Very important investigation for us, the Stardust Mission.

This diagram was first mentioned in the Getting Started Fall 2019 video in YouTube!

Sneak preview on syllabus is related to this analysis. Study both. Acceleration

Homework 3, eccentricity calculations

This is a horrible sentence.

When a scientist deals with huge numbers, as in astronomy, it is sometimes "close enough" if they have the same power of 10 in scientific notation.

1. Mars polar cap \(= 1.00 \times 10^{15}\, \text{tons}\)
2. Greenland ice cap \(2.85 \times 10^{15}\, \text{tons}\)

So a better sentence would be this: \(\text{\color{blue}The mass of frozen water in the Mars polar cap }\)\(\text{\color{blue}is of the same order as the Greenland ice cap}.\)

One commonly hears egghead scientists saying that two quantities "are about the same order," and by that they mean the two quantities are righteous and equivalent.

Small but mighty, the good and faithful rovers that have sent us so much data about Mars.

Using \(\pi r^2\) for the area here is an underestimation, because \(\pi r^2\) is good for a flat circle, but the polar cap is not flat! It is curvature.

However, using \(\pi r^2\) is

1. easy
2. and close enough

But the Viking landers still gave us a lot of good data on Mars.

We know this by looking for and measuring the infrared spectra of both \(H_2 O\) and \(CO_2\)

Cf., the famous Martian meteorite, ALH-84001.

Our pre-occupation with Mars, e.g., The War of the Worlds.

Astronomers' preoccupation with \(H_2 O\)

Sublimation. Good comparison to what \(CO_2\) ice does here at the surface of Earth.

Standard 1.00 atmosphere of pressure on Earth = 1.01325 bars, or, as they say on the Weather Channel, 1013.25 millibars. This is the atmospheric pressure on a day of fair weather at sea level. A similar fair day in Denver, one mile altitude, would be less than 1013.25 millibars.

Mars atmospheric pressure is 0.007 bar or 7 millibars.

For comparison: The central pressure of a hurricane is considered extremely dangerous if it gets to 900 millibars. E.g., Hurricane Irma hit the Florida Keys in 2017 at Category 4, 929 millibars central pressure. Very violent.

Nice estimate based on cratering rate. SO... it has been a long time since Mars has had a wet climate.

We would consider the dust clouds of Mars or of Earth (like in the Sahara) as different from the \(H_2 O\) clouds, which are microdroplets of liquid water held aloft by rising air currents.

Mysterious. Scientists definitely want to figure this out, if we are ever to colonize Mars

Compared to the Amazon River, this is shrimpy. The widest point of the Amazon is about 64 km.

$$e=\sqrt{1-\frac{b^2}{a^2}}$$

"...based on their paths." This is bass ackward relative to, e.g., Ptolemy. For Ptolemy, he based everything on circles and forced everything into a complex system involving epicycles, deferents, equants etc. To some degree, Copernicus and Galileo were also stuck thinking "circles." Kepler, however, took the path that Nature showed him in Tycho's measurements -- especially Mars' ellipse -- and then figured out a pattern from that. And he figured out three patterns, actually.

Observations can be refined but not ignored or contradicted!

We now leverage Kepler's Third Law to use in any star system for which we can measure orbital distance, e.g., by parallax, and orbital periods. Black holes, which we cannot see, can reveal themselves in this way.

Still a great university in Germany!!

Technical definition of ellipse, sounds rough... HOWEVER, it is the reason that the string method in Fig. 3 works. The length of the string is "always the same," if you are careful.

A supernova, 1572. Cf., APOD 03/17/09

Pluto the dwarf planet has a semimajor axis about 39.482 AU. Its orbital period is about 248 years

What a career-length project!

This shows the slowness of scientific development in those days.

There are objects that pass through the solar system on parabolic and hyperbolic orbits, such as the mysterious A/2017 U1 'Oumuamua (YouTube of its trajectory)

Correct. Comets and asteroids, however, do commonly have ellipticity of this level or more.

