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Alenkinab [10]
3 years ago
13

What is the approximate angular diameter of venus when it is a very slim crescent? (measure full diameter of the planet, not jus

t the crescent)
a. 15â

b. 30â

c. 60â

d. 60â?
Physics
1 answer:
gregori [183]3 years ago
7 0
This year Venus was slim crescent in March when the Earth-Venus was about L=42*10^6 km  (the minimum distance)
To find its angular diameter we apply the trigonometry
\tan \alpha = D/L
where D=21000 km is the planet diameter and L is the distance to the planet. For small angles we consider
\tan \alpha \approx \alpha
Thus the angular diameter of venus when it was slim crescent was
\alpha =D/L =21000/(42*10^6) =2.9*10^{-4} rad
In degrees this is 
\beta =\alpha*180/\pi = 0.0167 degree
We know that 3600 seconds correspond to 1 degree. Therefore
1''=1/3600 =2.8*10^{-4} degree
Hence
\beta = 0.0167/2.8*10^{-4} =60.12''

Therefore the angular diameter of Venus when it was slim crescent was 60''.

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