Question

Which close binary pair of stars will be more easily resolvable with a telescope - two red stars, or two blue ones? Assume the binary star systems are the same distance from Earth and are separated by the same angle.

Short answer

Answer: The pair of blue stars will be more easily resolvable with a telescope due to their shorter wavelength, which results in a higher angular resolution according to the Rayleigh criterion.

Step-by-step solution

Recall the Rayleigh Criterion

To determine the angular resolution of a telescope, we can use the Rayleigh criterion, which is given by the formula: θ = 1.22 * (λ / D) where θ is the angular resolution, λ is the wavelength of the light, and D is the aperture of the telescope.

Compare the wavelengths of red and blue light

Red light has a longer wavelength than blue light. Therefore, the value of λ for the red light will be larger than that for blue light.

Determine the effect on the angular resolution

Since the Rayleigh criterion states that the angular resolution is inversely proportional to the wavelength, a larger wavelength will result in a smaller angular resolution. Thus, the pair of red stars will have a smaller angular resolution than the pair of blue stars.

Conclusion

Based on the relationship between wavelength and angular resolution, the pair of blue stars will be more easily resolvable with a telescope due to their shorter wavelength, which results in a higher angular resolution.

Key concepts

Angular resolution

Angular resolution is a critical parameter in astronomy, determining how finely a telescope can distinguish between close objects in the sky. It's defined as the smallest angle between two points of light that can be distinctly separated by the telescope's optics. When considering celestial objects like binary stars, the ability to resolve them into two distinct points, rather than a single blob of light, relies heavily on the angular resolution of the observing instrument.

For example, finer angular resolution allows astronomers to differentiate between two stars that are very close together in the sky, making it paramount for studying complex systems. According to the Rayleigh Criterion, larger values of angular resolution enable clearer separation between objects. Consequently, telescopes aimed at achieving high angular resolution typically have larger apertures and use light with shorter wavelengths.

Binary star systems

Binary star systems consist of two stars orbiting a common center of mass. They are crucial for astrophysics because they allow scientists to determine stellar masses, which are fundamental to understanding stellar evolution. A challenge with binary star systems is that they can be difficult to resolve if they are very close to each other from our point of view on Earth.

Observing binary stars and distinguishing them as separate entities rather than a single point of light requires precise instruments. The ability to do this is not just about the telescope's power, but also about recognizing the limits set by angular resolution, which depends on both the telescope's aperture and the wavelength of light used.

Wavelength of light

Different colors of light have different wavelengths with red light having longer wavelengths and blue light shorter ones. This property is fundamental when considering the angular resolution as per the Rayleigh Criterion.

Shorter wavelengths, like those associated with blue light, inherently provide higher angular resolution, allowing for a closer and more precise separation of objects in space, such as binary stars. This characteristic is essential in choosing the type of light to use for different observational tasks in astronomy, such as distinguishing individual stars within a binary system.

Telescope aperture

The telescope's aperture, the diameter of its main optical component, has a profound impact on its angular resolution. Larger apertures allow telescopes to collect more light, which enhances their capability to see fainter objects and improves their angular resolution. This results in a sharper image and better differentiation between closely spaced celestial bodies.

When it comes to resolving binary star systems, a larger aperture works in favor of the astronomer, enabling the telescope to separate points of light that are closer together. This is why astronomical telescopes often strive for as large an aperture as practical, balancing size with technological and budgetary constraints.