Structure of the cosmos

Where the answer comes from: the table's orbital-period column lists Jupiter at 11.86 Earth years.

Step by step:

1. Find the column "Orbital period (Earth years)."
2. Look for the value closest to 12: Mars 1.88, Jupiter 11.86, Saturn 29.46, Neptune 164.8.
3. 11.86 rounds to about 12.

The answer is Jupiter.

Tip: Before answering a table question, point to the exact column the question names. Tables often have several columns of similar-looking numbers.

Where the answer comes from: the table lists Mercury (0.39 AU) at 167 °C and Venus (0.72 AU) at 464 °C. The notes say "Venus has a very thick atmosphere made mostly of carbon dioxide, a gas that traps heat" and "Mercury has almost no atmosphere."

Step by step:

1. In order of distance, temperatures are 167, 464, 15, −65, −110, −140, −195, −200.
2. Every value falls except one: Venus (464 °C) is hotter than Mercury (167 °C), even though Venus is farther from the Sun.
3. The notes give the reason: Venus's thick carbon dioxide atmosphere traps heat (a strong greenhouse effect), and Mercury has almost no atmosphere to hold heat in.

The answer is Venus, because its thick carbon dioxide atmosphere traps heat.

Tip: To find what breaks a pattern, list the data in order and look for the one value that goes the wrong way. Then look in the passage for an explanation.

Where the answer comes from: the table's diameter column: Ceres 940 km, Pluto 2,377 km, Haumea about 1,600 km, Makemake 1,430 km, Eris 2,326 km.

Step by step:

1. Look only at the last column, "Diameter (km)."
2. The two largest values are Pluto (2,377 km) and Eris (2,326 km).
3. Compare digit by digit: 2,377 is greater than 2,326 by 51 km.

The largest dwarf planet by diameter is Pluto.

Check: Eris is the farthest dwarf planet and has the longest orbital period, which tempts readers to pick it, but it is slightly smaller ✓.

Tip: Say the column name to yourself before you compare values. Being biggest in one column (distance) does not mean biggest in another (size).

Where the answer comes from: the table rows "| B | 10,000–30,000 | Blue-white | Rigel |", "| G | 5,200–6,000 | Yellow | The Sun |", "| K | 3,700–5,200 | Orange | Arcturus |" and "| M | 2,400–3,700 | Red | Proxima Centauri |".

Step by step:

1. Find each star's class: Rigel B, the Sun G, Arcturus K, Proxima Centauri M.
2. Class B is 10,000–30,000 K, hotter than G (5,200–6,000 K), K (3,700–5,200 K) and M (2,400–3,700 K).
3. The passage also says "The hottest stars glow blue." Rigel is blue-white.

The hottest star is Rigel.

Check: Even the coolest B star (10,000 K) is hotter than the hottest G star (6,000 K) ✓.

Tip: Star colors run opposite to everyday hot-and-cold color labels: in stars, blue is hottest and red is coolest.

Where the answer comes from: the table lists January 3 as "147.1 million km (closest)" with the Northern Hemisphere in "Winter," and July 4 as "152.1 million km (farthest)" in "Summer."

Step by step:

1. If being closer to the Sun caused summer, the Northern Hemisphere would have summer when Earth is closest.
2. The table shows the opposite: Earth is closest in early January, during Northern Hemisphere winter.
3. So distance cannot be the cause. (The tilt is: it changes the Sun's height and the length of daylight.)
4. The daylight and Sun-height data are true, but they describe what happens in each season. They don't test the distance idea.

The best evidence is that Earth is closest to the Sun in early January, during Northern Hemisphere winter.

Tip: To disprove a cause, look for a case where the supposed cause is present but the effect is the opposite.

Where the answer comes from: the passage says Earth's axis is tilted 23.5° and "always points in the same direction in space," and the table shows Northern Hemisphere winter on January 3. The diagram shows that in December the Northern Hemisphere is "tilted away" from the Sun.

