The diameter of the Moon is 3.78x10^6m. It subtends an angle of .00982 radians at the surface of Earth. How far is the Moon from Earth? (Please explain I can't wrap my head around this question.)
Arc length = angle * r
3.78*10^6 = r* .00982
r = radius (length moon is from earth)
http://www.coolmath.com/reference/circles-trigonometry.html
Ohhhh, I was using the radius of the moon as the r instead of the arc length… I feel dumb haha Thank you, Greatly appreciated!!
Don't feel dumb.. Glad you understand it now.
To calculate the distance between the Moon and Earth, we can use the concept of angular diameter and basic trigonometry. The angular diameter is the angle created by two lines from opposite edges of an object that intersect at the viewer's eye. In this case, the angular diameter is given as 0.00982 radians.
Here's how you can solve the problem step by step:
1. Recall that the angular diameter (θ) is related to the actual diameter (D) and the distance (d) by the formula: θ = D / d.
Rearranging the formula, we get: d = D / θ
2. Plug in the given values:
The diameter of the Moon (D) is 3.78 x 10^6 meters.
The angular diameter (θ) is 0.00982 radians.
3. Substitute the values into the formula:
d = (3.78 x 10^6 m) / (0.00982 rad)
4. Evaluate the division:
d ≈ 384,615,384.6 meters
Therefore, the distance from the Moon to Earth is approximately 384,615,384.6 meters.
Keep in mind that these calculations assume a simplified model in which the Moon's distance from the Earth remains constant, even though it actually varies slightly due to the Moon's elliptical orbit.