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Math Review for Space Travel How to work out how long space travel will take: When dealing with problems involving long distances to travel, and the time it takes to travel them, you may encounter different units of measure (light years vs. kilometers), as well as scientific notation. If your problem has different units of measure, it is important to convert your units to the same unit of measure before beginning your problem. The most common units of measure used in astronomy are AU (Astronomical unit), and light years. The table below shows the distance for AU and ly expressed in different ways: Astronomical Unit 150 million kilometers 150,000,000 km 1.5x108 km Light Year 9.5 trillion kilometers 9,500,000,000,000 km 9.5 x1012 km 3 6 9 12 Tip: 10 means thousand, 10 means million, 10 means billion, 10 means trillion Because light years are such a long distance, you often need to use scientific notation in your calculators. Different calculators provide this in different ways. Casio, Sharp, & Micronta To get the number 9.5 x 1012, press: Texas instruments To get the number 9.5 x 1012, press: 9.5 9.5 EXP 12 2nd 10x 12 To convert from AU to km multiply the number of AU by 150 million To convert from ly to km, multiply the number of ly by 9.5 trillion Working out the Time Then, if you know the distance, and the speed of travel, you can easily work out how long it takes to get to the destination: Distance in km Speed in km/h = Time in h Converting Time With any space problem, the time in hours is not a practical way to express your answer. For example, you would never tell someone you are 131400 hours old. It is often easiest to convert from hours to days first, and then converting from days to months or years. Converting from: Hours to Days (h--->d) Divide the hours by 24h/day Eg. Days to months (d-->mon) Divide days by 30.4 days/mo Eg. Days to years (d-->a) Divide days by 365 Eg. 131400 h 24h/day 5475 h 30.4d/mo 5475 h 365d/year = 5475 days = 180.1 mo = 15 years Using mixed units for time: Often, when converting from times, you will not get a whole number. For example, 6842 days is equal to 18.74 months. It is clearer to express this in months, and days (and perhaps even hours and minutes). 6842 days 365 days/year = 18.74 years .88 months x 30.4 days/months 26.75 days .74 years x 12 months/year = 8.88 months .75 days x 24h/day = 18h Final answer can then be expressed as 18 years, 8 months, 26 days, and 18h Math Review for Space Travel Practice Questions 1. Mars is 1.5 AU from the sun. How many kilometers is it from the sun? 2. Alpha Centauri is 4.1 ly from Earth. How many kilometers is it from earth? 3. The circumference of Earth’s orbit is 938 million kilometers. How fast does Earth travel in km/h? 4. NASA hopes to send people to Mars. The total distance to travel to Mars is 195 million km. If the spacecraft travels 31,250 km/h, how long will it take to get to Mars? (in h and a) 5. The European Space Agency (ESA) is planning to send a satellite to Pluto. Pluto is 39 AU away from the sun. If the satellite travels a speed of 27500 km/h, how long will it take to get to Pluto? Express your answer in years, months, and days. 6. Astronomers recently discovered a planet orbiting the star Vela, which is 36 light years away (which is relatively close). The planet, now named HD85512b, may be habitable (ie. The temperature is just right for water to exist as a liquid). Someone claiming to be a 600 year old alien arrives from this planet, and says the spacecraft can travel a speed of 3 million km/h. How long would it have taken this traveler to get to Earth? (in years) How old is the alien?