Cf.,"pin and string method" on YouTube.<br />

A huge topic for us this entire semester.

The scientific end of the celestial spheres, although celestial sphere is still a lovely image outside of science. : )

Good to keep in mind: a circle is just a specially symmetric case of an ellipse, \(e=0\)

Because even Mars is so close to a perfect circle, it has always amazed me that Kepler spotted it.

As previously stated, Kepler's Third Law is EVERYWHERE!!!!

: )

Scientists must always be humble about their findings

E.g., a comet really moving fast at perihelion and slowing down at aphelion. E.g., Uranus and Neptune. Nearly the same mass, but orbital semimajor axes 19.2 AU for Uranus and 30 AU for Neptune; their orbital "years" are 84 years for Uranus but 164 years for Neptune.

Physicists are always making assumptions like this, spherical galaxy, spherical planet, spherical this, spherical that. There is even a nerdish physics joke for which the punch line is, "Consider a spherical cow."

Physics humor. :\

Anyway, physicists do this to make things easier at the start, then they make more detailed, intricate models, as things progress

Yeah, what they SHOULD do.... ain't necessarily so.

...the sign of "dark matter"

TWENTY TIMES!!!! Holy Toledo! Visible matter is like a drip from a Slurpee!

This would be like Neptune orbiting faster than Earth!!!

Galactic rotation curves fail, which is the sign of dark matter.

There is a ton of fancy calculus behind the blue part of the graph. So the theory literally falls short of observations (red)

Astronomers were reluctant to accept this, but it is now undeniable.

Gravitational lensing

Like the absorption features of the Sun, various colors picked out by the upper layers of the chromosphere and very hot atmosphere of the sun.

Sir Isaac Newton figured out why this is true, in his theory of universal gravitation -- which is a few chapters ahead.

Symmetry is a powerful tool, because it is not subjective -- it can be expressed mathematically. E.g., the symmetry of positive and negative numbers relative to zero, whereby \(\left( -2 \right)^2 = \left( 2\right)^2\) and both \(=4\)

but not at UCF, of course!! ;)

Cool animations!

It was left to Johannes Kepler to break this concept.

Good description, in a nutshell, for Copernicus' contribution

YES! This is what scientists want to do: predict the position of a previously unseen planet like Neptune, predict the landing place of a spacecraft sent to Mars, etc.

I.e., Galileo's famous experiment at the leaning tower of Pisa! .JPG)

One short sentence, but powerful. Thank you, Professor Kepler!

Bypass this calculation until end of the semester.

Main source of forces and motion = convection. Huge blobs of molten lava convect from core to surface, like water boiling in a pot on the stove or a thunderstorm convecting water vapor and liquid water in the atmosphere.

Unlike some moons and planets which are geologically dead. Good example of dead geologically is our moon.

Consider, for example, the layers of sedimentary rocks in the Grand Canyon.

Another example: the Himalayas. They formed when the subcontinent of India bashed northward into Eurasia.

Convection!!

Yup -- asteroids and comets are chunks of history going all the way back.

or pinkish up in Georgia!!!!

We will have a lot to say about Io.

There are tons of volcanoes in the solar system. The largest volcano we know of is on Mars!!

Hmmmm...

Or, more simply, read it off the diagram.

There is a legend about this, that this relation came to Hubble as he drove down to Pasadena after a night's observing. He pulled his car over on the shoulder and stopped to think. It is a twisty mountain road; I have driven it myself. At some time later, hours later as the legend goes, a traffic cop pulled alongside to check him out. All was well -- he was just thinking of what it all meant, that the entire universe was expanding. Edwin Hubble was probably very late for his breakfast, and we still ponder this meaning today.

Hubble figured it out.

They were especially looking at the near-ultraviolet H and K lines of calcium, $$\lambda_H=396.8\:nm\longrightarrow\text{toward red, longer wavelengths}$$

$$\lambda_K=393.4\:nm\longrightarrow\text{also toward red, longer wavelengths}$$

Here is an image of the sun in a filter that only transmits the Ca K line, very purply blue.

