M&P Exam 01

Question 1

State 3 facts about Mercury that could possibly threaten its definition as a planet if the definition were the one from the 2006 IAU.

Answer 1

Mercury is very small (smaller than some moons like Titan & Ganymede)

Mercury’s orbit is highly eccentric & egg-shaped

Mercury does not have a substantial atmosphere - exosphere of atoms blasted off by solar wind

Question 2

You have 5 steel spheres with diameters of 0.01, 0.1, 1.0, 10, and 100 mm. Show those diameters on linear and logarithmic scales.

Answer 2

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Question 3

You determine the number of stars in a galaxy by measuring the rotation rate, applying Kepler’s laws to get the mass and then dividing by the average mass of a star. In one or two short sentences, why might the answer be too high?

Answer 3

The mass will likely be too high due to taking the average mass of a star. Mass refers to all parameters that contribute to mass like dark matter, gas and dust. Most mass comes from dark matter. Instead, after finding the rotational velocity, measure the radius, R and find the rotational period. Finally, use Kepler’s 3rd law to get an accurate mass.

Question 4

State 3 properties of water that make it important for human life.

Answer 4

pH neutral = good medium for chemical reactions

Water has highest “latent heat” for cooling - energy transfer

Water is denser than ice - ice floats, melts, more liquid - maintain stable water temperature

Question 5

Draw the graph of average molecular velocity (vertical axis) versus temperature with logarithmic axes for He, H2O, O2, and CO2 gases. Then add ozone (O3) to the graph.

Answer 5

pic

Question 6

The graph in a) can help predict a planet’s atmospheric chemical conditions. State 3 other factors that might affect that composition.

Answer 6

Subsurface water
Stellar winds that strip atmosphere
Stellar UV that dissociates H2O
Planet’s escape velocity

Question 7

Use a diagram of forces and one sentence to explain why a rotating gas cloud tends to collapse to a disk.

Answer 7

Vertical gravitational force components cause the rotating cloud to collapse to a disk as it is unbalanced.

Question 8

Describe 3 effects caused by the early sun that caused the difference in composition between the Terrestrial and Jovian planets.

Answer 8

Photon Pressure pushes lighter elements outward
- Terrestrials: Overabundance of lighter elements outside, leaving heavier elements in the center.
- Jovians: Further from the sun, so they retain a lot of the lighter elements & they accumulate in their atmospheres

Chemical Sticking of Planetesimals that gravitationally collect in orbit (temp & density dependent)
- Terrestrials: planetesimals are close together & gravitationally collect, sweeping up debris
- Jovians: further apart = less collisions in Jovians, gaseous

Accretion & Cooling
- Terrestrials: form molten Terrestrial planets that then solidify (more surface area = cools faster (αR^2) - heavier elements sink
- Jovians: Turbulent eddies trap planetesimals which collect into warm liquid jovians… chemical & temperature differentiations occur

Question 9

Why was it essential to NASA to determine a more accurate value of the AU before 1962?

Answer 9

Accurate measurements of AU are needed to navigate to other planets, such as Venus in the Mariner Missions.

Question 10

Describe three reasons why radar was not used in 1961 to determine the distance to Mars.

Answer 10

Mars is much further away
Mars disk is much smaller
Time between Mars conjunctions is larger than Venus (Venus more frequent)
Mars signal return takes longer

Question 11

Explain, with 2 short sentences or equations & a diagram, why the solar energy flux at a planet must be divided by 4 to determine the average flux over its whole atmospheric surface.

Answer 11

Geometric Correction: body of radius r receives piR^2 area of sunlight, but energy is heating 4piR^2 of total surface area.

Solar flux must be divided by 4 to get average input flux heating the planet = 655

Question 12

With 2 short sentences, explain why much more solar radiation energy passes through the atmosphere of Venus than the ground radiation energy does. Be specific but numbers are not necessary.

Answer 12

Venus’ atmosphere is 96% CO2 and is transparent to incoming solar radiation. It is highly opaque to infrared radiation emitted by the surface. This traps heat through the greenhouse effect & prevents ground radiation from escaping.

Question 13

What parameters make up a planet?