Step by step:

1. On January 3 the Northern Hemisphere is tilted away from the Sun, so it has winter.
2. Earth is one solid ball. If the north half tips away, the south half tips toward the Sun.
3. Tipped toward the Sun means a higher noon Sun and longer days, so Australia has summer.
4. Earth happens to be closest to the Sun then, but that is not the reason. The passage's data show distance does not cause seasons.

It is summer in Australia, because the Southern Hemisphere is tilted toward the Sun.

Tip: A choice can have the right fact and the wrong reason. Check both parts.

Where the answer comes from: the table and the passage: tidal range is "the difference in height between high tide and low tide," and "The Sun's gravity also produces tides."

Step by step:

1. Tidal range for each day:
   • Day 1 (new moon): 2.9 - (-0.3) = 3.2 m
   • Day 8 (first quarter): 2.2 - 0.4 = 1.8 m
   • Day 15 (full moon): 2.8 - (-0.2) = 3.0 m
   • Day 22 (third quarter): 2.1 - 0.5 = 1.6 m
2. The largest ranges are on Days 1 and 15, at new moon and full moon.
3. At both new and full moon, the Sun, Earth and Moon are in a straight line, so the Sun's tidal pull adds to the Moon's. Higher highs and lower lows result. These are called spring tides. At the quarter phases, the Sun and Moon pull at right angles and partly cancel, giving small neap tides.

The answer is Days 1 and 15, because the Sun, Moon and Earth are lined up and their pulls combine.

Tip: Subtracting a negative low tide makes the range bigger: 2.9 - (-0.3) = 3.2, not 2.6.

Where the answer comes from: the passage says "In a lunar eclipse, Earth passes between the Sun and the Moon, and Earth's shadow falls on the Moon, so it can happen only at full moon."

Step by step:

1. Earth's shadow always points away from the Sun, toward the right side of the diagram.
2. The Moon can enter that shadow only when it is directly behind Earth: position 5.
3. At position 5, Earth is between the Sun and the Moon, which is full moon. That matches the passage.
4. Position 1 is where a solar eclipse could occur (the Moon's shadow falls on Earth).

The answer is position 5, because Earth is between the Sun and the Moon.

Tip: Solar eclipse = the Moon blocks the Sun (new moon). Lunar eclipse = Earth's shadow covers the Moon (full moon). The name tells you what gets darkened.

Where the answer comes from: the graph shows speed rising steadily with distance, from Galaxy A (50 million light-years, 1,100 km/s) to Galaxy E (470 million light-years, 10,200 km/s). The passage says redshift means a galaxy is "moving away from us," and "an observer in any galaxy would see the other galaxies moving away in this same pattern."

Step by step:

1. All five galaxies are moving away (all are redshifted with positive speeds).
2. The farther the galaxy, the faster it recedes. The points lie close to a straight line through the origin.
3. This is exactly what happens if space itself is expanding: every galaxy moves away from every other one.
4. Because observers in every galaxy would see the same pattern, it does not put us at the center.

The best conclusion is that the universe is expanding, with more distant galaxies moving away faster. This evidence supports the Big Bang theory.

Tip: Reject conclusions that go further than the evidence ("we are at the center") or that reverse the trend.

Where the answer comes from: the passage says "The Moon's orbit is tilted about 5° compared with Earth's orbit around the Sun. So in most months, the new moon passes a little above or below the Sun." Eclipses happen "only when a new or full moon occurs near one of the two points where the Moon's orbit crosses the plane of Earth's orbit."

Step by step:

1. A solar eclipse needs the Moon directly between the Sun and Earth.
2. Every new moon, the Moon is roughly between them, but because of the 5° tilt it usually passes a little above or below the Sun–Earth line.
3. Then the Moon's shadow misses Earth, so there is no eclipse.
4. Only when new moon happens near a crossing point does the shadow land on Earth.

The answer is the Moon's orbit is tilted about 5°, so at most new moons its shadow passes above or below Earth.

