1.3.2 Sending a satellite to Mars! (Activity) Okay so let's start our work as human computers! Our goal is to use a Hohmann orbit to get a small satellite from Earth to Mars. For this we need to figure out one key thing. Key Question: At what position relative to Earth should Mars be in order to land a satellite on Mars using a Hohmann orbit? Below we have an image of what is happening with the Hohmann orbit. Puzzle(s) 1.1 Label the image with the following quantities. Earth is 1 Astronomical Unit (AU) from the Sun. Mars is about 1.52 AU from the Sun. Great, now we need to do a bit of calculating. Puzzle(s) 1.2 Find the length of the semi-major axis of the Hohmann orbit we have in the image. Hint: the Sun is not at the center of the Hohmann ellipse. Puzzle(s) 1.2 Find the length of the semi-major axis of the Hohmann orbit we have in the image. Hint: the Sun is not at the center of the Hohmann ellipse. Section 1 Page 7 Cal State East Bay Now we will use Kepler's third law which tells us how to calculate the period of the Hohmann orbit. If we turn the law into an equation it says: P = ka where P is measures in years and a is measured in AU. We can apply this formula to any object (Earth, Mars, a satellite, etc.) in orbit around the Sun. We'll apply it twice in the next puzzle. Puzzle(s) 1.3 1. First, we're going to use the equation above to find the value k. Use the P and a value we know for Earth to find k. 2. Using the k value you just found and the equation above, find what P is for the Hohmann orbit that the satellite will be traveling on. 3. Now that you have P for the satellite, convert P from years to days. Puzzle(s) 1.4 How many days after we launch the satellite from Earth will it take for the satellite to enter the orbit of Mars? (Remember that the satellite is traveling along the Hohmann orbit.) Section 1 Page 8 Cal State East Bay Great, so this tells us something we'll need when figuring out *when* to launch our satellite from Earth. We want to time things just right so that when the satellite gets to the orbit of Mars, Mars is there to meet it! This means we want to know where Mars should be in it's orbit on the day we launch the satellite. Great, so this tells us something we'll need when figuring out *when* to launch our satellite from Earth. We want to time things just right so that when the satellite gets to the orbit of Mars, Mars is there to meet it! This means we want to know where Mars should be in it's orbit on the day we launch the satellite. Puzzle(s) 1.5 It takes Mars about 687 days to go around the sun. How many degrees around the sun does Mars travel in 1 day? (Hint: think about the ratio of degrees to days.) Puzzle(s) 1.6 Mars will travel on it's orbit for the same number of days that the satellite will travel. How many degrees will Mars travel in the days that the satellite is traveling? Puzzle(s) 1.7 We want Mars to be at position 180 so that it meets the satellite. At what degree location should Mars be in our graphs when we launch the satellite ? Puzzle(s) 1.8 Pretend you're going to explain the answer you got on the previous puzzle to a 7th grade student. Write a few sentences of what you would say to explain what the value you calculated represents.