Question

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

a. 15â

b. 30â

c. 60â

d. 60â?

Answer 1

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''.