Tip: Do not confuse the Moon's 5° orbital tilt (eclipses) with Earth's 23.5° axis tilt (seasons). Match the number to the topic.

Where the answer comes from: the passage says "When a light source moves away from an observer, its light waves are stretched to longer, redder wavelengths. This is a redshift." The table also lists Galaxy K as moving "Away from us" at 2,600 km/s.

Step by step:

1. A redshift means the light waves are stretched.
2. Light is stretched when the source moves away from the observer.
3. So Galaxy K is moving away from the Milky Way, as the table confirms.
4. A redshift does not mean the galaxy looks red or is cool; it describes a shift in the wavelengths of all its light.

The answer is Galaxy K is moving away from us.

Check: Andromeda, which moves toward us, shows the opposite, a blueshift ✓.

Tip: Remember red = recede (move away), blue = approach.

Where the answer comes from: the passage says that at new moon and full moon "the bulges add together. This gives spring tides, with the highest highs, the lowest lows and the largest tidal range." In the table, the lowest lows were −0.2 m (new moon) and −0.1 m (full moon), while the quarter moons had lows of 0.6 m and 0.7 m.

Step by step:

1. The group needs the lowest low tides.
2. The lowest lows come with spring tides, at new moon and full moon.
3. April 24 is a full moon, so the tides near April 24 should give the lowest lows.
4. About a week earlier is the first quarter moon, which gives neap tides with higher lows.

The best choice is April 24, at the full moon.

Tip: For tide questions, link the phase to the alignment: lined up (new or full) = extreme tides; right angle (quarters) = mild tides.

Where the answer comes from: Table 1 gives main-sequence lifetimes of "about 32 million years" for 10 solar masses and "about 10 billion years" for 1 solar mass. The passage says a star with "more than about 8 times the Sun's mass" explodes as a supernova, leaving a neutron star or black hole.

Step by step:

1. Star X: 100 million years is more than its 32-million-year lifetime, so it has already left the main sequence.
2. At 10 solar masses (more than 8), it becomes a red supergiant and then a supernova, leaving a neutron star or black hole, not a white dwarf.
3. Star Y: 100 million years is only 1% of its 10-billion-year lifetime (0.1 \div 10 = 0.01), so it is still on the main sequence.
4. Notice the pattern: more massive stars burn their fuel much faster, so they live shorter lives.

The answer is Star X has likely already exploded as a supernova, while Star Y is still a main-sequence star.

Tip: Watch units in tables: "million" and "billion" differ by a factor of 1,000. Also, bigger stars live shorter lives, which surprises many test takers.

Where the answer comes from: the table shows that the orbital period always gets longer with distance: 2.8 AU → 4.6 yr, 39.5 → 248, 43.1 → 284, 45.8 → 306, 67.7 → 559.

Step by step:

1. 50 AU lies between Makemake (45.8 AU, 306 years) and Eris (67.7 AU, 559 years).
2. So the period should be between 306 and 559 years.
3. 50 AU is much closer to Makemake's distance than to Eris's, so the period should be closer to 306 than to 559.
4. About 350 years is the only choice in that range.

The most likely period is about 350 years.

Check: Kepler's third law gives \sqrt{50^3} \approx 354 years, confirming the estimate ✓.

Tip: To predict from a table, bracket the new value between its two nearest neighbors first. Any answer outside that bracket can be crossed out.

Where the answer comes from: the table lists Galaxy L at a distance of "300" million light-years. A light-year is the distance light travels in one year.

Step by step:

1. If a galaxy is 300 million light-years away, its light needs 300 million years to reach us.
2. So the light arriving tonight left Galaxy L about 300 million years ago.
3. The photo shows Galaxy L as it looked then, not as it looks today.
4. (Because the universe is expanding, this is an approximation, but it is the best answer from the data given.)

The light left Galaxy L about 300 million years ago.

Check: The same idea applies close to home: sunlight is 8.3 minutes old when it reaches us, because the Sun is 8.3 light-minutes away ✓.