Answer 13

Size
Shape
Mass
Orbital Tilt
Orbital Eccentricity
Chemical Composition
Orbital Domination
Energy Source
Atmosphere

Question 14

What is the definition of a planet according to IAU 2006?

Answer 14

A planet a) orbits the sun, b) has enough mass to assume nearly spherical shape, c) clears its orbital neighborhood

Question 15

What are some problems with the IAU 2006 definition?

Answer 15

Pluto becomes a dwarf planet, Earth has not cleared its orbital debris (no planet has) because of meteorites, why is Jupiter not classified as a brown dwarf binary?, becoming spherical depends on more than just mass.

Question 16

Why is Pluto considered a dwarf planet?

Answer 16

It is not massive enough & it has an incredibly eccentric orbit, passing into the Kuiper Belt.

Question 17

Why is Jupiter not considered a brown dwarf binary star?

Answer 17

There is no clear reason.

Question 18

What is the Drake equation? Give answers.

Answer 18

A means of measuring the number of planets with intelligent life in our universe today (Nc)

N* = # of stars in our universe today (10^11)
fp = fraction of stars that have planetary systems (1)
NL = # of planets ever suitable for life in a planetary system (1)
fL = fraction of suitable planets that ever evolve life (1)
fi = fraction of life-bearing planets that ever evolve intelligence (10^-1)
ft = fraction of a star’s lifetime that intelligence survives (10^-2)

Question 19

What is the original drake equation?

Answer 19

of intelligent civilizations in our galaxy that can communicate with us today (Nc)

R* = rate of star formation in our galaxy
fp = fraction of stars that have planetary systems
NL = number of planets ever suitable for life in a planetary system
fL = fraction of suitable planets that ever evolve life
fi = fraction of life-bearing planets that ever evolve intelligent life
fc = fraction of intelligent life forms that ever produce interstellar signals
L = how long do they reproduce that communication

Question 20

How do we estimate the number of stars in a galaxy?

Answer 20

Determine the rotational velocity, v near the outer edge using angle of inclination
Find the rotational period using the radius, p = 2piR/v

Use Kepler’s 3rd law to determine the mass, Mp^2/R^3

Question 21

Draw the rotational velocity curve for typical galaxies.

Answer 21

pic

Question 22

How does dark matter affect the calculation of the number of stars?

Answer 22

It has no effect on mass since all mass affects rotational velocity. Reduce the number of stars by 80% if dark matter does NOT produce stars or planets.

Question 23

What are some methods of exoplanet detection?

Answer 23

Pulsar Timing
Microlensing
Transit
Doppler
Direct Imaging

Question 24

What are the requirements for life?

Answer 24

Liquid Water
- pH neutral = good for chemical reactions
- Liquids have latent heat for cooling
- Water is denser than ice - stabilizes water temperature

Protective Envelope
- Solar wind particles strip the atmosphere & are diverted by the magnetic shield
- Short wavelength, high energy light is blocked by atmosphere (UV)

Question 25

Define a habitable zone.

Answer 25

Depends on parent star type - brightness, temperature, mass - Not too hot or too cold for liquid water - Not too much uv radiation & stellar wind particles - Far enough away to be tidally locked

Question 26

What are the principles of atmospheric retention?

Answer 26

Surface temperature vs. gravity - Assume gases are produced from warm surface - Higher surface temp = molecules move faster = escape - More surface gravity = must move faster to escape - Equipartition of energy: all particles in a gas have same kinetic energy - Massive molecules move slower at a given temperature

Question 27

How do we calculate escape velocity?

Answer 27

sqrt (2GM/R)

Question 28

Describe the relationship between an object’s escape velocity and a molecule’s average velocity.

Answer 28

- Velocity of molecules decreases as surface temperature decreases - Heavier molecules move slower than lighter molecules - Plot escape velocity & surface temp of moons/planets - If body is above molecular line, its escape velocity is > molecule’s average velocity (holds onto that gas)

Question 29

When were the earliest traces of life on Earth found?

Answer 29

3.5 billion years ago

Question 30

What are some problems with calculating the fraction of life bearing planets that evolve intelligence? That ever evolve life? The fraction of a star’s life that intelligence exists?

