Question

When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter.

Answer 1

Hey buddy,

# Answer- d = 1.4×10^5 km

# Given-
Distance of Jupiter from the Earth
D = 824.7×10^6 km = 824.7 × 10^9 m
Angular diameter
θ = 35.72“ = 35.72×4.874×10^-6 rad

# Formula-
Angular diameter of jupiter is given by relation,
θ = d/D
d = θ.D
d = 824.7×10^9×35.72×4.872×10^-6
d = 143520.76×10^3 m
d = 1.435 × 10^5 Km

Hence, diameter of jupiter is 1.4×10^5 km.

Hope this was helpful...

Answer 2

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Distance of Jupiter from the Earth, D = 824.7 × 106 km = 824.7 × 109 m

Angular diameter=35.72" = 35.72 × 4.874 × 10^-6 rad

Diameter of Jupiter = d

Using the relation,

θ = d/D

=> d = D θ = 824.7 × 10^9 × 35.72 × 4.874 × 10^-6

= 1.435 × 10^5 km

I hope, this will help you

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