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Challenge Questions




Final Challenge Question 9 (April 27, 1996):

This question is focused on Mars, which is the subject of the next Passport to Knowledge adventure. This project, called Live From Mars, promises to be lots of fun for everybody. In that spirit we bring you this last Challenge Question :

Question:
Let's say you have just been appointed Baseball Commissioner for Mars. You would like the game to be similar in difficulty to the game as played on Earth. With that in mind, how far back should you place the center field fence (so that it is just as hard to hit a home run).

Assume that a center field fence on Earth is 410 feet from home plate.

Answer Answer from Alan Federman:
As a first approximation, we need to look at the relevant equation:

    F = MA Force is equal to Mass times Acceleration.

The acceleration we are interested in, is due to the gravity field of Mars. Mars gravity is equal to 0.38 of Earth's, so as a first approximation, the "A" on Mars is .38 * 980 cm/s/s = 370 cm/s/s. If the Force of Gravity were the only effect on the ball, 410ft / 0.38 = 1079 feet (or 323 meters).

To make the game "play the same" Other factors need to be considered. For example, atmospheric effects. The thin atmosphere means less air resistance so balls will carry further. How fast people can run wearing space suits, would also be a problem. Maybe changing the mass of the players and their equipment is an option.

While rain-outs are not going to be a problem, games may need to be called on account of wind or sandstorms!

Good Luck, Commish!

Answer from Bryan Glenn:
The old baseball Commish will have quite a problem on his hands placing that fence in the right location. There are actually 2 variables he will have to consider, gravitational differences and atmospheric differences. Both will have a significant impact, but the latter will be much less predictable that the first.

When gravitation is compared, Earth's would be +/- 978 cm/sec2, while Mars' is estimated @ 371cm/sec2. 978/371= 2.64, so the 410 ft x 2.64 = 1081ft. That would seem a mighty drive for anyone, if the two atmospheres were comparable. But they are anything but!

Earth's gravity and Venus' gravity are almost identical, but if we were putting up a fence on Venus, a 410 ft fence might as well be 2 miles away. Atmospheric pressures on Venus are 100 times that of Earth, so driving a ball through that layer of carbon dioxide smog would require a mighty, mighty bat.

Mars' atmospheric pressure is estimated at 0.6% that of Earth's. Again, some quick calculations should yield the lower atmospheric drag on the bat and ball to determine the "atmospheric" adjustment. But it is not so simple; here again we cannot think of this in Earthly terms. The extreme thinness of the atmosphere and the generally colder temperatures will produce some very "Mars Only" considerations. This thin atmosphere is easily varied by minor climatic events that would produce far less change in Earth's heavier atmosphere. Martian temperature changes could easily produce sudden gusty winds roaring over 100 miles/hour. As winter approaches and more of the CO2 becomes crystallized at the poles, the already thin atmosphere will become even thinner. Parks near the poles will play far differently than those near the Martian equator. Home runs will be even easier to hit then, unless the ball runs into an unexpected 200 mile/hr blast of wind on its way to the fence!

Good luck commissioner. Your Martian game will add elements never dreamed of back on good ol' Earth!



Challenge Question 8 (April 22, 1996):

This Challenge Question is from our Pluto Planet Advocate, Marc Buie

Question:
If you want to tell what season it is on Pluto, which is a better tool to use: a thermometer or a barometer? And why?

Answer:
A barometer is a much better tool for determining Pluto's seasons. Pluto has a great deal of nitrogen frost on its surface. It also has gaseous nitrogen in its atmosphere. At any given time, there is an equilibrium between these two quantities. As Pluto moves closer to the sun, the extra solar energy is used to turn the frozen nitrogen frost into more gaseous nitrogen (as the equilibrium shifts). So the temperature of atmosphere doesn't increase; instead the atmospheric pressure rises. As long as there is more frozen nitrogen to absorb the extra energy (and turn to gas), the temperature will continue to remain steady.

The converse is true as Pluto moves away from the sun and receives less solar energy.

An analogy is a glass of water with ice cubes in it. As long as there is both water and ice, the water temperature will remain 32 degrees F. It doesn't matter if the glass of ice-water is in a hot desert or a frozen tundra. But in the hot environment, only once the ice melts will the temperature of the liquid will begin to rise.



Challenge Question 7 (April 15, 1996):

This Challenge Question is from our Neptune Planet Advocate, Heidi Hammel

Question:
There are many telescopes much larger than Hubble. The Hubble Space Telescope has a 2.4-meter mirror. At Mauna Kea Observatory alone, there are four telescopes with mirrors more than 3 meters across, including the world's largest telescope, the 10-meter Keck Telescope (more than 4 times bigger than Hubble!). Why is the Hubble Space Telescope so special?