So a galaxy's K line will be less purply blue, maybe an aqua blue or even green... i.e., shifted toward the red end of the Roy G. Biv spectrum

Yes, definitely handy, because if we make a big telescope we can see and catch spectra of really distant, faint galaxies! E.g., from Kirshner, PNAS, 2004,

How it was discovered

Bypass

Bypass My balloon analogy in Mini-Lecture C is better.

BINGO! An unexpected result.

Which helps keep lava in its molten state!

Excellent graph and caption, visual definition of half life.

For Florida students, this term, snow, indicates a rare solid form of \(H_2 O\) which,at low temperatures, forms six-sided crystals that are very cold and fall from the upper atmosphere. Rare in Florida since the last Ice Age.

Using the idea of "radioactive half-life" of an element.

Compared to Earth, where impact craters are rare, the Moon is loaded with craters. That is because Earth has weather, volcanoes, earthquakes and continental drift.

Like radioactive carbon-14 \(^{14}C\) spontaneously emitting an electron from its nucleus to become nitrogen-14 \(^{14} N\) which is stable. Most nitrogen, 99.632%, is nitrogen-14.

• Nucleus of carbon-14 = 6 protons, 8 neutrons
• Nucleus of nitrogen-14 = 7 protons, 7 neutrons. (The seventh proton used to be a neutron in carbon-14!)

A lovely definition of half-life!

"only" 11,000 mph!

...where they are also heated up by the sun and become visible.

about 107,000 mph!!

Important vocabulary terms: aphelion and perihelion.

Similar to aphelion and perihelion but relative to Earth. You hear the guys at Mission Control in Houston talk about perigee and apogee. E.g., the ISS right now has perigee of 408 km altitude, apogee of 410 km altitude.

I usually use NASA's Planetary Fact Sheet. All sorts of neat data.

Unlike the surface rocks most places on Earth. E.g., the Florida limestone bedrock which, in its oldest layers, is about 35 million years, less than 1% of the age of the solar system.

Not labeled well, but compare to the Mini-Lecture A in YouTube.

Important concept. They loiter out by their aphelion, but when they get in close to perihelion, they are really moving fast. So visible comets are only visible for weeks, if that.

This means, as emitted by the source if it were in a stationary laboratory.

\(\Delta \lambda=\left(\lambda_{lab}-\lambda_{observed}\right)\)

So \(\frac{\Delta \lambda}{\lambda}\) is the percent change in wavelength.

Similar expressions exist for frequencies \(f_{lab}\) and \(f_{observer}\)

We will tackle this kind of calculation in Module 3 when we study galaxies.

So \(\Delta \lambda = 0.3 nm\) which is in the numerator of the equation below.

So a radio wave that has a smaller frequency than normal is redshifted. An xray wave with a higher frequency is blueshifted... all of this even though we do not perceive radio or xray as having color.

Another redshift.

This is also the equation programmed into a policeman's radar gun, for measuring the speed \(v\) of speeders.

Like the beautiful red \(H_{\alpha}\) line, for which the lab wavelength is \(\lambda=656.27\) nanometers.

absorption OR emission lines can display redshift and blueshift

I.e., \(\frac{\Delta \lambda}{\lambda}\)

Definition of supermassive black hole. Some galaxies' central black hole is even larger than ours.

SNR

This is about 8000 AU, so much larger than our solar system, way past Neptune, out into the Oort Cloud. But comets from the Oort Cloud have orbital periods on the order of 200,000 years or so. But the stars in this image take a few decades!! Extremely fast, because gravity is so strong, due to Sgr A*

First one with a good orbital track was S2, on a 15.2 year orbit about the black hole Sgr A*.

Cf., Schödel R. et al., "A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way" Nature 419, 694–696 (2002),

Very hot. How was it heated to this temperature?

It works out to about \(R=46 \,LS\), which would be well inside Mercury's orbit, \(0.39\, AU=193\, LS\)

Astronomers are always looking for signs of water on planets, comets, asteroids, moons and on exoplanets.

