Calculating the Apparent Angle of the Moon's Diameter from Earth

[onetroubledguy]

The problem is -

Consider the following accept constants:

Radius of the moon = 1.74 x 10^6 m
Average moon-earth distance = 3.84 x 10^8 m

a) What is the apparent angle the diameter of the moon subtends, as seen from the earth? Answer in units of degrees.

I doubled the radius of the moon to get the diameter, and then divided the result by the moon-earth distance. Then, I took the inverse tangent of the result.

I get 51.92 degrees. My college website is telling me this is wrong. Do you get a different answer?

 

[Astronuc]

tan(51.92°) = 1.276, so it would appear there is an error in the computation.

The ratio of 2*Lunar Diameter to Earth-Moon distance is ~0.009, so the tan^-1 should be small - less than 1°.

 

[David]

Then, I took the inverse tangent of the result. I get 51.92 degrees. My college website is telling me this is wrong.

Did you check that your calculator was set to the appropriate degrees/radians setting?

 

[quasar987]

Why did you doubled the lunar radius before taking the inverse tangeant? The tan thing works on rectangle-triangles only. I say find the angle subtented by half of the moon, and then multiply that angle by 2 to get the total angle subtented by the diameter.

 

[onetroubledguy]

Why did you doubled the lunar radius before taking the inverse tangeant? The tan thing works on rectangle-triangles only. I say find the angle subtented by half of the moon, and then multiply that angle by 2 to get the total angle subtented by the diameter.

Wouldn't you get the same answer?

Well, the angle subtended by half the moon is 25.96. So 25.96*2 = 51.92

 

[quasar987]

I get 0.2596; 100 times less.

 

[onetroubledguy]

I get 0.2596; 100 times less.

I thought 0.2596 needs to be converted into a percent? Is that the only mistake I made?

Yeah I'm an idiot. Now that I actually picture how insane of a degree 51.92 would be, it's clear as day. Thanks for the help!

 

[cks]

Even you have made a mistake by changing it into percentage, but I don't understand why you have to double the radius of the moon. Isn't it
arc tan(radius of the moon/moon-earth distance) is the answer? Thank you.