THE SOLUTION TO Weekly Challenge 5: Dr. Jeff’s Interplanetary Travel Agency
Posted by DrJeff on August 7th, 2009
Filed under 1.1. Dr. Jeff's Weekly Challenge, 1.2. Solutions to Weekly Challenges, 4. The Earth, 5. Space Science, 5.1. Our Solar System, 5.1.2. The Moon, 5.1.3. Planets, 6. Cool Spacecraft
Copyright 2009 | About this blog
Read Original Challenge HERE.
This post is a Dr. Jeff’s Weekly Challenge.
Nice to see you again! Now that you’re back from your interplanetary romp through the Solar System, let’s see those cool photographs you took for the Dr. Jeff’s Interplanetary Travel Agency tour brochure.
[Hmmm …. silence.] You there?? Earth to my contracted photographer, you seem to be processing all this a bit slowly. I suspect you’re suffering from ‘rocket lag’. It’s perfectly understandable after traveling over 10 billion miles and visiting 7 worlds. I don’t think any photographer has ever been this dedicated. You’re clearly worth more than I’m paying you. So take a load off, and first re-read Weekly Challenge 5 to get back up to speed.
And now the answers—
Now that you’ve re-read Weekly Challenge 5, let’s take a look at those photographs and your notes.
I sent you to Earth’s Moon, and to moons of Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. What I wanted to know was how big each moon’s parent planet looks from that moon’s surface, compared to how big the Full Moon appears from the surface of Earth. As creatures living on the surface of Earth, we have a sense of how large the Full Moon looks. So using the Full Moon as a ruler of sorts, how many Full Moons across would, e.g., Neptune appear from the surface of its moon Triton?
The key is to recognize that the apparent size of the planet depends on the actual size of the planet and its distance from you. The larger the actual size of the planet, the larger it will appear. The more distant the planet, the smaller it will appear. The answers are below. I’ve described how I got the answers in the last section of this post.
Compared to the Full Moon in Earth’s sky:
From the Moon, Earth appears nearly 4 times wider than the Full Moon in Earth’s sky. Imagine the view, the continent of Africa—nearly 3 Full Moons across; the browns and greens of the land masses, the blues of vast expanses of ocean, and an ever-changing global arrangement of clouds afloat in the atmosphere. All this as Earth slowly rotates once every 24 hours, with whole continents passing from daylight, through a region of twilight, to darkness—or the reverse—depending on the phase of Earth as seen from the Moon. And since the same side of the Moon always faces Earth, from the Moon’s surface you see an Earth that never sets. It hangs forever in your sky. The sight must be beyond words.
From Phobos, Mars appears 80 times (!) wider than the Full Moon. Mars’ 4 largest volcanoes—Ascraeus Mons, Pavonis Mons, Arsia Mons, and Olympus Mons—all found in the same Tharis region on the planet, each appear more than 5 Full Moons across. And the Martian canyon system Valles Marineris—which is as long as the Continental U.S. (making the Grand Canyon look like a small ditch)—can be seen cutting across the face of Mars, appearing more than 50 Full Moons long.
As you look around on Phobos where you’re standing, you see it’s nothing more than a large rock whose edge is only 5 to 8 miles (9 to 13 km) in any direction. Hang on to something, because gravity is pretty weak here—and definitely don’t jump. Why? Well, imagine a jump on Earth where you rise to a height of 2 feet. The same jump on Phobos would take you 4,000 feet—3/4 mile—(1.2 km) above the surface. (I guess some of you are now going to want to jump. Think of the extreme sports you could dream up.)
From Io, Jupiter appears 37 times wider than the Full Moon. The largest planet in our Solar System, like Saturn, Uranus and Neptune, has no solid surface. You’re witnessing what might be described as an organized maelstrom, with bands of multicolored clouds that ring the planet interacting to form swirls and hurricane-like storms of immense size. One storm, the Great Red Spot—big enough to swallow 2 to 3 Earths—appears 9 Full Moons across.
On the Ionian horizon, thankfully a good distance from where you are standing, multiple volcanoes are seen erupting with plumes shooting hundreds of miles into the sky.
From Tethys, Saturn appears 45 times wider than the Full Moon; but Saturn’s visible rings are much wider than Saturn. From Tethys the ring system would be 105 Full Moons across! It is equivalent to sitting in the back row of an IMAX theater and Saturn is filling the massive screen. Tethys always presents the same side to Saturn, so from Tethys surface Saturn never sets. You see this immense planet, as if pinned in place to the starry sky, rotate once every 10.5 hours. Looking at the center of Saturn’s disk from the surface of Tethys, the planet rotates through the width of a Full Moon every 4 minutes. You can SEE the planet rotate. Like carefully watching a hand on a giant clock to truly see the flow of time, every 8 seconds you can noticeably see that the planet has turned.