Here is a freight train blowing its horn as it passes the rail fan's video camera. At about 0:39, the horn shifts from a high note (while approaching) to a lower note (while moving away from the camera).

This is a Doppler Shift for sound waves.

Electromagnetic waves -- radar, visible light, even xrays -- also experience Doppler shifting. It is how the sheriff's deputy nabs speeders with his radar gun, and it is how we can measure velocities toward or away from Earth.

Using Kepler's third law and a radar rangefinder to actually get the orbit.

This means that water ice has a relatively high radar reflectivity. It does not dissipate the incoming radar beam, but bounces back a lot: strong return signal, "bright."

Sand is a silicate mineral -- most white sands are principally silicon dioxide \(Si\:O_2\).

Here is a set of diagrams that show the aphelion and perihelion in true proportion,

Also using a radar rangefinder.

Also similar to Earth's core. However the metallic part of Earth's core is not nearly as big a fraction of Earth, compared to Mercury

Helpful for comparisons.

E.g.,

E.g., Clearwater Lake Recreation Area, up in Ocala National Forest, about 31 miles northwest of UCF.

A good analogy.

In the mountains above Los Angeles. Unfortunately, LA is too smoggy now and Mount Wilson is not such a hot observatory these days.

OH MY GOODNESS!!!!!!!

Musician and astronomer. NICE!

Because of the spectral lines of heavier elements like calcium,

Skim this section for basic information about the discovery of the structure of atoms. Prior to Rutherford, we though atoms were just blobs of something sprinkled with electrons.

Skim this section, because it relates to discrete spectra, one of our important tools in astronomy.

Study this section carefully: Basic info for using isotopes

Conceptual definition of isotope. It is the number of protons that defines which element you have, but the nucleus can have any amount of neutrons it can hold onto.

IMPORTANT definition!!!!

This is the remarkable fact about atoms: they are mostly empty space! Makes a person think.

$$e=0.055$$

Cf., the NASA Space Science Data Center planetary fact sheet.

Important parts of the theory, though it is not yet a stone cold lock.

Cf., lecture 8, Spring '18

Yes, as the moon rocks from Apollo show. They have been analyzed for decades and compared to terrestrial rocks.

Cf., mentions of oxygen isotopes in Lecture 8 Spring '18, (Edward D. Young et al. Science 2016;351:493-496) especially the relation of lunar materials to terrestrial rocks like the Mauna Loa lavas.

nicknamed Theia

Big result, very tough to calculate.

As mentioned in the previous annotation

A big maybe. Scientists make large models with pixels representing stars of various masses and a gravitational interaction, then let the pixels evolve on the computer. This figure is a rough view of such simulations. A good simulation can be helpful, but they are very tough to make.

Excellent example is the Allende meteorite, which fell as a larger object that broke up, down in Mexico, on Feb. 8, 1969.

like what a centrifuge does.

Cool!

Isotopes tell us this age!

This is a huge mystery, the handedness of sugars and amino acids.

Comets are an entire other subject!!

The other kind of molecule that astronomers are always alert for!!

Pretty technical -- we will bypass this section, too.

For stars and galaxies, apparent luminosity (what we see on Earth) depends on its distance and its intrinsic luminosity (as measured at the galaxy or star itself).

Handy cepheid variable stars!

I cannot find the original image on NASA servers. However, this image from 2014 is helpful for visualizing a Type Ia supernova: Image: Katzman Automated Imaging Telescope/LOSS

"Type Ia supernovae have acquired global importance in recent years through their use as distance indicators..."

Bypass this. We will concentrate on Cepheid variables and Type Ia supernovas

We will discuss this after Exam 1.

What a fruitful friendship!

Another indication of the slowness of scientific development in that era.

A very important diagram to keep in mind for most topics this semester, because most of the information about the stars and galaxies of the universe comes to us from starlight and its spectral lines!

Interesting but we will bypass this section.

Don't forget to review the "syllabus" type YouTube, https://youtu.be/7jSqOscLwWs