Tip: Distance in light-years = travel time in years. Looking far away means looking back in time.

Where the answer comes from: the sample table (Earth rocks "about 4.0 billion years," zircon grains "about 4.4 billion years," Moon rocks "about 4.5 billion years," meteorites "about 4.57 billion years") and the passage: "Plate tectonics and erosion constantly recycle Earth's surface, so very old Earth rocks are rare. Most meteorites have changed very little since they formed along with the solar system."

Step by step:

1. Meteorites formed along with the solar system and have barely changed, so their age (about 4.57 billion years) dates the solar system's formation.
2. Earth formed as part of the solar system, so it is about the same age.
3. Earth's oldest rocks (4.0 billion years) are younger because Earth's early surface has been recycled. The rocks show only a minimum age.
4. Moon rocks (4.5) and zircon grains (4.4) are consistent with this.

The best-supported conclusion is the solar system, including Earth, formed about 4.5–4.6 billion years ago, and Earth's oldest rocks are younger because Earth's surface has been recycled.

Tip: The oldest rock you can find gives a minimum age. Look for the passage's reason why older material is missing.

Where the answer comes from: the passage says "For stars in the long, stable main sequence stage, more massive stars are hotter, bluer and brighter, and they use up their fuel much faster. So massive blue stars live only millions of years, while small red stars can shine for many billions."

Step by step:

1. Star P is blue, so it is hot, which on the main sequence means it is more massive.
2. Star Q is red, so it is cooler and less massive.
3. More massive stars burn fuel much faster, so Star P will have the shorter life.

The answer is Star P is more massive than Star Q and will have a shorter life.

Check: The table agrees on temperature: blue stars (O and B) are above 10,000 K, while red M stars are 2,400–3,700 K ✓.

Tip: Big stars live fast and die young. More fuel does not mean a longer life, because a massive star burns it much faster.

Where the answer comes from: the table shows Andromeda at 2.5 million light-years moving toward us, while every other galaxy moves away, faster with distance. The passage explains: "Over short distances, the gravity between neighboring galaxies can be stronger than the expansion and pull them toward each other."

Step by step:

1. Galaxies J, K, L and M all move away, and their speeds rise with distance (1,100 → 2,600 → 6,600 → 13,200 km/s).
2. Andromeda moves toward us, the opposite direction, so it is the exception.
3. Andromeda is by far the closest (2.5 million light-years), so the pull of gravity between it and the Milky Way is strong enough to beat the expansion.

The answer is Andromeda, because it is close enough that gravity pulls it and the Milky Way together.

Check: Galaxy J is the closest receding galaxy and the slowest, which fits the pattern ✓.

Tip: When asked to explain an exception, look for a special condition that applies only to that case (here, being very close).

Where the answer comes from: the passage says "On the two days of the year when neither hemisphere is tilted toward the Sun, the equinoxes, day and night are each about 12 hours long almost everywhere on Earth." In the diagram, the axis leans sideways at positions B and D.

Step by step:

1. At A, the North Pole leans toward the Sun: long days in Chicago, short days in Sydney.
2. At C, the North Pole leans away from the Sun: short days in Chicago, long days in Sydney.
3. At B and D, the axis leans to the side, neither toward nor away from the Sun. These are the equinoxes.
4. At the equinoxes, both cities have about 12 hours of daylight.

The answer is positions B and D.

Check: The two hemispheres always have opposite seasons, so the only time they can match is when neither is tilted toward the Sun ✓.

Tip: Solstices are the tilt-toward and tilt-away positions; equinoxes are the two in between.

Where the answer comes from: the passage says carbon-14 has a "half-life 5,730 years" and "can date once-living things up to about 50,000 years old; older samples have too little carbon-14 left to measure." It adds that "To date rocks that are millions or billions of years old, geologists use isotopes with long half-lives."

