The Doppler effect significantly supports the Big Bang theory through the observation of redshift in distant galaxies. According to the Big Bang theory, the universe began from an extremely hot and dense state and has been expanding ever since. This expansion leads to the stretching of light waves, causing them to shift towards the red end of the spectrum as observed from Earth. The greater the redshift, the faster a galaxy is moving away, which implies a continuously expanding universe. This observation aligns with the Big Bang theory's prediction of an expanding universe. Moreover, the uniformity of the redshift across the observable universe corroborates the idea that the expansion is not centred around any particular point but is a universal phenomenon. This evidence is one of the cornerstones of modern cosmology, providing strong empirical support for the Big Bang theory.

Yes, the Doppler effect is a crucial tool in detecting exoplanets, planets orbiting stars outside our solar system. This method, known as the radial velocity method, involves observing the slight changes in the star's spectrum caused by the gravitational influence of an orbiting planet. As the planet orbits, it causes the star to move in a small orbit as well, resulting in periodic changes in the star's velocity towards and away from us. These velocity changes lead to small Doppler shifts in the star's light, alternately redshifting and blueshifting its spectrum. By measuring these shifts, astronomers can infer the presence of a planet, its mass, and its orbital period. The technique has been highly successful, leading to the discovery of many exoplanets since the 1990s. However, it's more effective for detecting large planets close to their stars, as their gravitational influence is stronger.

The Doppler effect plays a significant role in understanding dark matter in galaxies through the analysis of rotational velocities of stars within galaxies. According to Newtonian mechanics, stars at the outer edges of a galaxy should rotate slower than those near the center, as the gravitational pull weakens with distance. However, observations using the Doppler effect reveal that stars in the outskirts of galaxies rotate at roughly the same speed as those nearer the center, defying these expectations. This discrepancy suggests the presence of an unseen mass - dark matter - exerting additional gravitational force. By studying the Doppler shifts in the light from stars at various distances from a galaxy's center, astronomers can map the galaxy's rotation curve and infer the distribution of dark matter within it. This understanding is crucial for cosmology and astrophysics, as dark matter constitutes a significant portion of the universe's total mass.

The Doppler effect can be more pronounced in radio frequencies than in optical frequencies for certain astronomical objects due to the nature of the emitted waves and the observing conditions. For objects like pulsars and certain types of stars, the emitted radio waves have longer wavelengths compared to their optical emissions. When these objects move relative to the Earth, the change in wavelength (and therefore frequency) of the radio waves is more easily detectable due to their longer baseline wavelengths. Additionally, radio astronomy can be less affected by atmospheric distortion and light pollution, providing clearer and more consistent data for Doppler analysis. This is particularly important for studying objects with subtle movement or those located in dense, dusty regions of space where optical observations might be obscured.

The Doppler effect is instrumental in studying binary star systems, particularly in determining their orbital characteristics. In a binary system, as each star orbits the common center of mass, it moves towards and away from the Earth over its orbit. This motion causes periodic Doppler shifts in the light emitted by each star. When a star moves towards us, its light is blueshifted; when it moves away, the light is redshifted. By analysing these shifts, astronomers can determine the stars' orbital velocities and periods. Furthermore, this data can be used to calculate the mass of the stars using Kepler's laws of planetary motion. In cases of eclipsing binaries, where one star periodically blocks the other, the Doppler effect also helps in determining the inclination of the orbital plane. This comprehensive analysis provides valuable insights into the physical properties of stars and their interactions in binary systems.