Answer 30

What is intelligence? What is life? We have not died yet, so we don’t know the fraction of a star’s life that we live. How did life form? Intelligent civilization longevity, conditions on exoplanets.

Question 31

What is the answer to the Drake Equation?

Answer 31

100,000,000 bodies in any galaxy that have intelligent life today

Question 32

What are some other forms of the Drake Equation?

Answer 32

Niu = NgNc – # of bodies with intelligent life in our universe today (10^18) Nicu = Niufc – # of planets with life in our universe that can communicate with us (10^12)

Question 33

Describe the factors that cause a cloud to collapse?

Answer 33

High temperature, molecules move faster = more pressure = cloud dissipates High mass, more gravity = molecules move faster to escape = cloud collapses

Question 34

Define Jeans Mass, how do we measure its parameters?

Answer 34

Critical mass for a cloud to collapse. Set kinetic equal to potential energy – Mj = 45T^(3/2)n^(-½)

Question 35

If a cloud's mass is less than Mj, why are there stars?

Answer 35

Molecular clouds undergo fragmentation into denser cores.

Question 36

Describe the steps to star formation.

Answer 36

Disk Formation: - Angular momentum conserved, faster rotation = vertical forces cause cloud to collapse - Central gas temperature increases to fuse H to He and increases gas pressure Collapse of inner cloud stops = stable star H & He Outward: - Photon pressure from star pushes H & He outward - UV ionization & solar win also push them out = overabundance of H & He Chemical Sticking: - Molecules form planetesimals (temperature & density dependent) Inner Disk Accretion & Cooling - Planetesimals gravitationally collect in orbit to form molten terrestrials - Terrestrials solidify - More volume (αR^3) – slower - More surface area (αR^2) – faster Outer Disk Accretion – Jovians - Planetesimals further apart = collisions are seldom

Question 37

What evidence is there for the age of our solar system?

Answer 37

Zircon - 4.375 bil yrs Meteorites Oldest moon rocks 4.57 bil yrs old

Question 38

What is Radiometric Dating?

Answer 38

Radioactive nuclei decay to another element with a known half-life, Tau pic

Question 39

What are the problems with circular orbits?

Answer 39

There are less collisions & planetesimals will not be made. Early debris could have been in eccentric orbits that were forced circular by gravitational forces.

Question 40

What are the cardinal locations of an inner planet?

Answer 40

Superior Junction Inferior Junction - Venus is closest Greatest Eastern Elongation (evening) Greatest Western Elongation (morning)

Question 41

What is AU?

Answer 41

Average distance between Earth & sun – leads to every astronomical distance: geometric parallax > cepheid variable > hubble constant > stellar brightness based on distance to stars

Question 42

How do we find AU?

Answer 42

Solar Parallax: Earth’s radius + solar parallax angle Orbital Periods of Earth & Venus: Kepler’s 3rd => ratio of their orbit sizes Transits of Venus: Observers at 2 latitudes see different transit durations Distance & Position of Venus

Question 43

What is RADAR & how is it used to measure AU?

Answer 43

Radio Detection & Ranging used to accurately measure AU. Sends out pulses & receives echoes in wavelengths.

Question 44

Why was it difficult to detect Venus by RADAR & what mistake was made in 1958?

Answer 44

Soviets jam radio systems – NOMAC reduce noise 1958: LL sent 5 pings & measured AU = 149,467,000 (132,000 km too small) 2 pings 0.24 sec apart, thought the higher ping was the real one

Question 45

Who achieved the first radar echo from Venus? Who did it?

Answer 45

JPL (GALCIT) Mariner Mission - 2 radio dishes (Bistatic – pulses sent & received at once… no need for switching to receive mode & estimating timing) - 1961 – continuous wave transmission AU = 149,599,000 Today AU = 149,597,870.700

Question 45

How does distance affect radar echo brightness?

Answer 45

Α 1/R^4. Mars would be 1.7% strength of Venus.

Question 45

How was Venus’ rotation velocity measured using radar?

