Air mass (astronomy)

In astronomy, observing the stars requires looking through Earth's atmosphere. Air mass is a measurement used to describe the amount of air a light ray passes through along its line of sight. This measurement is vital because the atmosphere affects how we perceive celestial objects. As light travels from a star toward an observer, it undergoes attenuation. Attenuation is the reduction in the intensity of light. This happens because light is lost to scattering and absorption as it hits particles in the air.

This process of light loss is known as atmospheric extinction. It is described mathematically by the Beer–Lambert law.

To understand the mechanism, we must look at the path of the light. When a celestial body is at the zenith, it is directly overhead. At this point, the light travels through the shortest possible path. The relative air mass at the zenith is defined as exactly 1. As the object moves toward the horizon, the light must travel through a much thicker layer of air. This increase in path length leads to greater attenuation. Consequently, celestial bodies near the horizon appear less bright than those near the zenith.

The air mass increases as the angle from the zenith increases, reaching a value of approximately 38 at the horizon.

Astronomers use different models to calculate these values. A simple model is the plane-parallel atmosphere. This model assumes the atmosphere is a homogeneous, flat layer where density is constant. In this scenario, the air mass is simply the secant of the zenith angle. For example, at a zenith angle of 60 degrees, the air mass is approximately 2. However, this model is only accurate for zenith angles up to about 60 or 75 degrees. It fails near the horizon because it ignores the curvature of the Earth.

More complex models account for the Earth's spherical shape. A nonrefracting spherical atmosphere model can treat the atmosphere as being concentrated in the lower 9 km of height. In a homogeneous spherical model, the air mass can be calculated using the Earth's radius, which is 6371 km. These models help scientists understand how the density of air changes with elevation. In a real atmosphere, density is not constant; it decreases as you move higher above sea level. Scientists also use isothermal models, where the atmosphere has a constant temperature.

History shows that many researchers have worked to refine these calculations. Allen created an abbreviated compilation of air mass values from earlier sources. Other scientists, such as Kasten and Young, developed formulas to help with these measurements. Different formulas have been designed to fit specific needs. Some work well for high zenith angles, while others attempt to be accurate near the horizon. However, calculating air mass near the horizon is extremely difficult. This is because low-altitude extinction is heavily affected by the concentration of aerosols and local temperature gradients.

Refraction is another critical factor in these calculations. Atmospheric refraction causes light to follow an approximately circular path rather than a straight line. This makes the actual path through the air slightly longer than a geometric straight line. Refraction also causes a celestial body to appear higher in the sky than it actually is. At the horizon, the difference between the true zenith angle and the apparent zenith angle is about 34 minutes of arc. Because of this, many formulas are based on the apparent zenith angle rather than the true one.

Ultimately, air mass connects the physics of light to the structure of our planet. By understanding the density, temperature, and pressure of the atmosphere, astronomers can correct their observations. This allows them to see the true brightness of stars. Whether using a simple plane-parallel model or a complex layered model, the goal remains the same. Scientists want to account for every bit of air that sits between their telescope and the vastness of space.