Answer:
Most important, it is in outer space, above the Earth's atmosphere. This has two results. First, you get clearer sharper images, since you don't have to look through the atmosphere. Second, you can look at ultraviolet wavelengths, which are blocked by our ozone layer. Also, the mirror was made EXTREMELY carefully and precisely, much more precisely than the mirrors used in bigger ground-based telescopes.



Challenge Question 6 (April 8, 1996):

This Challenge Question is from Karla Peterson.

During December 1995, HST observed a fairly blank patch of sky for many days without interruption. This incredible picture of very distant and faint objects has been named the "Hubble Deep Field" and was revealed to the public in January.

Question:
What special property must a target have in order for HST to observe it for a long time without interruption?

Props to help work on the question:

  • globe (to represent the earth)
  • piece of wire (to represent the circular orbit of HST around earth - HST is in a very low orbit, only about 600 km off the earth)
  • bead (to represent HST in its orbit around earth)
  • protractor (to help you make the orbit have an inclination of 28 degrees - inclination is the angle between the orbit and the earth's equator)

Answer:
A target that has a declination near 62 or -62 degrees can be viewed for many days at a time. (Declination is sort of the celestial equivalent of latitude on the earth, but it doesn't turn with the earth.) This is because the earth does not block HST's view of the target. We call this the "continuous viewing zone" or CVZ.

How to use the props to see this:

1) Make a loop of wire that will fit around the equator of the globe with room to spare. (You might want to figure out exactly how far off the globe the wire should be to truly represent the height of HST off the earth.)

2) String the bead on the loop of wire.

3) Hold the orbit around the globe so that it is just above the equator. This would be a zero inclination orbit.

4) Now tilt the orbit so that the orbit crosses the equator, but the angle between the equator and orbit is about 28 degrees. (Remember that satellites orbit the center of the earth.)

5) So it is easy to demonstrate, make the orbit cross the equator at 90 degrees west longitude. and 90 degrees east longitude. Make the tilted up part of the orbit cross northern Africa and tilted down part of the orbit cross a little above New Zealand.

6) Now have someone stand with their hand directly above the Bering Straights (and at least a foot or two from the globe. Their hand represents the location of the CVZ (at about 62 degrees declination).

7) Move the bead around the orbit and notice that the earth never blocks the view of the CVZ point. (Note that there is also another CVZ point just east of the Sandwich Islands at about -62 degrees declination.)

8) Once you have that all lined up, forget about the positions on the globe, because the earth is actually turning around once every 24 hours while the stars in the sky stay still. The orbit is not fixed in space, but it turns more slowly than the earth. The orbit of HST precesses (just like a top precesses) once every 56 days. That means that the patch of sky which is in the CVZ now will be in the CVZ again in 56 days.



Challenge Question 5 (April 1, 1996):

This Challenge Question is from our Pluto Planet Advocate, Marc Buie. It is perhaps the toughest challenge so far.

Question:
Pick two spots on Pluto (other than the poles) that are on opposite hemispheres. From these two vantage points, describe the phases of the moon, Charon, that you would see. (Hint: there are two periods of time to worry about, one long and one short.)

Answer:
We have two different answers to this question, one from Marc Buie and another from Sanjay Limaye of the University of Wisconsin - Madison:

Marc Buie writes, "There are three parts to this answer."

1. Let's pick two spots on Pluto. To make life easy, both locations are on the equator, one at 0 degrees longitude (Pluto's equivalent of Greenwich, England), and one at 180 degrees longitude (Pluto's equivalent of the international date line). The trick here is knowing that the length of Pluto's day is exactly the same as Charon's orbital period. That means Pluto always presents the same face toward Charon and Charon always presents the same face toward Pluto. This is just what our own Moon does. What is different, is that standing on Pluto, Charon does not appear to move relative to the horizon. That means you never see a moonrise from Pluto's surface. This also means that over half the planet, you can never see Charon. The longitude system is defined such that 0 degrees longitude is in the center of the hemisphere that can see Charon. So, from 180 degrees you wouldn't see any phases at all. The rest of the answer will deal just with the side of Pluto where you can see Charon.

2. The quickest change in the phase of Charon happens during one orbit of Charon around Pluto. This orbit takes about 6.4 days. Let's consider the time when the Sun is directly over the equator. This time of "year" coincides with the start of spring. At "new" moon, Charon would be directly in front of the Sun and we'd see an eclipse. Then as Charon moves in it's orbit it would progress through the same phases that our own moon exhibits every month, taking only 6.4 days to complete the cycle.

