You are invited to send original student answers to us. We will list the names of these folks online and token prizes will be given out to a small number of the students with the best answers. Send your answers to Jan Wee at jwee@mail.arc.nasa.gov. PLEASE include the words "CHALLENGE QUESTION" in the subject of the email.

Question #6: Week of November 18, l996

Here is our last puzzler:
The Mars Global Surveyor (MGS) took off in November and is scheduled to arrive at Mars between Sept. 11 and Sept. 22, 1997. The Mars Pathfinder (MPF) takes off sometime in December. No matter when it leaves, it is scheduled to arrive on July 4, 1997.

Why does the Pathfinder get to Mars earlier, even though it leaves later?

And how can the Pathfinder have an exact arrival date even though its liftoff date may vary?

Answer from Cheick Diarra:

There are several reasons for Pathfinder's earlier arrival at Mars. Pathfinder is much smaller and lighter than Mars Global Surveyor. As a result, the rockets sending it to Mars can get it going at a faster velocity. Also, Pathfinder goes on a much more direct route to Mars than MGS, which takes a longer, more looping path. So not only is MPF going faster, it has less miles to travel.

There is a good reason for MGS's more looping path. The arrival velocity depends on the type of trajectory. The more looping trajectory provides a slower arrival velocity. Since MGS is an orbiter, NASA wants it to arrive at Mars with as little speed as possible. This is because it will need to be slowed down with a retro burn to be captured by Mars's gravity. That maneuver is called the Mars Orbit Insertion maneuver, or MOI for short. The slower MGS is going relative to Mars, the smaller the retro burn. And a smaller retro burn means less fuel (and weight and dollars). So that is why MGS is on a more looping trajectory which will allow for a slower arrival speed. MPF, on the other hand, is not going into orbit, so it can arrive at a faster speed, and thus its more direct route to Mars.

To help understand why a more looping trajectory results in a slower arrival speed, consider a golf ball being putted on a slanting green toward the hole. A golfer can hit the ball hard right toward the hole and the ball will arrive relatively quickly. Or else, the ball can be putted more gently toward the uphill side of the hole; in that case, the ball will loop down towards the hole and arrive at a slower speed.

Finally, about the issue of the fixed arrival date for MPF. When we travel to Mars, we have the opportunity to do Trajectory Correction Maneuvers (TCMs) that let us correct not only our aim point at Mars arrival but also the time of arrival. Early on, NASA decided July 4 would be a good day to arrive. This was partially historical. In 1976 when the Viking spacecraft went to Mars, it was expected to land on July 4 for national reasons (July 4 is America's Independence Day). But when Viking arrived, there was a raging dust storm that prevented this scheduled landing so the team missed a July 4 landing and decided to remain in orbit until July 20 (July 20 is the anniversary of the first Apollo landing). So this time NASA has decided that Pathfinder should land on July 4. The TCMs for Pathfinder will be performed to remain true to the July 4 landing date.

Classroom Answers

This is the last Challenge Question until sometime in March (six weeks before the second LFM broadcast in April). However, this doesn't have to be the end to sending out challenging questions. Students should make up their own Challenge Questions for each other. These are known as Student Stumpers and examples can be found in the Kid's Corner at: http://passporttoknowledge.com/lfm/kids/stumpers.html

Check out this Web site and send your stumpers to Sandy Dueck at: sandy@quest.arc.nasa.gov

Question #5: Week of November 11, l996

The largest crater on the larger of the two Martian moons, Phobos, is named Stickney. Ms. Stickney was not an astronomer but she played a critical role in the discovery of the Martian moons. Who was Ms. Stickney and why did she have this prominent surface feature named after her?

Answer from Bill Gutsch:

The two moons of Mars were discovered by astronomer Asaph Hall at the US Naval Observatory in 1877. According to the story, after many nights of searching for satellites that might be in orbit around Mars, Hall was ready to give up. His wife, however, encouraged him to give it "one more try." That night, Hall found Deimos and Phobos, the two Martian moons. In honor of her encouragement, without which Hall might not have made his discovery, astronomers in the 1970s decided to name the largest crater on Phobos "Stickney" -- Mrs. Hall's maiden name.

Question #4: Week of November 4, l996

Sometimes the winds on Mars can blow at hundreds of miles per hour and kick up giant dust storms that blanket the entire planet. Yet, if you stood on the surface of Mars at one of these times, you would probably not be blown over. Why?

Martian winds can be swift but the Martian air is so thin that it packs very little punch. In more scientific terms, this means that there wouldn't be nearly as many air molecules striking you per second in a Martian wind storm as there would be in a similar storm on Earth. Far fewer molecules translates into much less pressure (force per square inch) pushing against your body. Such "thin winds" can still create giant dust storms, however, because the Martian surface dust is very, very fine and so can easily be lifted into the Martian sky.

Classroom Answers

Question #3: Week of October 28, l996

Mars has two moons: Deimos and Phobos. If you stood on the surface of Mars and looked up into the night sky, you would see Deimos slowly travel from east to west across the sky while Phobos would be slowly traveling from west to east. In other words, the two Martian moons travel in opposite directions across the Martian sky. Yet both moons actually orbit Mars in the same direction.
Explain this apparent paradox.

Answer from Bill Gutsch

The closer a satellite (natural or artificial) is to the planet it orbits, the faster it travels around that planet. Both Martian moons travel around Mars from west to east. Deimos, however, is sufficiently far from Mars (like the Earth's moon is from Earth) that it travels around the planet slower than Mars rotates on its axis. Thus, to an observer on the surface of Mars, Deimos appears to be "left behind in the sky" and appears to move from east to west. Phobos, on the other hand, is much closer and actually orbits around Mars faster than Deimos.

Classroom Answers

Question #2: Week of October 21, l996

The Valles Marineris is much larger and deeper than the Grand Canyon in Arizona. Yet, if you stood at the rim of the Valles Marineris, it probably wouldn't seem as impressive to the eye. Why?

Answer from Bill Gutsch

While the Valles Marineris is big, deep and wide, Mars is a much smaller planet than Earth. This means that on Mars, the horizon curves out of the way much closer to you than it does on Earth. The result is that differences in elevation in surface features are not as impressive. On Earth, for example, you can stand at the North or South Rim of the Grand Canyon and see the whole breadth of the canyon -- all the way over to the opposite rim. In places, however, the Valles Marineris is over 100 miles from rim to rim. This is so great compared with Mars's tiny size that if you stood on one rim of the Valles Marineris, you wouldn't be able to see the other rim because it would be out of sight over the horizon!

Classroom Answers

Question #1: Week of October 14, l996

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.

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, 410 ft / 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 farther. 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!

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 than the first.

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

Earth's gravity and Venus's 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's 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 carbon dioxide 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!

Classroom Answers

*******************************************************************