Respuesta :
Answer:
θ₂/ θ₁= 2.58
Explanation:
In this exercise you are asked to compare the angular diameters of Mars and Jupiter. The angular diameter or angle in radians is
θ = D / R
where D is the diameter of the body, the distance from Earth to the body of interest and θ is angle in radians
The different distances are tabulated with respect to the Sun
Sun -Earth 1,496 10¹¹ m
Sun- Mars 2.28 10¹¹ m
Sun - Jupiter 7.78 10 m
The Radii of the planets are
Mars 3.37 10⁶ m
Jupiter 6.99 10⁷ m
let's calculate the angles for each body
a) Mars
θ₁ = 2r / R'
the distance from the ground is
R ’= D_planet - D_earth
R ’= 2.28 10¹¹ - 1.496 10¹¹
R ’= 0.784 10¹¹ m
let's calculate
θ₁ = [tex]\frac{2 \ 3.37 \ 10^6 }{0.784 \ 10^{11}}[/tex]
θ₁ = 8.6 10⁻⁵ radians
b) Jupiter
R ’= 7.78 10¹¹ - 1.496 10¹¹
R ’= 6.284 10¹¹ m
let's calculate
θ₂ = [tex]\frac{2 \ 6.99 \ 10^7}{6.284 \ 10^{11}}[/tex]
θ₂ = 2.22 10⁻⁴ radians
the ratio of the angular diameters is
θ₂/ θ₁ = [tex]\frac{2.22 \ 10^{-4}}{8.6 \ 10^{-5}}[/tex]
θ₂/ θ₁= 2.58