3. Another longer term cycle also affects the phases and that is Pluto's orbit around the sun. Since Pluto's rotation axis is tipped on its side, it has very pronounced seasons. Unlike our Moon, Charon also undergoes the same exact seasons. The only time you'd see a completely full moon would be at the start of spring or fall. At the start of summer or winter, just over half the surface would be illuminated at its fullest, either the north or south polar regions depending on the season.

Marc has made illustrations available which may help you better understand this complex answer.

Sanjay Limaye from the University of Wisconsin - Madison writes:
What an excellent question! However, the answer is not easy unless you are familiar with the Pluto/Charon geometry. Let's begin at the beginning.

To describe the phase of Charon from Pluto requires a knowledge of
1) Charon's orbit around Pluto
2) Pluto's orbit around the Sun
3) the orientation of Pluto in orbit

Remember, that "phase" describes the amount of illumination from the Sun, so we need to determine the relative positions of the Sun and Charon as seen from a point on the surface of Pluto.

Pluto's orbital is now relatively well known, although future improvements are likely since Pluto has now been observed since its discovery in 1930 for less than one third of its orbit around the sun (one Pluto year equals 248 earth years). Its orientation has been determined from the knowledge of the orbit of its moon, Charon, which has a period of 153 hours 18 minutes (6.38722 days) around Pluto. Charon is believed to be in synchronous rotation around Pluto, meaning that Pluto must also rotate about itself in the same period, 6.38722 days. Further, Charon's orbit is believed to mark the equatorial plane of Pluto, i.e. the spin axis of Pluto is parallel to that of Charon. This direction can be described by the location of Pluto's 'pole' position, or the positive spin axis (don't look up any books on astronomy, you won't find this information there!) which is at 311.63 degrees right ascension and 4.18 degrees declination (right ascension and declination are astronomical equivalents of longitude and latitude in the equatorial co-ordinate system). But exactly where is this direction? Unless you can visualize RA and Dec values into position in the sky, here is a clue. Between 1985 and 1990, we know that earth was in the plane containing the orbital plane of Charon (and hence Pluto). This how the surface of Pluto was first mapped, by observing the obscuration of Pluto by Charon every 153h1 18m apart as Charon came in front of Pluto and went behind it as it moved in its orbit. It is easy to locate earth and Pluto during that period, and that gives a good idea of the orientation of Charon's orbit around Pluto, and hence of where Pluto's spin axis is pointed at. We need to know to see how the phase of Charon would appear from Pluto.

Since the orientation of the spin axes does not change as Pluto and Charon move in their respective orbits, it is clear that at some point in future, roughly a quarter of the orbital period from about 1985, or, around 2050 (=1987+248/4), the equatorial plane would be normal (90 degrees) with the direction to the Sun. At that point, from any point on Pluto, the phase of Charon would be half moon, continuously, from either the north or the south hemispheres of Pluto, and in fact, the entire northern hemisphere of Pluto will be in continuous sunlight and the southern hemisphere will be in continuous darkness (ignoring for the moment the orbital inclination of Pluto, which is actually substantial, 17 degrees). This situation will change when Pluto changes its orbital position enough so that its spin axis is sufficiently away from the direction to the sun from Pluto, until half an orbital period later, when it will recur, except that the dark and lit hemispheres of Pluto will be switched. In between, roughly half an orbital period from 1985-1990, the earth will pass again through the Charon orbital plane, recreating the mutual eclipse events. At that time, Charon will undergo a complete change between new moon and full moon every 153 hours. Of course, Charon and solar eclipses will also occur occasionally,

At other times in its orbit, Charon will depict crescent and gibbous phases repeating every 153 hours or so, never achieving full phase or new moon.



Challenge Question 4 (March 25, 1996):

This Challenge Question is from our Neptune Planet Advocate, Heidi Hammel.

Question:
If your spaceship needed some emergency repairs, and you were in the vicinity of Neptune, where would you decide to land? Why there?

Answer:
You couldn't land on Neptune. Before you got deep enough to find a solid surface to land on, the weight of the atmosphere above you would crush your spaceship. The best place to land would be the moon Triton.



Challenge Question 3 (March 18, 1996):

This Challenge Question is from our Pluto Planet Advocate, Marc Buie. It's a tough one, so you will have to really do some critical thinking!

Question:
You are packing for your vacation on Pluto. Of course, you want to bring along your camera to take pictures of the fantastic scenery. What would happen to your photography plans if you forgot to bring you camera's tripod?

Answer:
The basic answer comes from knowing that Pluto is much further from the Sun than we are here on Earth. That greater distance means that sunlight will be fainter. How much? Pluto is currently at 30 AU (Astronomical Units) which means it is 30 times further from the Sun than the Earth (that's right Earth is at 1 AU from the Sun). There is a law in physics known as the "inverse square law" that means if you move twice as far away from a light bulb (or star) that the light bulb will appear four times fainter. So, you take the distance, square it and that is how much fainter. For Pluto at 30 AU, this means that the Sun appears to be 30 * 30 or 900 times fainter than what we see here on Earth.