Answer 45

Power spectra of radar echoes, bandwidth of echoes indicates rotation velocity at equator. Bright feature seen at red shifted side. If in retrograde (rotation cancels revolution), no wavelength shift.

Question 46

How do we calculate planet temperature without the greenhouse effect?

Answer 46

Calculate Solar Energy Flux onto the atmosphere Predict Solar Energy Flux at Venus SEF @ Earth = 1370 W/m^2 & Venus is 0.723 Earth’s distance from the sun SEF is α 1/R^2 => SEF @ Venus = 2620 W/m^2 (1370/0.523) - Geometric Correction: body of radius, r receives πR^2 area of sunlight, but energy is heating 4πR^2 of surface area Divide SEF by 4 => Average Input Flux Heating the Planet = 655 Albedo Correction – Light reflected by top of atmosphere Albedo = average ratio of intensity of reflected to incident light Venus Albedo = 0.75 Surface Input Flux = 655(1-0.75) = 164 W/m^2 Set equal to flux radiated by warm surface to get equilibrium temp Venus Temperature From Energy Flux (𝜎 = 5.57x10^-8) Stefan-Boltzmann: radiated energy, F = 𝜎T^4 Surface Input Flux = Radiated Flux T = (F/𝜎)^(¼) = 232k

Question 47

How do we correct for the greenhouse effect to get a planet’s temperature?

Answer 47

Depends on Atmospheric Absorption Factor - Surface flux increased to correct for outgoing atmospheric absorption g = Fraction of surface radiation blocked by atmosphere Escape Flux = surface flux radiated x (1 - g) @ Equilibrium, escape flux = input flux = surface flux (1-g) Surface Flux = (input flux)/(1-g)

Question 48

Describe Venus’ greenhouse effect.

Answer 48

CO2 blocks & absorbs heat from the planet = greenhouse effect making Venus very hot.

Question 49

How do we predict g (surface radiation blocked by atmosphere)?

Answer 49

Blackbody Radiation & Wien's Law: wavelength at peak intensity is α 1/T Photosphere = 5,500k, solar radiation peak = 500nm (green) Venus atmosphere = 96% CO2 (transparent to solar radiation, sunlight heats efficiently) T = 730k Peak ground radiation at 4 microns u (infrared)… CO2 is opaque to Venus ground radiation (infrared), so it absorbs heat emitted from surface Because Venus radiated energy is blocked, there is a strong greenhouse effect… 724k Venus is @ Equilibrium

Question 50

What is the runaway greenhouse effect?

Answer 50

Trapped heat = more surface outgassing = more opacity = more trapped heat. When atmospheric escape from exosphere = outgassing = reaches equilibrium

Question 51

How did Venus get so much CO2?

Answer 51

Inner solar nebula had water - Strong solar uv light dissociated water - Hydrogen escaped & stripped by solar wind - O2 combined with carbon to form CO2 - CO2 transparency to visible & opacity to IR = stronger greenhouse effect = high temperature

Question 52

Describe the problem with Phosphene on Venus.

Answer 52

- 14 september 2020: PH3 linked to life, may be no abiotic way for its production on Venus - PH3 denser at mid latitudes… needs abiotic source to be produced

Question 53

How much of Earth’s mass is water?

Answer 53

0.02%

Question 54

Describe the problems with Earth’s water.

Answer 54

Where did Earth’s water come from? - Water ice existed in cold interstellar space, but inner regions of the early solar disk were hot - water dissociation should have occurred - Hydrogen would have been pushed out by solar wind & radiation (no water) - Earth would have been at boiling point - Hydrogen has isotopes (H) & (D) - Earth has 7 times ratio of D/H When did it thaw to liquid? - % of He in stellar cores increases with age => He falls to center, forcing core outward & expands => increase in star size = Brighter - Faint Young Sun Paradox - Earth sun was only 73% its brightness: should have been frozen

Question 55

What are some solutions to Earth’s water?

Answer 55

Water from Comet Nuclei - Made of water ice, D/H is very different from Earth (Hartley), isotopes do not work Water from Meteorites - Carbonaceous 20% water, D/H too high - Enstatite (H rich), earth’s building blocks would have 20 times more H - Asteroid Collisions found hydrated rocks in asteroids (not enough)

Question 56

Describe the problems and solutions to the Sun's angular momentum.

