venus, earth, & sidereal timekdouglass/classes/ast111/lectures/07_lecture_print.pdfsidereal time...

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VENUS, EARTH, & SIDEREAL TIME

Problem set 3 due Tuesday at the beginning of lecture

19 September 2019 ASTRONOMY 111 | FALL 2019 1

VENUS, EARTH, & SIDEREAL TIME

Sidereal time: what is it, and why do we care?

Venus as a twin of Earth: rock composition, tectonics, volcanism, and differentiation

Melting the insides of infant terrestrial planets with radioactivity

Loss of water and organic molecules from hot infant planets

Earth as a planet

Venus, Earth, and atmospheric circulation: Hadley cells

Venus, Earth, and the greenhouse effect

Distinctive features of Earth

Life and its influence on geology and the atmosphere

Plate tectonics

The core and the global magnetic field


Venus and Earth as seen from the Magellan and Apollo 17 missions, respectively.

https://www.universetoday.com/22551/venus-compared-to-earth/

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HOW DO WE DEFINE TIME?


SIDEREAL TIME (ST)

Sidereal time at some location is defined to be the hour angle of the vernal equinox at that location; it has the same value as the R.A. of any body that is crossing the local meridian.

When the vernal equinox crosses the local meridian, LST = 00h00m00.0s .

An object will be highest in the sky when the ST is equal to the object’s R.A.


Office of Naval Research

https://www.onr.navy.mil/

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SIDEREAL TIME V. SOLAR TIME


WHY DO WE CARE ABOUT (L)ST?

RA - LST = HA

Hour angle (HA): object’s position relative to observer 0h occurs when the object is at its highest

position in the sky

At a given (L)ST, the sky will always look the same.

So, if you know the R.A. of the object, and you know the (L)ST, then you can figure out where to look in the sky for the object! (Our telescope does this math for us.)


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MOMENT OF INERTIA OF A DIFFERENTIATED SPHEREFor example: density decreasing linearly from a central value of 𝜌" to zero at the surface:

𝜌 = 𝜌" 1 −𝑟𝑅

This time, we have to do an integral to get 𝑀 and 𝜌" in terms of each other:𝑑𝑚 = 𝜌 𝑟 𝑟+ sin 𝜃 𝑑𝑟 𝑑𝜃 𝑑𝜙

𝑀 = 1𝑑𝑚 = 𝜌" 1"

+2𝑑𝜙1

"

2sin 𝜃 𝑑𝜃1

"

3𝑟+ 1 −

𝑟𝑅 𝑑𝑟

M = 𝜌" ⋅ 2𝜋 ⋅ 2 ⋅𝑅8

3−𝑅8

4=𝜋3𝑅8𝜌"

𝜌" =3𝑀𝜋𝑅819 September 2019 ASTRONOMY 111 | FALL 2019 7

MOMENT OF INERTIA OF A DIFFERENTIATED SPHERE

𝐼 = 1𝑟<+ 𝑑𝑚

= 1"

+2

1"

2

1"

3

𝑟 sin 𝜃 +𝜌" 1 −𝑟𝑅

𝑟+ sin 𝜃 𝑑𝑟 𝑑𝜃 𝑑𝜙

= 𝜌" 1"

+2𝑑𝜙1

"

2sin 𝜃 8 𝑑𝜃1

"

3𝑟= 1 −

𝑟𝑅 𝑑𝑟

=8𝜋3𝜌"

𝑅?

5−𝑅?

6=8𝜋3𝜌"𝑅?

30

=415𝑀𝑅+ = 0.267𝑀𝑅+


The integrals over 𝜃and 𝜙 are the same as before (4/3 and 2π) and will be as long as the density does not depend on an angle.

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VENUS’ VITAL STATISTICSMass 4.8685×10+F g (0.815𝑀⨁)Equatorial radius 6.0518×10J cm 0.949𝑅⨁Average density 5.243 g/cm3

Moment of inertia 0.33𝑀𝑅+

Albedo 0.67

Orbital semimajor axis 1.0821×10L8 cm (0.72333 AU)Orbital eccentricity 0.00677323

Sidereal revolution period

224.701 days

Sidereal rotation period

-243.686 days

Length of day 116.75 days

Magnetic field 0


C. Hamilton (Galileo/JPL/NASA)

VENUS’ ATMOSPHERE’S VITAL STATISTICS

Surface pressure: 92 earth atmospheres

Average temperature near surface: 737 K (464° C) Compare to 327 K expected for its orbit

Diurnal (day-night) temperature range: ~0

Surface wind speeds: 0.3-1.0 m/s

Atmospheric composition (near surface, by volume): 96.5% CO2, 3.5% N2, 0.015% SO2, 0.007% Ar, 0.002% H2O


Ultraviolet image of Venus’ cloud tops by the Akatsuki (JAXA)

https://solarsystem.nasa.gov/galileo/index.cfm

http://www.planetary.org/multimedia/space-images/venus/global-view-of-venus-from-akatsuki.html

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PHASES OF VENUS

At most, Venus gets 47° from the Sun – as noted by the ancients – and displays phases, as first noted by Galileo (1610). These facts directly show that Venus orbits the Sun, not the Earth.


