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 solve the problem of finding the diameter of the Earth as seen from the Moon in degrees, we can follow these steps:

### Step 1: Understand the relationship
The distance from the Moon to the Earth is given as 60 times the radius of the Earth. We denote the radius of the Earth as \( R_e \). Therefore, the distance \( D \) from the Moon to the Earth can be expressed as:
\[ D = 60 R_e \]

### Step 2: Use the formula for angular size
The angular size \( \theta \) (in radians) of an object can be calculated using the formula:
\[ L = D \cdot \theta \]
where \( L \) is the linear size (diameter of the Earth) and \( D \) is the distance to the object. The diameter of the Earth \( L \) is:
\[ L = 2 R_e \]

### Step 3: Substitute the values into the formula
Substituting the values into the formula gives:
\[ 2 R_e = (60 R_e) \cdot \theta \]

### Step 4: Solve for \( \theta \)
We can simplify this equation to find \( \theta \):
\[ \theta = \frac{2 R_e}{60 R_e} = \frac{2}{60} = \frac{1}{30} \text{ radians} \]

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

### Step 6: Calculate the value
Calculating the above expression:
\[ \theta \text{ (in degrees)} = \frac{180}{30 \pi} = \frac{6}{\pi} \]

Using the approximate value of \( \pi \approx 3.14 \):
\[ \theta \text{ (in degrees)} \approx \frac{6}{3.14} \approx 1.91 \text{ degrees} \]

### Step 7: Round the result
Rounding this value gives approximately:
\[ \theta \approx 2 \text{ degrees} \]

### Final Answer
Thus, the diameter of the Earth as seen from the Moon is approximately **2 degrees**.

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