Question

Understand how the luminosity, temperature and radius of a star are related. How does its brightness depend on distance from us?

Answer 1

The luminosity, temperature, and radius of a star are related through the Stefan-Boltzmann Law, which states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. In terms of a star, this can be expressed as L = 4πR2σT4, where L is the luminosity, R is the radius, T is the temperature, and σ is the Stefan-Boltzmann constant.

The brightness of a star as seen from Earth, also known as its apparent brightness, depends on both its luminosity and its distance from us. This relationship is given by the inverse square law, which states that the apparent brightness is equal to the luminosity divided by 4π times the square of the distance: B = L / (4πd2). This means that the apparent brightness decreases with the square of the distance. So, a star that is twice as far away will appear four times dimmer.

Step-by-step explanation:

One might guess that bright stars are closest and faint stars are farther away. If all stars were the same intrinsic brightness, that would be true. However, for "normal" stars, the brightness of stars is correlated with the mass of the star. And when stars evolve to become "red giants" or "supernovae" they also brighten. With a telescope, we measure the apparent brightness of a star. We can translate this to an absolute scale to learn the true luminosity of a star only if we know the distance to the star. Think for a moment about how you would measure the distances to stars. It's not easy - this has been a major effort in astronomy over the past few decades.

Answer 2

The luminosity, temperature, and radius of a star are interrelated and determine its inherent brightness. A star's apparent brightness from Earth is affected by its luminosity and the distance. Astronomers calculate the distance to a star by its luminosity and apparent brightness, which can be difficult due to the variety of intrinsic luminosities among stars.

Step-by-step explanation:

The luminosity, temperature, and radius of a star are interconnected in defining the star's characteristics. Luminosity is the total energy a star emits per second. A star's temperature influences the energy it radiates, and its radius determines the surface area through which this energy is emitted. These factors collectively affect how bright a star appears from Earth, known as its apparent brightness.

The apparent brightness of a star diminishes with the square of the distance from the observer to the star. This is why two stars with identical luminosity can appear to have different brightness levels; if one is farther away, it will look dimmer in comparison to one that's closer. Consequently, by knowing a star's luminosity and observing its apparent brightness, astronomers can calculate its distance from Earth, utilizing magnitudes to express relative light intensities based on human vision.

The challenge for astronomers is to determine a star's intrinsic luminosity, which can be complex due to the variety of luminosities among stars. Stars do not possess a standard wattage like light bulbs, thus a dim appearance could imply either a low-luminosity star that's nearby or a high-luminosity star that is far away.