Photo by Wah!

VISITS TO VENUSVenus was the first planet to receive an Earthly spacecraft on its surface: the Soviet Venera 7, in 1970, lasted 23 minutes and made the first in situ report of temperature and pressure (748 K, 90 atmospheres).

Including missions with other final destinations, there have been 27 successful visitsbetween Mariner 2 (1962) and the current JAXA Akatsuki (2010-present), highlighted by many Soviet Venera landers.

Also a large number of failures, mainly in the Soviet Sputnik, Zond, and Cosmos series.


Venera 9 landing site: the first image retrieved from the surface of a planet besides the Earth-Moon system (Ted Stryk)

mailto:[email protected]

http://planetary.org/explore/space-topics/space-missions/missions-to-venus-mercury.html

http://planetimages.blogspot.com/

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THE COMPOSITION OF VENUS’ SURFACEFive of the Venera landers made composition measurements on soil and/or rock. Venera 8 reported a composition similar to granitic (felsic) rocks; all the others obtained a mafic composition.

The best measurements come from Venera13 and 14, which landed in the highlands (13) and lowlands (14) of Beta Regio and drilled into solid rock.

Both measured compositions similar to alkaline basalts, similar to those retrieved from mid-ocean ridges on Earth and distinctively different from Lunar mare basalts.


X-ray spectra of Venereal rocks (solid curves) by Venerai13 (top) and 14

(right) compared to ocean-floor basalts (points) (Surkov et al. 1984)

THE STRUCTURE OF VENUS’ SURFACE

The most mapping of Venus has been made by (cloud-penetrating) radar maps, such as those by the NASA Magellan and ESA Venus Expressorbiters.

Venus Express also includes high resolution infrared cameras capable of thermal imaging and shows the warmest (coolest) parts of the surface lie at the lowest (highest) elevations.


VIRTIS/Venus Express (ESA)

http://adsabs.harvard.edu/abs/1984JGR....89..393S

http://www.esa.int/Our_Activities/Space_Science/Venus_Express/New_map_hints_at_Venus_wet_volcanic_past

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VENUS’ SURFACE STRUCTURE

The radar maps reveal many of the features of plate tectonics and volcanism that we know on Earth: Many deep, asymmetrical troughs that resemble subduction zones, and long ridges that resemble mid-ocean ridges

Some large shield volcanos and unique lava vents such as coronae and “pancake domes” Lava flows are seen to stretch many hundreds of km from such volcanoes.

Hardly any impact craters


Magellan/JPL/NASA

VENUS’ SURFACE STRUCTURE

Most of this activity is extinct, though.

The tectonic-like features do not link up to make a global plate boundary system as on Earth.

Still has active volcanoes, but not very many.

Overall, there has not been much tectonic activity over the past few hundred million years, although there was some long ago.


Magellan/JPL/NASA

https://www2.jpl.nasa.gov/magellan/images.html

https://www2.jpl.nasa.gov/magellan/images.html

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VENUS’ INTERNAL STRUCTURE

Like Mercury and Earth, Venus is differentiated: It has a large bulk (average) density (5.243 g/cm3) but its surface is covered in mafic silicate rocks (3.2 g/cm3)

It has a rather small moment of inertia 𝐼 = 0.33𝑀𝑅+ , too small to represent uniform

density 𝐼 = 0.40𝑀𝑅+ . As might be suspected a priori, Venus’ internal structure appears similar to Earth’s, which we think includes a liquid iron-nickel core, plastic mantle, and crust.


Diagram by UCAR (U. Michigan)

WHY NEW PLANETS ARE MOLTEN AND THUS BECOME QUICKLY DIFFERENTIATEDBrand-new terrestrial planets are usually very hot, hot enough for most or all of the volume to be molten. If the interior is molten, buoyancy rules: dense metals and minerals can sink freely to the center, and lighter ones can float to the surface.

There are two reasons why the interiors are so hot. Accretion. The gravitational potential energy of a planet’s ingredients decreases from zero to very large negative values in the act of forming, and since energy is conserved, this leads to very large positive energy in the form of heat.