Step by step:

1. 2 billion years is about 2{,}000{,}000{,}000 \div 5{,}730 \approx 349{,}000 carbon-14 half-lives.
2. After even 10 half-lives, less than 0.1% remains. After hundreds of thousands, essentially none is left to measure.
3. Carbon-14 is also used for remains of once-living things, not volcanic rock.
4. Potassium-40 (half-life 1.25 billion years) or uranium-235 (704 million years) would suit a 2-billion-year-old rock.

The answer is carbon-14's half-life is so short that virtually none would remain to measure.

Tip: Match the clock to the job: choose an isotope whose half-life is not tiny compared with the age you expect.

Where the answer comes from: the decay graph shows 25% remaining after 2 half-lives. The table gives potassium-40's half-life as 1.25 billion years. The passage says Earth is "about 4.6 billion years old."

Step by step:

1. Count halvings: 100\% \to 50\% \to 25\%, so 2 half-lives.
2. Age: 2 \times 1.25 \text{ billion} = 2.5 \text{ billion years}
3. Compare: 2.5 billion years is less than Earth's 4.6 billion years, so the result makes sense. A rock can't be older than the planet.
4. Carbon-14 would be useless here: its half-life (5,730 years) is far too short, and it dates remains of living things only up to about 50,000 years.

The best conclusion is that the rock is about 2.5 billion years old, which fits within Earth's age of about 4.6 billion years.

Tip: Match the isotope to the age range. Short half-lives date young samples; long half-lives date old rocks.

Where the answer comes from: the passage says a star "with more than about 8 times the Sun's mass" becomes a red supergiant, fuses elements "up to iron," and "explodes as a supernova, scattering these elements into space, where they can become part of new stars and planets." The core becomes a black hole "if the star began with more than roughly 20–25 times the Sun's mass."

Step by step:

1. 30 solar masses is more than 8, so the star follows the massive-star path: red supergiant, then supernova.
2. 30 is also more than 20–25, so the collapsed core becomes a black hole, not a neutron star.
3. The supernova scatters heavy elements into space, where they can become part of new stars and planets.
4. A massive star also lives a short life, only millions of years.

The most likely future: it becomes a red supergiant, explodes as a supernova that scatters heavy elements into space, and leaves behind a black hole.

Tip: When a passage gives cutoff numbers, place the star's mass on that number line first. Then read off its path.

Where the answer comes from: the passage says Hubble found "nearly all galaxies show redshifts and that farther galaxies are moving away faster," which is "strong evidence that the universe is expanding." It also says nearby galaxies can be pulled together by gravity, and that the cosmic microwave background supports the Big Bang.

Step by step:

1. Expansion predicts redshifts for distant galaxies, larger for farther ones.
2. The opposite, blueshifts for most distant galaxies with the farthest approaching fastest, would mean the universe is contracting. That contradicts expansion.
3. A nearby galaxy moving toward us is already explained by gravity (like Andromeda), so it does not contradict expansion.
4. Finding the cosmic microwave background again supports the Big Bang, and the color of stars does not test expansion at all.

The strongest contradiction would be finding that most distant galaxies show blueshifts, with the farthest ones approaching fastest.

Tip: To find evidence that would contradict a theory, state what the theory predicts, then look for the reverse of that prediction on a large scale.

Where the answer comes from: the table gives Betelgeuse's distance as "about 550 light-years," and the passage says "we always see a distant object as it was when its light left it, not as it is today."

Step by step:

1. Light from Betelgeuse takes about 550 years to reach Earth.
2. If the star exploded 200 years ago, the light from the explosion has traveled for 200 years, covering 200 light-years.
3. It still has 550 - 200 = 350 light-years to go.
4. So people on Earth would first see the explosion about 350 years from now. Today we still see Betelgeuse as it was 550 years ago, before the explosion.

The answer is about 350 years from now.

Check: Explosion 200 years ago + 350 more years = 550 years of travel, matching the distance ✓.

Tip: In look-back problems, compare the travel time with the time since the event. If the light is still on its way, the event is in our future.