Question

The moon has a diameter of 3.48 x 106 m and is a distance of 3.85 x 108 m from the earth. The sun has a diameter of 1.39 x 109 m and is 1.50 x 1011 m from the earth. Determine (in radians) the angles subtended by (a) the moon and (b) the sun, as measured by a person standing on the earth. (c) Determine the ratio of the apparent circular area of the moon to the apparent circular area of the sun. These calculations determine whether a total eclipse of the sun is really "total."

Answer 1

0.00903 rad

0.00926 rad

6.268\times 10^{-6}

Step-by-step explanation:

s = Diameter of the object

r = Distance between the Earth and the object

Angle subtended is given by

`\theta=(s)/(r)`

For the Moon

`\theta_m=(3.48* 10^6)/(3.85* 10^8)\\\Rightarrow \theta_m=0.00903\ rad`

The angle subtended by the Moon is 0.00903 rad

For the Sun

`\theta_s=(1.39* 10^9)/(1.5* 10^(11))\\\Rightarrow \theta_s=0.00926\ rad`

The angle subtended by the Sun is 0.00926 rad

Area ratio is given by

`(A_m)/(A_s)=(\pi r_m^2)/(\pi r_s^2)\\\Rightarrow (A_m)/(A_s)=(d_m^2)/(d_s^2)\\\Rightarrow (A_m)/(A_s)=((3.48* 10^(6))^2)/((1.39* 10^9)^2)\\\Rightarrow (A_m)/(A_s)=6.268* 10^(-6)`

The area ratio is
`6.268* 10^(-6)`