UNIT 7: Kilo Hoku - Astronomy & Navigation Teacher s Notes for Part C: Comparing Planets Mass, Density & Gravity

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1 UNIT 7: Kilo Hoku - Astronomy & Navigation Teacher s Notes for Part C: Comparing Planets Mass, Density & Gravity 1. How much would a can of soda weigh on Pluto? Weigh pennies and place them in soda cans to get the approximate weight of a can on each planetary object or use a material such as quickcrete instead. (More advanced students can calculate the number of pennies needed for each can.) It is helpful to use a different type of soda can for each or paint each can a different color. This allows the students to say, for example, the Coke can represents what a can of soda would weigh on Jupiter and the Pepsi can represents what a can of soda would weigh on Neptune. Tape the tops of each soda can so that the pennies will not fall out. The amount of gravity a planet possesses depends on its mass and volume (density) and radius. Function of mass and radius: g = (GM/R 2 ) where: G = 6.67x10-11 m 3 kg -1 s -1; M =mass of object; R = radius of object A person's weight depends on the mass of the person, mass of the planet and the planet s radius. Therefore a person will weigh less on a planet that has less mass and similar radius than the Earth and weigh more on a planet that has a larger mass than the Earth and similar radius. This is illustrated by using a simple can of soda pop. On Earth a 16-ounce can weighs 386 grams. Take several other empty soda cans and fill them with material (lead pellets, marbles, rock, etc.) until they weigh the amounts for each planet shown on the table below (this lists how much a full can of soda would weigh on various planetary objects as well as other statistics about the planetary objects). Body grams Pennies Mass (kg) Radius (km) Density kg/m 3 *Gravity (GM/R 2 ) Sun 10,808 ~ E+30 69,595 1, Mercury E+23 2,440 5, Venus E+24 6,052 5, Earth E+24 6,371 5, Moon E+22 1,738 3, Mars E+23 3,390 3, Jupiter E+27 71,492 1, Saturn E+26 60, Uranus E+25 24,973 1, Neptune E+26 24,764 1, Pluto E+22 1,151 2, **Relative Gravity * g = (GM/R 2 ) where G = 6.67x10-11 m 3 kg -1 s -1; M =mass of object; R = radius of object ** Object of interest/earth s Gravity, e.g., for the Sun /9.82 = 27.9 Ka Hana Imi Na auao A Science Careers Curriculum Resource Go to: 1

2 Activity: Ask students try to put the cans in order from lightest to heaviest. Then show the students which can correlates to which planet so they can see how heavy or light a can of soda would be on the different planetary objects. The goal here is for the students to make the connection that in general, the more massive the planet the larger the gravitational pull, and therefore the can will weigh more on larger planets. However, some planets which are larger than Earth, such as Saturn and Uranus, have lower gravity. This is because Saturn and Uranus have a lower average density and much greater radius than Earth. Note, the heaviest soda can goes with the largest planet. If further guidance is needed, the correlation with size and mass can be pointed out to them. It will be necessary to explain that Saturn and Uranus have similar gravities to Earth. Here is a good place to talk about the difference between mass and density. Graphing Exercise: Have the students plot of grams of a can of soda on the planet versus: 1. mass of the planets; 2. radius of the planets; 3. gravity on each planet; and 4. density of the planets (see graphs below). None of the graphs show any correlation except for the graph of grams of a can of soda versus gravity. Ask students to interpret each graph in one or two sentences. ANSWER KEY for Exercise: A Graph A is a plot of how much a can of soda would weigh on a planetary body versus the mass of the planet. The y-axis in graph A is written in scientific notation (Scientific notation, or exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation, e.g., 5,720,000,000 = 5.72 x 10 9 ) Ka Hana Imi Na auao A Science Careers Curriculum Resource Go to: 2

3 B Graph B is a plot of how much a can of soda would weigh on a planetary body versus the radius of the planet (data is listed in the above table). Diamond symbols represent terrestrial planets; Mercury is blue/gray diamond, Venus is a royal blue diamond, Earth is a green diamond, and Mars is a red diamond. Circles represent gas giants; Jupiter is shown as an orange filled circle, Saturn is a pale yellow filled circle, Uranus is a cyan filled circle, and Neptune is a dark blue filled circle, Pluto is shown as a white square and the Earth s Moon is a gray triangle. On the next page, Graph A is a plot of how much a can of soda would weigh on a planetary body versus the gravity of the planet and Graph B is a plot of how much a can of soda would weigh on a planetary body versus the density of the planet (data is listed in the above table). Diamond symbols represent terrestrial planets; Mercury is blue/gray, Venus is a royal blue diamond, Earth is a green diamond, and Mars is a red diamond. (Note that in graph A, Mars and Mercury plot on top of one another; Mercury s symbol is the inner, smaller diamond.) Circles represent gas giants; Jupiter is shown as an orange filled circle, Saturn is a pale yellow filled circle, Uranus is a cyan filled circle, and Neptune is a dark blue filled circle, Pluto is shown as a white square and the Earth s Moon is a gray triangle. Ka Hana Imi Na auao A Science Careers Curriculum Resource Go to: 3

4 A B Agood website that allows students to compare masses of planets is at: n/planet_mass_comp_full.htm A Bonus Assignment is to have the student select an object and determine what it would weigh on each of the planets. This object can be themselves or anything else that they know the weight of. It may be necessary to do an example on the board, as well as give them a worksheet to fill out Two websites to check the answers to the bonus assignment are: Ka Hana Imi Na auao A Science Careers Curriculum Resource Go to: 4

5 2. Calculating Weight on Different Planetary Objects Answer Key Student handout is printed in Part C of Unit 7 of the curriculum. Source: Your Weight on Other Worlds Answers are according to what a person who weighed 100 lbs on Earth would weigh on the other planets (and Pluto). 1. On what planet would you weigh the closest to what you weigh on Earth? Saturn, On what planet would you weigh the least? Mars, On which planet would you weigh the next least? Mercury, On what planet would you weigh the most? Jupiter, On which planet would you weigh the next most on? How does this compare with what you weigh on Earth? Neptune, and Fairly close 6. On which 2 pairs of planets would you weigh almost the same? (your answer should list 4 planets) Mercury Mars and Venus Uranus (0.1) and (1.8) Individually, calculate how much would you weigh on the other 7 planets plus Pluto if you weighed a 100 lbs on Earth. Location Mass on Earth Gravity Calculated Weight Mercury 100 X.378 = 37.8 Venus X.907 = 90.7 The Moon X.166 = 16.6 Mars X.377 = 37.7 Jupiter X = Saturn X = Uranus X.889 = 88.9 Neptune X = Pluto X.067 = 6.7 Ka Hana Imi Na auao A Science Careers Curriculum Resource Go to: 5