Finally:
From Ariel, Uranus appears 29 times wider than the Full Moon
From Triton, Neptune appears almost 16 times wider than the Full Moon
From Charon, Pluto appears 13 times wider than the Full Moon
Our lives are constrained to the surface of Earth, which greatly limits our experiences. One day, something akin to Dr. Jeff’s Interplanetary Travel Agency will be a reality. Future generations will be able to book a trip, board a rocket at a local spaceport, and with some equipment changes along the way travel to these other worlds in our neighborhood. They will be able to see these remarkable sights for themselves, and talk to their children about an era not too long ago when these trips were only a vision of the future.
Teachers and Parents:
Explore with your child or your class the relationship between the APPARENT size of an object, the physicial size of the object, and the distance to the object. Here are some ideas:
1. A thumb is clearly a lot smaller than a person. Have kids explore how they can make their thumb APPEAR larger than a person. All they need to do is close one eye, and place their thumb at just the right distance from their open eye to cover up a person in the distance. Once the person is covered up, it’s clear their thumb APPEARS larger than the person. This demonstrates two things:
something small (your thumb) can APPEAR large if it’s placed close to you
something large (the person) can APPEAR small if placed at a great enough distance from you
2. Take a photo of kids that APPEARS to show them holding something really large in their hand, like a tree or a tall building. Position each child and the camera so that the child’s hand APPEARS big enough to hold the large object that’s obviously at a great distance.
3. Take what was learned in 1 and 2 above and discuss how this applies to what you might see in your sky from the surface of another world.
And now—how did I come up with those Answers?
Since we’re comparing the planet’s apparent size to the Full Moon, we’re interested in two things:
1) how much bigger is the planet’s diameter than that of Earth’s Moon? (The diameter of Earth’s Moon is 3,475 km.)
Let’s call this “SIZE”, where:
SIZE = planet diameter / Moon’s diameter
and
2) how much farther is the planet from its moon, than Earth is from Earth’s Moon? (The Earth-Moon distance is 384,400 km.)
Let’s call this “DISTANCE”, where:
DISTANCE = planet-moon distance / Earth-Moon distance
The apparent size of the planet in units of Full Moons = SIZE / DISTANCE
Some examples:
If SIZE = 10 (so planet is 10 x the diameter of the Full Moon), and DISTANCE = 10 (so planet-moon distance is 10 x Earth-Moon distance) then SIZE/DISTANCE = 10/10 = 1 and the planet appears 1 Full Moon across.
If Size = 10 (so planet is 10 x the diameter of the Full Moon), and DISTANCE = 0.5 (so planet-moon distance is 1/2 Earth-Moon distance) then SIZE/DISTANCE = 10 / 0.5 = 20, and the planet appears 20 Full Moons across!
Here are the answers:
Earth diameter: 12,756 km; SIZE = 3.7 Moon diameters
Earth-Moon distance: 384,400 km; DISTANCE = 1 Earth-Moon distances
SIZE / DISTANCE = 3.7 / 1 = 3.7 Full Moons Across
Mars’ diameter: 6,792 km; SIZE = 1.95 Moon diameters
Phobos-Mars distance: 9,380 km; DISTANCE = 0.0244 Earth-Moon distances
SIZE / DISTANCE = 1.96 / 0.0244 = 80.3 Full Moons Across
Jupiter’s diameter: 142,984 km; SIZE = 41.1 Moon diameters
Io-Jupiter distance: 421,600 km; DISTANCE = 1.1 Earth-Moon distances
SIZE / DISTANCE = 41.1 / 1.1 = 37.4 Full Moons Across
Saturn’s diameter: 120,540 km; SIZE = 34.7 Moon diameters
Tethys-Saturn distance: 294,700 km; DISTANCE = 0.77 Earth-Moon distances
SIZE / DISTANCE = 34.7 / 0.77 = 45.1 Full Moons Across
Saturn’s Diameter across visible rings: 280,400 km; SIZE = 80.7 Moon diameters
Tethys-Saturn distance: 294,700 km; DISTANCE = 0.77 Earth-Moon distances
SIZE / DISTANCE = 80.7 / 0.77 = 104.8 Full Moons Across
Uranus’s diameter: 51,120 km; SIZE = 14.7 Moon diameters
Ariel-Uranus distance: 191,200 km; DISTANCE = 0.5 Earth-Moon distances
SIZE / DISTANCE = 14.7 / 0.5 = 29.4 Full Moons Across
Neptune’s diameter: 49,530 km; SIZE = 14.3 Moon diameters
Triton-Neptune distance: 354,800 km; DISTANCE = 0.92 Earth-Moon distances
SIZE / DISTANCE = 14.3 / 0.92 = 15.5 Full Moons Across
Pluto’s diameter: 2,340 km; SIZE = 0.67 Moon diameters
Charon-Pluto distance: 19,400 km; DISTANCE = 0.05 Earth-Moon distances
SIZE / DISTANCE = 0.67 / 0.05 = 13.4 Full Moons Across
Photo credit: Michael Collins (NASA)
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