Space Math: Measuring Distance in Space The mass of the earth is "5.972 x 1024" kg. Write that as a regular number: _____________________________________________________ Numbers used to measure distance and mass in ___________ can be extremely large! The distance between the Earth and the Sun is _______________________________ km. Because numbers are so large, we use _________________________ _____________________. Scientific Notation Scientific notation is based on powers of _______. When we write numbers in scientific notation, the first part of the number is always between _____ and _____. Example 1 The mass of Jupiter is 1 898 000 000 000 000 000 000 000 000 kg. Write in scientific notation. Step 1: Move the decimal place until it is positioned after the ___________ digit. Step 2: Count how many times you moved the decimal place. This is your _____________________. Step 3: Remove all of the zeroes on the ____________ and write in scientific notation! Step 4: Round the number portion to one decimal place. Example 2 The closest star to earth,_______________ _______________, is 38 000 000 000 000 km away. Write this distance in scientific notation. Astronomical Units Sometimes it would be better to have a totally different system for measuring distance in the ______________________, because measuring in km sometimes doesn't make sense.. To measure distances within our own galaxy we can use _____________________ ___________. 1 _________________________ _______________ or 1 AU is __________________________ km. 1 AU is also the distance from __________________________ to _________________________. Example 1 Proxima Centauri is 38 000 000 000 000 km away. What is the distance in astronomical units? Step 1: Divide the distance in km by 149 600 000 km. Step 2: Round your answer appropriately. Example 2 The distance from the Sun to Mercury is 57,910,000 km. What is that in AU? Example 3 The distance from the Sun to Neptune is 4,503,000,000 km. What is that in AU? Light Years Some distances in the universe are so large that even Astronomical Units aren't large enough to measure appropriately! For example, the distance from earth to the Andromeda galaxy is _______________________ AU. As you can see, writing that in Astronomical Units is still pretty crazy! Instead, we use ___________________ ______________! A light year is the distance that ___________________ can travel in _________ ________________. Light can travel 300 000 km in one second. 1 Light Year = _________________________ km. So… 1 Light Year = _________________________________ AU. Example 1 The distance from Earth to the Andromeda Galaxy is about 160, 000, 000, 000 AU. How many light years is it from Earth to the Andromeda Galaxy? Example 2 Pluto is about 7.5 billion km away. a. Write this distance in scientific notation. b. Write this distance in AU. c. Write this distance in light years. Space Math Practice 1. Pick 2 distances within our solar system, measured in km and convert them to scientific notation. a. Distance from Mars to Saturn in = 1 400 000 000 km b. c. 2. Pick 2 distances within our galaxy, and convert them to Astronomical Units. a. Distance from Earth to Pluto = 7 500 000 000 km b. c. 3. Pick 2 distances beyond our solar system and convert them to Light Years. a. Distance from Earth to Vega = 1 584 155 AU b. c.