km 15pts 1. How far is a parsec (pc) in kilometers? 1 pc [Use scientific notatio

Question

km 15pts 1. How far is a parsec (pc) in kilometers? 1 pc [Use scientific notation; round to 3 decimals.J 12 pts l light-year 9,460,700,000,000 km Write this number in scientific notation: 1 parsec 3.2616 light-years Show your work for determining a parsec, use dimensional analysis: 10 pts totall[Work 3 pts AU [5 pts 2. Convert a parsec (pc) into astronomical units (AU). 1 pc [Use scientific notation; round to 3 decimal places. Given: 1 AU 1.496 x 105 km and 1 pc km (Copy value from #1 pt Show your work for converting a parsec into AUs, use dimensional analysis: [10 pts totalliWor 4ptsl 3. Models of Earth, Moon, and Mars are proportionally sized in a 1300 million scale. Earth and Moon are really 384,400 km (238,855 mi) apart. Moon, Earth, and Mars in 1300 million scale to each other. Earth and Moon at 1300 million scale distance from each other. This photo was taken on a dining room table. Using our 1:3 x 105 scale, Earth and Moon would be how far apart? [Part a 5 pts. Part b 5ptsl cm (b) (a) [Give your answer in centimeters and inches. Round to 1 decimal. Hint Use proportions, remember that 2.54 cm in.] Show your work (round each answer to 1 decimal): 20 pts tot 10 pts

Explanation / Answer

1) 1 light year is equals to = 9460700000000 km

or 1 light year is equals to= 94607 * 108 ( in a scientific notation)

1 pc = 3.2616 light year ( given)

so if we will convert it into km then the value of 1 pc will be

1 pc = 3.2616 * 94607  * 108 = 308570.191  * 108 km or 3.086  * 1013 km

2) 1 pc = 3.086  * 1013 km

1 AU = 1.496 * 108 km (given)

so if we will convert it into AU then the value of 1 pc will be

1 pc = 3.086  * 1013 / 1.496  * 108 = 2.0628 * 105 AU

3) distance between earth and moon is = 384400 km

if we will convert it into cm then distance between earth and moon is = 384400 * 1000 * 100 = 384.4 * 108 cm

according to given scale which is 1: 3 * 108   , 384.4 * 108 / 3 * 108 = 128.133 cm

so if 1 cm on the table is represent 300 million cm then we can say that distance between earth and moon is 128.133 cm on the table.

and if we will convert it into inch then the distance will be = 128.133 / 2.54 = 50.446 inch

4) Distance between earth and sun = 1 AU

distance between mars and sun = 1.5 AU

so distance between mars and the earth = distance between mars and sun - Distance between earth and sun

= 1.5 - 1 = 0.5 AU

1 AU = 1.496 * 108 km

so the distance between mars and the earth in the km is =0.5 * 1.496 * 108 km = 0.748 * 108 km

1 AU =9.296 * 107 mile

so the distance between mars and the earth in the mile is =0.5 * 9.296 * 107 km = 4.648  * 107 mile

5) (a) 200 billion stars = 200 * 109 = 2 * 1011 stars

(b) 200 billion stars * 1 star per second = 200 billion seconds = 2 * 1011 seconds

days in a year(365.25) * hours in a day (24) * minutes in a hour (60) * seconds in a minute(60) = 31557600 seconds in a year

(c) seconds in a year = 31557600 = 3155.76 * 104 seconds

(d) convert seconds in a year = 2 * 1011 / 31557600 = 6337.61 year

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