Answers to Homework #2 (Astr 212 -- Fall 2003)

Venus and Mars -- Due Fri Nov 14


 

1) By counting the number of craters per square mile on Venus, astronomers have estimated the average age of Venus's surface to be less than 500 million years old. This means that

(A) Venus has never "resurfaced" its crust, (B) Venus "resurfaces" its crust more slowly than the Earth, (C) volcanoes can not "resurface" a planet's crust, (D) the surface of Venus is as old as the moon's, (E) answers A, C, and D.

Correct: (B) Presumably, all terrestrial planets once had surfaces like the moon and Mercury -- saturated with craters formed by impacts in the late stages of heavy bombardment. Venus has clearly been resurfaced, since any trace of this ancient surface is gone, and the few craters that do exist there are crisp and fresh (recent). Earth is the same, though it has even fewer craters than Venus (on average, Earth's surface is about 200 million years old). The textbook summarizes this on pages 477-8.

 

2) Measurements of the magnetic field of Venus reveal that the

(A) planet has a large iron core, (B) interior of the planet is molten, (C) planet has no detectable magnetic field, (D) planet rotates backwards, (E) magnetic field is responsible for large auroral displays (northern lights) on Venus.

Correct: (C) On p. 483, Seeds reports the observational fact that spacecraft have not detected a magnetic field around Venus (also see Figure 22-11). This is surprising, given that Venus's size and density are similar to Earth's -- it should still be warm inside, and should have a large iron core like Earth. Perhaps Venus's slow rotation speed is to blame -- one of the key ingredients in producing a magnetic field by the dynamo effect (planetary rotation, along with convection in an electrically conducting fluid like Earth's molten iron core) is missing.

 

3) Which of the solar system objects listed below is most similar to Earth in terms of mass and density?

(A) Mercury, (B) Venus, (C) Earth's moon, (D) Mars, (E) Deimos.

Correct: (B) Venus is Earth's "twin" (p. 472-3).

 

4) Mars has a sufficient mass and a low enough temperature that water molecules could exist in its atmosphere. Why doesn't Mars's atmosphere contain a significant amount of water?

(A) Mars formed in a part of the solar nebula that lacked oxygen, (B) Mars formed in a part of the solar nebula that lacked hydrogen, (C) All of the water was released in the impact that formed Deimos, (D) Ultraviolet light from the sun breaks the water molecules into other molecules, (E) The water molecule combines readily with chlorine to form hydrochloric acid.

Correct: (D) According to Figure 22-15, Mars's gravity is strong enough to retain its water molecules (H2O) -- they will not escape into space (the point for Mars in the figure lies above the curve for H2O, indicating the planet's escape velocity is higher than the velocity of the H2O molecules in Mars's atmosphere). So where did they go? Mars has no ozone layer (like Earth does), so ultraviolet light from the Sun can enter Mars's atmosphere and break apart the H2O molecules, leaving H2 and O. The H2 is light enough to escape into space (the curve for H2 in Figure 22-15 is above the dot for Mars, indicating its molecules move faster than Mars's escape velocity), while the O stays and eventually bonds with iron in the soil to form rust. This process accounted for the gradual loss of water on Venus too.

 

5) The canals of Mars were found to be

(A) irrigation ditches dug by Martians, (B) faults in the Martian crust, (C) straight mountain ranges, (D) sinuous rilles, (E) an optical illusion.

Correct: (E) See page 484-5 and Figure 22-12. Sometimes people see what they want to see. Astronomers often think of Percival Lowell's bitterly embarrassing tale before they announce a new discovery. It reminds them to be critical of their own work -- to ask "have I presented enough evidence so that other people will believe my claim?"

 

6) Mars is intermediate in mass and radius between Earth and Earth's moon. Based on how fast different spheres cool, this tells us that

(A) the interior of Mars should be hotter than that of the Earth, (B) the interior of Mars should be cooler than that of the Earth, (C) the interior of Mars should be hotter than that of the moon, (D) the interior of Mars should be cooler than that of the moon, (E) answers B and C.

Correct: (E) Smaller spheres cool faster. Mars is smaller than the Earth, so should cool faster (answer B). Mars is larger than Earth's moon, so should cool more slowly than the moon (answer C). Therefore, we expect Mars's interior to be somewhere between Earth's (partly liquid iron core and semi-solid, "plastic"rocky mantle) and the moon's (solid all the way through). See page 490-1.

 

7) The flow patterns found on the surface of Mars suggest that

(A) today, Mars is a world rich in water, (B) the climate on Mars was warmer and wetter in the past, (C) there are may active volcanoes on Mars today, (D) the greenhouse effect is causing Mars's polar caps to melt, (E) the walls of the canals dug by the Martians were not strong enough and occasionally broke.

Correct: (B) The outflow channels and runoff channels (see p. 493-4 and Figures 22-20 and 22-21) indicate that water once flowed on Mars's surface. No liquid water is seen there today -- in fact, it couldn't because today Mars's atmosphere is to thin (liquid water would boil away due to the low pressure). Craters on the channels indicate they are old -- several billion years or so. The thinking is that Mars's atmosphere was thicker in the past (when the volcanoes were actively outgassing CO2), giving rise to a greenhouse effect that warmed the planet. A thicker, warmer atmosphere would allow liquid water to exist on the surface.