Radioactivity. Just as in nuclear reactors, it converts nuclear electrostatic potential energy to kinetic energy of the products, which heat the medium. And planetary ingredients were a lot more radioactive then than now.


https://www.windows2universe.org/?page=/our_solar_system/solar_system.html

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WHY NEW PLANETS ARE MOLTEN

We will not be discussing accretion, heat transport, or the temperatures of planetary interiors until next month. But we can get an appreciation for the temperatures using what we now know about the surface temperatures and radioactivity: Radioactivity occurs throughout the interior, and its heat input can be calculated from just the mass if the composition is typical of the materials out of which the planets were built: 𝑃rad = 𝑀Λrad 𝑡 The heating rate per gram, ΛSTU, decreases with time since there is no means to replenish decayed radionuclides with fresh material from the interstellar medium.

In turn, this heat input can just be added to that due to sunlight to work out the temperature of the surface.


WHY NEW PLANETS ARE MOLTENRadioactive heating rates for primitive (carbonaceous chondrite) meteoritic material, currently and at the birth of the Solar System.


Radionuclide Daughter(s) Half-life [Myr] Heating today [10-8 erg/s/g]

Heating 4567 Myrago [10-8 erg/s/g]

40K 40Ar, 40Ca 1248 2.91 36.8232Th 208Pb 14050 1.04 1.30235U 207Pb 704 0.0500 4.60238U 206Pb 4468 1.52 3.1326Al 26Mg 0.717 0 2540036Cl 36S, 36Ar 0.301 0 60100060Fe 60Ni 2.60 0 4640000

𝚲𝐫𝐚𝐝(𝒕) for primitive meteorites [erg/s/g] 5.52x10-8 5.27x10-2

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RADIOACTIVE HEATING

Consider the surface temperature 𝑇\ for a spherical planet (mass 𝑀, radius 𝑅) of solar-system composition a distance 𝑟 from a star with luminosity 𝐿.

𝑃_ sunlight and radioactive heating = 𝑃ij_k^lmn + 𝑃STU = 𝑃pjn blackbody radiation

𝐿4𝜋𝑟+ 𝜋𝑅

+ + 𝑀ΛSTU 𝑡 = 4𝜋𝑅+𝜎𝑇\=

𝑇\ =𝐿𝑅+ + 4𝑀Λuvw 𝑡 𝑟+

16𝜋𝜎𝑟+𝑅+

L/=

The Sun’s luminosity was larger by a factor of about 2.5 back then, but ΛSTU was larger by a factor of almost one million.


RADIOACTIVE HEATING

Results, assuming that each body lacks an atmosphere and formed in a time short compared to the half-life of 60Fe. Compare to the melting points of planetary ingredients: 1000-1500 K for silicate rocks, 1800 K for iron.

And, though we have not learned how to calculate interior temperatures yet, most of us will realize that each body is hotter inside, if heated from within.

Venus was almost certainly molten all the way through when new, and probably Mercury as well.

Planet 𝑻𝒔 now [K] 𝑻𝒔 4567 Myrago [K]

Venus 327 1003

Mercury 447 845

Moon 278 664


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LOTS OF VOLATILE MOLECULES FROM NEWBORN PLANETSVenus’ original ingredients were no doubt similar to the small primitive Solar-system bodies we find as meteorites and were rich in organic molecules and ices.

These molecules contain nearly all the carbon, nitrogen, and hydrogen in meteorites. A little oxygen, too.

When Venus was molten, these molecules all evaporated into a temporary atmosphere.

Ultraviolet sunlight quickly breaks such molecules up into atoms, which are all light enough to escape the gravity of the planet.

Thus, Venus, like every other terrestrial planet, is very poor in carbon, nitrogen, and hydrogen, compared to other Solar System bodies.


EARTH’S VITAL STATISTICS Mass 5.9736×10+F gEquatorial radius 6.3781×10J cm

Average density 5.515 g/cm3

Moment of inertia 0.33𝑀𝑅+

Albedo 0.37

Effective temperature 254.3 K

Orbital semimajor axis 1.49597887×10L8 cm (1.00000011 AU)

Orbital eccentricity 0.01671022

Sidereal revolution period

365.256 days

Sidereal rotation period

23.9345 hours

Length of day 24.0000 hours

Magnetic field 0.5 gauss


Earth as seen from Suomi NPP (NASA)

https://www.nasa.gov/multimedia/imagegallery/image_feature_2159.html

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VENUS, EARTH, AND ATMOSPHERIC CIRCULATIONIn 1735, George Hadley, who was interested in explaining the direction and steadiness of the trade winds, extended an earlier suggestion by Edmund Halley. Warm air is less dense than cold air; if one makes

a warm (cold) “bubble” of air somewhere in the atmosphere, it will rise (sink) through the rest of the atmosphere.

