Week 9 - Studying the Solar System

Name: Key Studying The Solar System Size of the Planets On the board you will see a drawing of the Sun. a) The diameter of the Sun in the Model is 200 cm . To figure out how big other planets are in this scale model, we can use the following relationship: Diameter of Planet in Model = Diameter of Sun in Model Actual diameter of planet Actual diameter of Sun So, with a little bit of algebra: Diameter of Planet in Model = Diameter of Sun in Model x Actual diameter of planet Actual diameter of Sun A word about units : The actual diameter of the planet and the actual diameter of the Sun must be in the same unit. The diameter of the planet in the model will be in the same unit as the diameter of the Sun in the model. b) On the table below you will see the actual diameter of each planet. Calculate the diameter of each planet in the model. Note: The actual diameter of the Sun is 1,392,000 km. Planet Name Actual Diameter of Planet (in km) Diameter of Planet in Model Mercury 4,878 0.70cm Venus 12,102 1.74cm Earth 12,756 1.83cm Mars 6,794 0.98cm Jupiter 142,984 20.54cm Saturn 120,536 17.32cm Uranus 51,118 7.34cm Neptune 49,528 7.12cm

c) Before the lab started you drew circles to estimate the size of Jupiter, Earth, and Mercury. Measure the diameters of the circles you drew for the three planets and include them in the table below. Also copy the calculated diameter of the planet in the model from the table on the previous page. For each of the three planets, tell whether your estimate was too small or too large, and calculate how many times too large or too small it is. Remember: How Many Times Too Large or Small = Larger of the Two Numbers / Smaller of the Two Planet Diameter of Circle You Drew Diameter of Planet in Model Estimate Too Large or Too Small? How Many Times Too Large or Small? 1) Which planet were you the most accurate in your estimate? 2) Are you surprised by the model size of the planets? Explain why or why not. d) Calculate the distance from the Earth to the Moon in this model. The Moon is 384,400 km from the Earth. Hint, you will use the same equation, but this time instead of the diameter of the planet, you will put in the actual distance from the Earth to the Moon. Distance from Earth to Moon in Model = 200 cm x 384,400km = 55cm 1,392,000km e) Calculate the distance from the Earth to the Sun in this model. The Sun is 1 AU = 1.5 x 10 8 km from the Earth. Distance from Earth to Sun in Model = 200 cm x 1.5 x 10 8 km = 21551cm = 215.51m 1,392,000km f) Answer the following questions: 1) Which type of planets (gas giant / terrestrial) are the largest? Gas Giants 2) How many times bigger is the Sun compared to Earth? 200 cm / 1.83 cm = 109x 3) How many times bigger is the Sun compared with Jupiter? 200 cm / 20.54 cm = 9.7x 4) How many times bigger is Jupiter compared with the Earth? 20.54 cm / 1.83 cm = 11.2x

1) Which planet has the largest density? Earth 2) Which planet has the smallest density? Saturn 3) Which type of planets have the larger densities? Is this what you expected? Terrestrial planets 4) Explain why the planets that weigh the most and have the largest diameters don’t have the largest densities. Hint: Think about what the different types of planets are made of. Terrestrial planets are all rock and iron while gas giants have a lot of hydrogen and helium. 5) The density of water is 1 g/cm 3 . If something has a density less than water then it will float! What does this say about Saturn? Saturn would float in water! 6) The density of our moon is 3.34 g/cm 3 . Based on this density, do you expect our moon to have an interior more like the terrestrial planets or the gas giants? Explain. More like the terrestrial planets because 3.34 g/cm 3 is closer to the density of the terrestrial planets than the gas giants. This also makes sense because the Moon has a structure (iron core with rocky outer layer) that is like the terrestrial planets. 4. Weight on a Planet a) We are going to figure out how much you would weigh in you were on the surface of each planet. b) Before you do any calculations, answer the following questions: 1) What planet do you think you will weigh the most on? Why? 2) What planet do you think you will weigh the least on? Why? c) Your weight on the surface of a planet is a combination of the mass of the planet and the radius of the planet. You can calculate your weight on each planet using the following equation: Weight on a planet = Your Weight on Earth x Mass of Planet Compared to Earth (Diameter of Planet Compared to Earth) 2

d) For each planet, calculate the weight of a 100 pound person. Record your answers in the table below. Planet Mass of Planet Compared to Earth Diameter of Planet Compared to Earth Weight on Planet Mercury 0.055 0.382 38 lbs Venus 0.815 0.949 90 lbs Earth 1 1 100 lbs Mars 0.107 0.533 38 lbs Jupiter 317.9 11.19 254 lbs Saturn 95.18 9.46 106 lbs Uranus 14.54 3.98 92 lbs Neptune 17.13 3.81 118 lbs e) Answer the following questions: 1) Which planet would you be the heaviest on? Which planet would you be the lightest on? Heaviest = Jupiter, Lightest = Mercury or Mars 2) Were your initial guesses from step b) above correct? If not, explain why you think you were wrong initially. 3) Imagine that you could go to any planet and take part in a high jump competition. Which planet will you jump the highest on? Explain your answer. Jump highest on the planet where you weigh the least – so either Mars or Mercury. f) To calculate the height that you can jump on a different planet, you use the following equation: Jump Height on a planet = Jump Height on Earth x (Diameter of Planet Compared to Earth) 2 Mass of Planet Compared to Earth 1) The average jump height for an NBA basketball player is 28”. Calculate how high they would be able to jump on the planet you chose for the high jump competition above. Jump Height = 28” x (.382) 2 = 74” (which is 6’2”)! . .055 2) It isn’t a planet, but calculate how high a basketball player would jump on the moon. The mass of the moon compared to Earth is .0123 and the diameter of the Moon compared to Earth is 0.27. Jump Height = 28” x (.27) 2 = 166” (which is 13’10”)! .0123