A satellite `X` moves round the earth in a circular orbit of radius `R`. If another satellite `Y` of the same mass moves round the earth in a circular orbit of radius `4R`, then the speed of `X` is ____________ times that of `Y`.

Answer

To solve the problem, we need to find the relationship between the speeds of two satellites, X and Y, orbiting the Earth at different radii.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Satellite X orbits at a radius \( R \).
- Satellite Y orbits at a radius \( 4R \).
- Both satellites have the same mass.

2. **Use the Formula for Orbital Speed:**
The orbital speed \( v \) of a satellite in a circular orbit is given by the formula:
\[ v = \sqrt{\frac{GM}{r}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the radius of the orbit.

3. **Calculate the Speed of Satellite X:**
For satellite X, which orbits at radius \( R \):
\[ v_X = \sqrt{\frac{GM}{R}} \]

4. **Calculate the Speed of Satellite Y:**
For satellite Y, which orbits at radius \( 4R \):
\[ v_Y = \sqrt{\frac{GM}{4R}} = \sqrt{\frac{GM}{4} \cdot \frac{1}{R}} = \frac{1}{2} \sqrt{\frac{GM}{R}} = \frac{1}{2} v_X \]

5. **Find the Ratio of Speeds:**
To find how many times the speed of satellite X is compared to satellite Y, we take the ratio:
\[ \frac{v_X}{v_Y} = \frac{v_X}{\frac{1}{2} v_X} = 2 \]

6. **Conclusion:**
The speed of satellite X is 2 times that of satellite Y.

### Final Answer:
The speed of \( X \) is **2 times** that of \( Y**.