 

8) The shape and extreme size of the volcanoes of Mars indicates that

(A) the crust on Mars is very thin and flexible compared to Earth's crust, (B) water once flowed in streams on Mars, (C) large moving crustal plates did not form on Mars, (D) much of the gas destined for Mars's atmosphere was vented directly into space, (E) Martians are extremely enthusiastic mountain climbers.

Correct: (C) Volcanoes on Mars, like Olympus Mons, grow very large. The thinking goes that they stay fixed over a convective hotspot in Mars's mantle (a rising plume of hot lava) for many millions of years. Eruption after eruption, they grow larger and larger (see p. 491). Moving crustal plates like on Earth did not form on Mars (the Hawaiian Islands are a chain of shield volcanoes located over a hotspot, but the plate on which the volcanoes sit keeps moving slowly westward, "pulling the rug out from under" the volcanoes (review the centerfold on Volcanoes on pp.480-1).

Incorrect: (A) The volcanoes actually indicate that Mars's crust is thicker and stronger than Earth's, because large volcanoes like Olympus Mons do not have a "moat" around them (see p. 491 and the inset to Figure 22-18).

 

9) How rapidly a planet loses its atmosphere depends on

(A) the planet's escape velocity, (B) the composition of the planet's atmosphere, (C) the planet's rotation period, (D) the temperature of the planet's atmosphere, (E) answers A, B, and D.

Correct: (E) This goes back to Figure 22-15, an important Figure because it enables us to understand how the atmospheres on different planets survived or escaped into space. The dot for each planet is placed at the temperature of the planet's atmosphere (X-coordinate) and the escape velocity of the planet (Y-coordinate). The kinds gases that compose the atmosphere is important too -- light gases like H2 (two hydrogen atoms bonded together: atomic weight of 2) move faster, so have a higher curve than heavy gases like CO2 (two oxygen and one carbon atoms: atomic weight of 16+16+12 = 44).

 

10) Exploration of Mars by spacecraft

(A) has not yet happened because Mars is too far away from the Earth, (B) has consisted of a single flyby mission named Mariner 4, (C) has been extensive, including robotic missions that flew by, orbited, and landed on Mars, (D) has included two missions crewed by humans, (E) both C and D.

Correct: (C) The textbook mentioned Mariner 4, Viking, and Mars Global Surveyor. We talked more about these and other missions like Pathfinder in class. Spacecraft with human crews have not yet visited Mars (or any of the planets, only Earth's moon) -- it has been too expensive, robot spacecraft can do it more cheaply.

 

11) If the temperature of a planet's atmosphere is hot enough so that the speed of the molecules exceeds the planet's escape velocity,

(A) the atmosphere will cool off rapidly until the molecules' velocities are below the escape velocity, (B) the atmosphere will stay bound to the planet, (C) the atmosphere will gradually escape from the planet, (D) the planet's escape velocity will increase to compensate for the high temperature, (E) answers A and B.

Correct: (C) The gas temperature hotter than the escape velocity corresponds to the case in Figure 22-15 where the curve is above the line. The planet's gravity is not strong enough to prevent the gas molecules from escaping, and one by one, over time, they escape from the planet.

 

12) The moons of Mars are believed to be

(A) composed mainly of iron and nickel, (B) composed mainly of frozen water and carbon dioxide, (C) orbiting Mars in a direction opposite to the direction that Mars rotates, (D) formed from material ejected from Olympus Mons and other large volcanoes on Mars, (E) captured asteroids.

Correct: (E) These little, potato-shaped rocks look just like asteroids (see p. 497).

 

13) Astronomers have sketched out Mars's history. Which of the following is not part of the accepted story?

(A) the heavy bombardment covered Mars's early surface with craters; (B) volcanoes resurfaced some parts of Mars's original, cratered surface; (C) oceans, deeper than Earth's (over 3 km deep), once covered most of Mars's surface; (D) Mars differentiated into a iron core, a dense rocky mantle, and a lower-density rocky crust; (E) today, Mars is (or is nearly) geologically dead, and the surface changes only slowly due to erosion by wind-blown dust and very occasional impacts by larger meteoroids.

Correct: (C) Evidence suggests that water once did exist on Mars's surface, but not as much as answer C indicates. Some scientists think the smooth plains of the Northern hemisphere are an ancient seafloor (p. 490 and 496), but this covers less than half the planet (see Figure 22-17, the blue regions). On page 494, Seeds notes that if water was outgassed from lava flows, this would account for a planet-wide ocean about 20 meters (70 feet) deep -- nothing like 3000 meters suggested in answer C.

 

14) The points plotted in the graph below indicate the escape velocity of each planet along the vertical axis and the planet's surface temperature along the horizontal axis. The curves are the average speeds of gas particles as a function of temperature for various gases. Which of the planets listed below will retain ammonia gas (NH3), oxygen gas (O2), and carbon dioxide (CO2), while allowing its hydrogen gas (H2) and helium (He) to leak away into space?

(A) Earth, (B) Venus, (C) Mars, (D) Mercury, (E) Earth's moon.

Correct: (C) If the planet is to retain ammonia, oxygen, and carbon dioxide gases, the dot for the planet must be above the curves for these gases: Earth, Venus and Mars fit this criterion, while Mercury and Earth's moon do not (they are below one or more of these curves). If the planet is to retain its helium gas, the dot for the planet must be below the He curve: Mars, Mercury and the moon fit this criterion. Only Mars fits both criteria.

[The graph looks like Figure 22-15 in Seeds].


Andy Layden, Fall 2003.