwarf
planets have all the same characteristics of a normal planet, but their orbit is full
of detritus and they don’t have enough gravitational force to gather all these rocks in a single
object. But why there isn’t a planet between Mars
and Saturn? Why the formation of an object similar to the earth failed? Different theories
have been elaborated, but the major one says that is probably the enormous gravitational
attraction of Jupiter that has opposed to the accretion of materials around 2.8 UA.
We have gone through a long journey in the history of planetary observations, but we
need to answer just one last question: why does the Titius Bode law work? The majority
would say that it can’t be a coincidence that all planets are aligned according to
that sequence, but this is surprisingly wrong. Today we have understood that the Titius-Bode
law is not correct, it doesn’t have a proper mathematical and physical foundation. The
parameters of distance of Neptune and of the satellites of Jupiter and Saturn were totally
independent from the predictions made by the sequence. As a matter of fact, various scientific
journals have started to refuse articles that claim to have proved the correctness of this
law. The only thing that we can say is that in
some cases, given some particular parameters, a star system has a strong probability of
originating according to the Titius-Bode Law distances.
Some tests have been made on the positions of 68 different exoplanet systems and the
results showed that they follow a generalized Titius-Bode Law elaborated by Bovaird and
Lineweaver with a greater precision than our solar system. Although this theory is not
so rigorous, sometimes it has been useful to predict the positions of some exoplanets!
"This video ends here! Thanks for watching everyone! Did you find this topic exciting?
Are you amazed by the search for a “missing planet” in our Solar System which took place
around the first years of the nineteenth century? Are you excited by the different theories
about the origin of asteroids? Have you ever heard about “Phaeton” before? Is there
anything more you want to hear about the Titus Bode Law? Let me know in the comments below,
be sure to subscribe, and I'll see you next time on the channel!"