The ground and air adjacent to it are warmer at the equator than at the poles because of the different incidence angles of sunlight.

Therefore, there should be N-S circulation, with warm air at high elevations flowing toward the poles and cooler air at the surface flowing toward the equator.


From

Sun

Warm air rising

Cool air sinking

Equator

North pole

ATMOSPHERIC CIRCULATION

So far, this is Halley’s idea and does not explain the direction of the trade winds, which tend to be easterly between the tropics.

But Hadley realized that the N-S flow must be modified, since the planet and atmosphere are rotating about an axis. The rotational speed is higher at the equator, with the speed given by

𝑣u =2𝜋𝑅⨁day cos 𝜆 𝜆 = latitude

At the equator 𝜆 = 0 , Earth’s rotational speed is 0.46 km/s, but at 𝜆 = ±45°, it is down to 0.33 km/s, and at ±75°, the speed is 0.12 km/s. The rotational speed is (obviously) 0 at the poles.

The Earth rotates counterclockwise as viewed from the North. As warm air is pushed north or south, it finds itself moving into slower air, and each bubble of it moves out somewhat ahead of the normally-rotating airmass.


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ATMOSPHERIC CIRCULATIONThus, the warm flow turns toward the rotation direction as it goes. Underneath, the cooler return flow goes the other way.


Direction of rotation

Cool (surface)

flow

Warm (high-altitude)

flow


Between cooling and turning, the warm high-altitude flow only makes it to latitude ± 30° before sinking, driving surface flow back the way the warm flow came. This circulation pattern is called a Hadley cell.

Taking advantage of the extreme difference between rotational speed and solar heating from the poles to latitudes just below, another Hadley cell, usually called the polar cell in order to distinguish it from the equatorial one, works the same way between latitudes ±60° and the poles.

In between (i.e. in the temperate zones), a circulation pattern is driven by the Hadley cells that has the opposite sense of these two, counter to rotation. This one is called the Ferrel cell.


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The Northern hemisphere prevailing-wind system (W. Langford, U. Guelph)


ATMOSPHERIC CIRCULATION ON VENUS

The faster a planet rotates, the more bands of alternating Hadley and Ferrel cells are obtained in the atmosphere.

A slow enough rotator would have only one, ideal-looking Hadley cell per hemisphere, stretching all the way from the equator to the poles.

This is the situation of Venus, the slowest rotator among the planets. Most of the air circulation on Venus is north-south: by far the simplest atmospheric structure of the planets.

This is why the surface temperature on Venus is so uniform – as hot at the poles as the equator and as hot at night as during the day.


https://www.fields.utoronto.ca/programs/scientific/10-11/biomathstat/Langford_W.pdf

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VENUS, EARTH, AND THE GREENHOUSE EFFECT

Venus is also famous for having a dense, very dry atmosphere that make it the exemplar of the greenhouse effect, as was first realized by Rupert Wildt (1940) and first explained in detail by Carl Sagan (early-mid 1960s). Venus probably started off with the same ingredients as Earth, meaning that it had water after the surface cooled.

As we have mentioned, the water was mostly from asteroids and comets, rather than its original ingredients or the pre-solar nebula.

But the atmospheres of Earth and Venus also endow their planets with a substantial greenhouse effect: their surfaces are warmer than they would be just from solar illumination and blackbody radiation.


QUESTION!

What constituent of Earth’s atmosphere makes it the largest contribution to the greenhouse effect?

A. Carbon dioxide

B. Methane

C. Ozone

D. Nitrogen

E. Water

F. Argon


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THE GREENHOUSE EFFECT

𝑇 =𝐿⨀

16𝜋𝜎𝑟+L/=

=278 K𝑟 AU

The terrestrial planets emit most of their light at infrared wavelengths. They would all be brightest near a wavelength of 10 μm

Solar heating arrives mostly at visible wavelengths, where the atmosphere is transparent.


Created for Global Warming Art by Robert A. Rohde

THE GREENHOUSE EFFECTInfrared light is absorbed very strongly by molecules in the atmosphere, notably water and CO2.

Light can only escape directly to outer space through “windows,” the most important of which lie at wavelengths 8-13, 4.4-5, 3-4.2, 2-2.5, 1.5-1.8, and 1-1.4 μm.

Hotter blackbodies shine more at shorter wavelengths, so if not enough light escapes at 3-5 and 8-13 μm, the surface heats up until enough of the emission leaks out in the shorter wavelength windows.

This effect warms all three of the atmosphere-bearing planetary surfaces.