To fully answer this question, it helps to know a little about photography. First, a tripod is needed to hold a camera steady when you using really long (slow) exposures. I find that for a normal 50mm camera lens (the most common) you can take hand held pictures if the exposure time is 1/60 sec or faster.

Now, when taking a picture, there are three things you can control about your camera to adjust for different light conditions.

  • Exposure time (how long you let light hit the film)
  • Film speed (This is the ISO or ASA number like 100 or 200)
  • Lens aperture (This makes then lens collect more or less light)

A typical sunlight day with no clouds at noon would require these settings:

  • 1/125 second exposure time
  • f/11 aperture
  • 100 ASA film

So how would you adjust your camera settings for Pluto? If you expose the film for twice as long, then twice as much light can hit it. If you open the aperture wider you let more light in. This is a little trickier to figure out but the smaller the number, the more light you collect. An f/11 aperture lets 4 times as much light in as an f/22 aperture (factor of 2 on the number is a factor of 4 for light hitting the film). Finally, if you double the ASA rating, then the film is twice as sensitive to light.

So we need to adjust these settings by a factor of 900 to get a good picture on Pluto. We only have one notch to go on exposure time. If we set it to 1/60 second then we've adjusted by only a factor of 2, not nearly enough. Next, lets open the lens aperture to let more light in. My camera lens goes to f/1.8. Compared to f/11, that would let in 11/1.8 * 11/1.8 more light in, or a factor of 38 more light. Combined with the change in exposure time, we now have adjusted by a factor of 76, still not enough. If we don't change our film, we would definitely need a tripod since we'd have to use a 1/4 second exposure to record the scenery.

We could have planned ahead though and brought more sensitive film. You can get pretty good stuff that is 1000 ASA or 10 times more sensitive. That would do the job nicely. So, for Pluto, you'd set your camera to

  • 1/60 second exposure time
  • f/1.8 aperture
  • 1000 ASA film

and you wouldn't need a tripod. But, if you had a telephoto lens, you would definitely need a tripod because they need faster exposure times. Don't worry too much if all these adjustment factors don't come out to exactly 900. Film is pretty forgiving and you can still take a good picture even if thing are either a little too bright or a little too dark. The actual factor is 760 but that is close enough to 900 to work.

If you have access to a good camera, you might try a little experiment. Good 35mm cameras have a light meter built in that tells you how bright the scenery is that you point your camera at. You can put in these camera settings and adjust the brightness in a room by turning lights on or off until the camera tells you these settings will work to take a picture. When you match these settings and the light is right then you have just simulated how bright the light will be on Pluto.

I found that a room with the drapes drawn and no direct sunlight hitting the drapes on a sunny day is just about right. You could still read a book see colors, and there would be noticeable shadows. Similarly dark lighting would be during a strong thunderstorm here on Earth though that level of lighting would be in full Sun on Pluto (no clouds).



Challenge Question 2 (March 11, 1996):

Background Information:
Ancient astronomers noticed that as the stars seemed to move about the sky (as if they were lights attached to the inside of some great rotating sphere) they always stayed in the same positions relative to each other. The astronomers imagined patterns in the night sky we call constellations and named them for familiar objects: "Orion" the Hunter, The Great Bear, The Scorpion, etc.

But there were some lights that DID move! These wandered across a particular path in the sky they called the Zodiac. The Greeks called them "Planets" or "Wanderers". (We HST folks call them "Moving Targets").

To solve this Challenge Question, you will need a good star chart that shows right ascension and declination and the boundaries of the constellations (see page 23 of Teacher's Guide). You may have to dig a little to solve the following two-part riddle:

Question:
Use your tables and a star chart from the Library or a source like Sky and Telescope or Astronomy magazine to...

  • 1) determine what constellation Uranus and Neptune are near on March 14
  • 2) find out which planet is closest to Libra and Scorpio on March 14

Answer:

  • 1) Uranus and Neptune are near Capricorn on March 14
  • 2) Libra and Scorpio are closest to Scorpio on March 14



Challenge Question 1 (March 4, 1996):

Question:
Earth is often called "The Blue Planet." Neptune is sometimes called "The Other Blue Planet."
Why is Earth blue? Why is Neptune blue?

Answer:
Earth is blue because it is mostly covered in water, and water scatters blue light.

Neptune is blue for two reasons, and neither has anything to do with water. The atmospheric gas that has the most effect on Neptune's color is methane, and methane molecules absorb red light. Take away the red light, and what do you have left? Blue. Also, the particles in Neptune's clouds are actually slightly bluish in color. Both things make the planet blue.

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