Review of the Scale Problems Scale problems are problems of the style that ask how big or small would something be if all objects were scaled up or down.

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Presentation transcript:

Review of the Scale Problems Scale problems are problems of the style that ask how big or small would something be if all objects were scaled up or down in size. We’ll use a simple proportion to solve these types of scale problems

The working equation for all scale problems is where one object is given in its scaled size and you need to find the scaled size of the other object. Practice Problem 1: If every object in the Solar System were scaled down so that the Earth were shrunk to a diameter of 1 foot, how far from the Earth would the Sun be? Solution: Let the diameter of the Earth object 1 and the distance from the Earth to Sun be object 2. Answer in sentence: The Sun would be 11,759 feet or 2.23 miles from the Earth if the Solar System were scaled down so that the Earth had a 1 foot diameter.

The working equation for all scale problems is where one object is given in its scaled size and you need to find the scaled size of the other object. Practice Problem 2: If every object in the Universe were scaled down so that the Astronomical Unit were shrunk to a diameter of 1 inch, how far from the Earth would the nearest star be? Note the distance to Proxima Centauri (the nearest star beyond the Sun) is 4.3 ly. Solution: Let the AU be object 1 and the distance to Proxima Cenaturi be object 2. Answer in sentence: The nearest star beyond the Sun, Proxima Centauri, would be 4.28 miles from the Sun if the Universe were scaled down so that the 1 AU was equal to 1 inch.

The working equation for all scale problems is where one object is given in its scaled size and you need to find the scaled size of the other object. Practice Problem 3: If every object in the Universe were scaled down so that the Solar System (80 AU actual diameter) were shrunk to a diameter of 1 meter, how far from the Sun would the center of the Milky Way Galaxy be? Note the distance to the center of the galaxy is about 28,000 ly. Solution: Let the 80 AU be object 1 and the distance to the galactic center be object 2. Answer in sentence: The center of the Milky Way would be 9,840 kilometers from the Sun if the Universe were scaled down so that the Solar System was 1 meter in diameter.

The working equation for all scale problems is where one object is given in its scaled size and you need to find the scaled size of the other object. Practice Problem 1: If every object in the Solar System were scaled down so that the Solar System (80 AU actual diameter) had the diameter of a dinner plate (10.5 inch diameter), what would be the diameter of the Milky Way Galaxy 100,000 ly actual diameter? Solution: Let the diameter of the Solar System be object 1 and the diameter of the Milky Way Galaxy be object 2. Answer in sentence: The Milky Way Galaxy would have a diameter of 13,100 miles if the Solar System were scaled down so that it was the size of a dinner plate. This is equivalent to 50% greater than the diameter of the Earth.