A : More accurate formula for the Doppler effect which is valid when the speeds close to that of light, requires the used of Einsteins special theory or relativity.
R : Doppler effect is the basis for the measurements of the raidal velocities of distant galaxies.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To solve the question regarding the Doppler effect and its implications, we need to analyze the statements provided:

**Statement A**: More accurate formula for the Doppler effect which is valid when the speeds are close to that of light, requires the use of Einstein's special theory of relativity.

**Statement R**: Doppler effect is the basis for the measurements of the radial velocities of distant galaxies.

### Step-by-Step Solution:

1. **Understanding Statement A**:
- The classical Doppler effect formula is valid for speeds much less than the speed of light. However, when dealing with speeds that approach the speed of light, relativistic effects become significant.
- The relativistic Doppler effect formula accounts for these effects and is derived from Einstein's theory of relativity. This formula is essential for accurately calculating the frequency shift of light from objects moving at relativistic speeds.

2. **Understanding Statement R**:
- The Doppler effect is indeed used in astronomy to measure the radial velocities of distant galaxies. When a galaxy moves away from us, the light it emits is redshifted (its wavelength increases), and when it moves towards us, the light is blueshifted (its wavelength decreases).
- By measuring the shift in the wavelength of light from a galaxy, astronomers can determine how fast the galaxy is moving away or towards us, which is crucial for understanding the expansion of the universe.

3. **Analyzing the Relationship Between A and R**:
- Statement A is true because the relativistic Doppler effect is necessary for accurate measurements at high velocities.
- Statement R is also true as the Doppler effect is indeed used to measure the radial velocities of galaxies.
- Since both statements are true and R is a correct explanation of A, we conclude that the relationship is valid.

### Conclusion:
- Both statements A and R are true, and R is the correct explanation for A.