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

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

Angular diameter =  35.75" = 35.72 x 4.874 x 10^-6 rad

Diameter of Jupiter = d

Using the relation,

`theta = d/D`

`d = thetaD = 824.7 xx 10^9 xx 35.72 xx 4.872 xx 20^(-6)`

=143520.76 x 10³ = 1.435 x 10⁵ km

Answer 2

Given angular diameter θ = 35.72= 35.72 x 4.85 x 10^-6 rad

= 173.242 x 10^-6 = 1.73 x 10^-4 rad

Diameter of Jupiter D = θ x d = 1.73 x 10^-4 x 824.7 x 10⁹ m

=1426.731 x 10³ = 1.43 x 10⁸ m