Created for Global Warming Art by Robert A. Rohde

http://berkeleyearth.org/team/robert-rohde/

http://berkeleyearth.org/team/robert-rohde/

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STABILIZING THE GREENHOUSE EFFECT

If there is liquid water on the surface, the greenhouse effect can be self-stabilizing. Water droplets form clouds that reflect the sunlight. (CO2 forms neither droplets nor clouds.)

If the temperature rises,→ more water evaporates into atmosphere→ more clouds form→ albedo increases→ less sunlight reaches the surface→ temperature dropsAnd vice versa.

On Venus, sunlight and the greenhouse effect was sufficient to evaporate all the water, leaving no liquid bodies on the surface.


CARBON & THE GREENHOUSE EFFECT

Liquid water dissolves carbon dioxide from both the atmosphere and from rocks, creating carbonic acid:

H2CO3 (in solution, H3O+ + HCO3-)

The carbon can then be incorporated in carbonate minerals that can readily form in liquid water. These days, this is done most readily on Earth by ocean-dwelling organisms, creating CaCO3.

If there is a lot of liquid water, carbon from CO2 will eventually be locked up in carbonate minerals rather than allowed to be present in the atmosphere. This is the case on Earth, for example. On Venus, the lack of liquid water let the CO2 remain in the atmosphere.


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GREENHOUSE EFFECT ON VENUS

Under solar ultraviolet illumination, water molecules high in the atmosphere readily dissociate, producing atomic hydrogen and oxygen. Oxygen goes on to react with other molecules; hydrogen does not.

Hydrogen is too light to be retained by Venus’ gravity, so it escapes relatively quickly. Soon, there is no more water or the possibility for making any more water.

All the carbon and oxygen wind up in CO2, the atmosphere pressurizes, and the greenhouse effect cranks up to 735 K. A sterilized world.


IR view of Venus at night

(Akatsuki, JAXA)

THE EFFECT OF LIFE

The most distinctive feature of Earth – unique in the Solar System, as far as we know – is that it supports life. The chemical activity of organisms has had global influences: Abundant carbonaceous minerals. In the ocean, organisms such as corals and mollusks synthesize carbonaceous minerals from dissolved carbon dioxide in such large quantities that they are the leading producers of such minerals.

Lots of molecular oxygen in the atmosphere. Plants synthesize oxygen out of carbon dioxide and do it so well that the atmosphere, which probably started out with just a trace amount, is now about 20% oxygen.

This is very different from the CO2-dominated environment on Venus and Mars.


http://www.planetary.org/multimedia/space-images/venus/venus-in-infrared-from-akatsuki-1.html

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EARTH AND PLATE TECTONICS

Like Venus and Mercury, Earth is a differentiated body with a liquid-iron core, “plastic” silicate asthenosphere (mantle), and less-dense silicate lithosphere (crust).

The crust is broken into plates that float on top of the mantle.

Some of the plates are denser (mafic minerals) and are generated from mantle material at mid-ocean rises. These plates are returned to the mantle when subductedunder less-dense plates. They comprise the ocean floors.


US Geological Survey

EARTH’S PLATE TECTONICS

Some of the plates are dominated by lower-density silicates (felsic minerals), which float on top of everything else. These comprise the continents.

Earth’s plate-tectonic system is unique in the Solar System, possibly the result of the presence of water. Only Venus shows evidence of such activity, though it has been long extinct.


The last 750 million years of continental drift (C.R. Scotese 2001/PALEOMAP project)

https://geomaps.wr.usgs.gov/parks/pltec/index.html

http://www.scotese.com/

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EARTH’S CORE AND MAGNETIC FIELD

Earth’s iron core is mostly liquid, apart from the innermost part which is compressed into a solid phase.

The core also rotates differentially, with the inner parts going faster than the outer parts. The solid inner core spins the fastest of all (“superrotation”).

The core probably also undergoes convection: radial circulation of warmer core material outward, which is replaced by cooler material sinking inward.


Magnetic field twisting by differential rotation

EARTH’S CORE AND MAGNETIC FIELD

Iron is a conductor, and conductors exhibit magnetic flux freezing: moving conductors drag lines of magnetic force along with them, and vice versa.

The result is that a slowly oscillating, self-generating global magnetic field accompanies the core’s rotation: a dynamo.

Venus rotates too slowly for this, but Earth and Mercury have dynamo-generated fields.


Magnetic field stretching by differential rotation (MSFC/NASA)

https://depositphotos.com/187858030/stock-illustration-earth-magnetic-field-scientific-vector.html

https://solarscience.msfc.nasa.gov/dynamo.shtml

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