The distnace of the moon from the earth is about 60 times the radius of the earth. What will be diameter of the earth (approximately in degrees) as see from the moon?

Options

A. `1^(@)`
B. `2^(@)`
C. `4^(@)`
D. `6^(@)`

Explanation

To find the diameter of the Earth as seen from the Moon in degrees, we can follow these steps:

### Step 1: Understand the relationship between distance and angle
The angle subtended by an object at a distance can be calculated using the formula:
\[ L = r \theta \]
where:
- \( L \) is the linear size of the object (diameter of the Earth in this case),
- \( r \) is the distance from the observer to the object (distance from the Moon to the Earth),
- \( \theta \) is the angle in radians.

### Step 2: Define the parameters
Given:
- The radius of the Earth \( R_e \).
- The distance from the Moon to the Earth is approximately \( 60 \times R_e \).

The diameter of the Earth \( D \) is:
\[ D = 2R_e \]

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ L = D = 2R_e \]
\[ r = 60R_e \]

Using the formula \( L = r \theta \):
\[ 2R_e = (60R_e) \theta \]

### Step 4: Solve for \( \theta \)
Now we can solve for \( \theta \):
\[ \theta = \frac{2R_e}{60R_e} \]
\[ \theta = \frac{2}{60} = \frac{1}{30} \text{ radians} \]

### Step 5: Convert radians to degrees
To convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[ \theta \text{ (in degrees)} = \theta \text{ (in radians)} \times \frac{180}{\pi} \]
\[ \theta = \frac{1}{30} \times \frac{180}{\pi} \]

### Step 6: Calculate the angle in degrees
Now we can calculate:
\[ \theta \approx \frac{180}{30 \pi} \]
\[ \theta \approx \frac{6}{\pi} \]

Using \( \pi \approx 3.14 \):
\[ \theta \approx \frac{6}{3.14} \approx 1.91 \text{ degrees} \]

Rounding this gives approximately \( 2 \text{ degrees} \).

### Final Answer
The diameter of the Earth as seen from the Moon is approximately \( 2 \text{ degrees} \).

---