5. A friend tells you that a lunar eclipse wi take place the following week. You

Question

5. A friend tells you that a lunar eclipse wi take place the following week. You and your friends decide to stargaze and observe the eclipse. Having recently seen a special on imaging astrological objects, you are curious what the eclipse might look like from different perspectives in space. If the moon has a diameter of 2,59.14 miles, what is the maximum distance that it could be observed by the naked eye with enough detail that you could distinguish it from other celestial bodies (assuming that you have 20/20 vision)? Round to two decimal places. (2) (b) One of your friends wants to buy a telescope to stargaze. If you and your friends want to observe Mercury after sundown, what is the minimum magnifying power of the telescope needed? (the radius of Mercury is 1,516 miles, and it is 48 million miles away from the earth) Round to two decimal places. (2) 5b

Explanation / Answer

For 20/20 vision

a person can recognize details if the object subtends an angle of 1 minute of the arc on the eye

5. diamteter of moon D = 2159.14 miles

maximum distance that details on the moon can be seen = d

D/d = pi/60*180 radians

d = 2159.14*60*180/pi = 7422576.56 miles

sop details of moon can be seen as far as 7422576.5626 miles from the moon, which is greater than the distance of the moon from the earth

6. radius of mercury, r = 1516 miles

distance of mercury from the person = 40*10^6 miles

so, let magnification of telescope be m

then m*2*1516/40*10^6 = pi/60*180

m = 3.837

so a telescope of magnifying power 3.837 will be rtequired to identify details of mercury

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