Question

when a planet X is at a distance of 824.7 million km from earth it's angular diameter is measured to be 35.72 ^ 11 of arc calculate the diameter of X​

Answer 1

Answer:

Distance of X planet 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 X planet = d

Using the relation,

θ = d/ D

d = θ D = 824.7 × 109 × 35.72 × 4.872 × 10-6

= 143520.76 × 103 m = 1.435 × 105 Km

Answer 2

Distance of Jupiter from the Earth, D=824.7×10

6

km

Angular diameter 35.72

′′

=35.72×4.874×10

−6

rad

Diameter of Jupiter = d

Using the relation,

θ = d/ D

d=θ D = 824.7 x 10

9

x 35.72 x 4.872 x 10

−6

= 143520.76 x 10

3

= 1.435 x 10

5

Km

hope it helps❤️