Home PublicationsL&LIssuesVolume 27 (1999-2000) February (No. 5)

Bob and Paul present questions and investigations to help compare Earth and Mars in terms of mass, size, shape, volume, density, rotation speeds, gravity, and so on.

Web Resources
Note. These Web sites were valid when this issue of L&L went to press. We have no control over these sites, though, and the Web is very volatile. Please let us know if you find a broken link, and we’ll do our best to update it.

National Space Sciences Data Center: http://nssdc.gsfc.nasa.gov

The Mars Fact Sheet: http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

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Problems

1. Calculate the ratio of Mars’s mass to Earth’s and compare your answer to the ratio shown in Table 1.
2. What is the equatorial diameter of Mars? of Earth?
3. What is the polar diameter of Mars? of Earth?
4. Investigation. Why are the equatorial diameters of Mars and Earth greater than their polar diameters?
5. In circumnavigating Earth along the equator, how far do you walk and swim?
6. In circling Earth along a meridian, how far do you snowshoe, walk, and swim?
7. Investigation. In circumnavigating Earth, what countries do you pass through? What oceans, lakes, and rivers do you cross? What mountains do you climb? What towns and cities do you travel through?
8. You go to Mars and lope around its equator. How far do you travel?
9. Still fresh as a daisy, you circumnavigate Mars along a meridian. This takes you across both the north and south polar caps. How far do you walk and snowshoe?
10. Investigation. In circumnavigating Mars, what mountains do you climb? What craters do you cross? What valles (sinuous valleys; singular: vallis) do you cross? Do you cross any oceans, lakes, or rivers?
11. There are 360 degrees in a circle. As you circumnavigate a planet along its equator or a meridian, you turn through 360 degrees relative to the planet’s center. How far (in km) do you travel per degree along Earth’s equator? along an Earth meridian?
12. How far (in km) do you travel per degree along Mars’s equator? along a Mars meridian?
13. Extra for the trigonometrically unchallenged: In Shuhaw Hall at Santa Rosa Junior College in California, a benchmark is located at 122ƒ 43' 10" west longitude, 38ƒ 27' 20" north latitude. If you go around the meridian, how far do you travel? If you follow the latitude until you return to your starting point, how far do you travel?
14. Make a table showing:

    a. latitude from 0ƒ to 90ƒ in 10ƒ increments,

    b. radius of each circle of latitude in km,

    c. circumference of each circle of latitude in km, and

    d. distance in km/degree in traveling around each circle of latitude.

15. Do “#14” for Mars.
16. The volumetric mean radius of Mars is 3,390 km. Calculate the volume of Mars and compare your answer with the value in Table 1.
17. Use the mass and volume of Mars to calculate its density. Compare your answer to the value given in Table 1.
18. Convert 1,674 kilometers per hour to meters per second. (Answer: 465 m/s)
19. Suppose you are standing on Mars’s equator. How fast are you traveling because of the rotation of Mars in kilometers per hour? in meters per second?
20. Circles of latitude get smaller as you go from the equator toward either pole, but the rotational angular velocity is the same at every latitude (well, it’s zero at a pole). For Earth or Mars or both, make a table showing:

    a. latitude from 0ƒ to 90ƒ in 10ƒ increments, and

    b. the speed at which you are traveling at that latitude in kilometers per hour and meters per second.

21. Using the mass and polar radius given in Table 1, calculate Earth’s gravity at its poles.
22. Calculate Mars’s gravity at its equator and at its poles.
23. Using Earth’s solar irradiance, the Mars-to-Earth distance from the Sun ratio (1.5), and the inverse square relationship, calculate the solar irradiance on Mars and compare your answer with the value given in Table 1.
24. If a solar cell array can convert 15% of the solar irradiance to electricity, how many watts per square meter will it produce on Earth? on Mars?
25. Investigation. Where on Mars is water likely to be found and how can it be obtained?
26. Investigation. How can water (H₂O) be split into hydrogen (H) and oxygen (O)?
27. Investigation. How much oxygen does an average human adult consume per Martian solar day (24h 39m 35s)? How much water? How can this oxygen and water be recycled?
28. Investigation. In a habitat supplied with air that is 20% oxygen, 78% nitrogen, 1% argon, and 1% water vapor at a pressure of 1,014 millibars, what is the density of the air in kilograms per cubic meter? What is the total mass of the air in a habitat that has a volume of 1,000 cubic meters?
29. Investigation. Humans inhale oxygen and exhale carbon dioxide. How much carbon dioxide does one human produce per hour? In a closed environment, excess carbon dioxide must be removed from the air. How can this be done?
30. Investigation. Martians will grow plants for food. Plants consume carbon dioxide and give off oxygen. How much carbon dioxide does a bunch of plants consume per hour? How much oxygen does it produce per hour? Please quantify bunch (e.g., romaine lettuce with a total leafy surface area of one meter).
31. Investigation. How can atmospheric carbon dioxide (CO₂) be split into carbon (C) and oxygen (O)?
32. Investigation. How can methane (CH₄) be made from carbon (C) and hydrogen (H)? To burn methane as a fuel, what else is needed? When methane is burned, what are the exhaust products? Do they pollute the atmosphere of Mars?

Table 1. Mars and Earth data adapted from the Mars Fact Sheet of the National Space Sciences Data Center

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