Answer 56

- Sun has 99.85% of solar system’s mass, but only 0.3% angular momentum Solutions: - Sun’s rotation slowed way down (due to solar wind) - Sun’s surface rotates much slower than inner layers (due to solar photons) - Less angular momentum in Oort cloud - 99.9% of system’s mass was lost after sun formed

Question 57

How did the Earth-moon system lose angular momentum?

Answer 57

Earth should be spinning 304 times faster. Believe Earth formed by impact => angular momentum lost from impactor

Question 58

How do the tides on Earth affect its rotation & the moon’s orbit?

Answer 58

Earth’s tides slowed earth’s rotation & accelerated the moon’s orbit

Question 59

How does the rotation of Earth’s inner core differ from its outer core?

Answer 59

Solid metal inner core rotates eastward slightly faster than the surface. Liquid metallic outer core rotates westward due to IC magnetic field.

Question 60

What is precession?

Answer 60

Wobble of Earth’s rotational axis that traces a cone shape over 26,000 years. Does not affect the plane of Earth’s orbit (ecliptic), but changes orientation of Earth’s axis relative to other stars.

Question 61

What are the Planes of Reference?

Answer 61

Tilted 23.5° Ecliptic Plane: Sun’s apparent annual path due to our orbit Equatorial Plane: Imaginary extension of Earth’s equator

Question 62

Seasonal Markers & the Sun

Answer 62

Summer Solstice (June 21): Sun is 23.5° above celestial equator Winter Solstice (Dec 21): Sun is 23.5° below celestial equator Equinoxes (Mar 21 & Sep 21): Sun is at equator Sun appears to move 1° eastward each day due to Earth’s orbit & shifts 23.5° N to S and back over 1 year.

Question 63

Star Chart

Answer 63

Centered on Equatorial: ecliptic appears as sin wave Centered on Ecliptic: equator is a flipped sin wave... Sun’s apparent annual path due to our orbit

Question 64

Time & Years

Answer 64

Tropical Year: time it takes for the sun to return to the same position relative to celestial equator (equinox to equinox)... defines our calendar years. Sidereal Year: time it takes for earth to complete one full orbit… longer because precession shifts position of the equinox westward along the ecliptic. Shortens tropical year by 20 minutes.

Question 65

Precession & Coordinate System

Answer 65

Right Ascension: longitude… remains parallel to celestial equator Declination: latitude… does not change as Earth rotates hourly Designed to remain aligned with Earth’s equatorial plane.

Question 66

Why not use fixed stars as 0,0?

Answer 66

Precession causes celestial equator to shift over time, coordinate system would not align with Earth’s equator.

Question 67

Astrology & Precession

Answer 67

Zodiac signs in astrology are no longer aligned with original constellations due to westward shift of sun’s position due to precession Ophiuchus (Nov 29 - Dec 18)

Question 68

Why does the theoretical evolution of a star during its main sequence lifetime present a problem for our history of the evolution of life on Earth?

Answer 68

The early sun was only 73% of its brightness, so any water should have been frozen. However, geologic records show that liquid water was present very early on.

Question 69

We might assume there is more mass in the Oort cloud than we expected, but it would probably make the sun’s angular momentum problem even worse. Explain why.

Answer 69

More mass in the oort cloud would increase the total angular momentum of the solar system. A smaller amount of angular momentum is in the sun itself.

Question 70

State two ways you could eliminate Earth’s axial precession by changing details about it or its rotation or its orbit.

Answer 70

NO MOON. The sun’s axial precession is largely influenced by lunar gravity. Make the earth a perfect sphere so that precession stops.

Question 71

Describe how you can derive the difference, in days, between tropical and sidereal years, just from the period of Earth’s axial precession alone.

Answer 71

Period = 360° orbital revolution / 0.83 westward shift of vernal equinox = 26,000. Shift per sidereal year: 360/26,000 = 0.014°/year. Time difference: 365.256 days / 360 = 1.014 days.