Luminosity from Mass

The Luminosity from Mass calculator approximates the luminosity of a star based on its mass.

INSTRUCTIONS: Choose units and enter the following.

• (M)  Mass of Main Sequence Star

Luminosity (L): The calculator returns the luminosity of the star in Solar Luminosities, multiples of the luminosity of the of the Sun.

The Math / Science

There is a relationship between mass and luminosity for stars in the "hydrogen" burning phase of their life cycle (the so called "main sequence"). This formula estimates the luminosity of a main sequence star given its mass.  The formula for luminosity from stellar mass is:

    L = M^3.5

where:

• L = Luminosity
• M = Mass of the Star

What is a Main Sequence Star

A main sequence star is a star that is in the longest and most stable part of its life cycle, during which it fuses hydrogen into helium in its core. This phase of stellar evolution is characterized by a balance between gravitational forces pulling matter inward and the pressure from nuclear fusion pushing outward. Here are some key points about main sequence stars:

1. Hydrogen Fusion: The primary source of energy for main sequence stars is the fusion of hydrogen into helium in their cores. This process releases a tremendous amount of energy, which radiates outward and supports the star against gravitational collapse.
2. Stability: Main sequence stars are in a state of hydrostatic equilibrium, meaning that the inward pull of gravity is perfectly balanced by the outward pressure of radiation from nuclear fusion. This balance makes them stable over long periods.
3. Classification: Stars on the main sequence are classified by their spectral types, which range from the hot, massive O-type stars to the cooler, less massive M-type stars. These types are further categorized into subclasses (e.g., G2 for the Sun, which is a G-type star).
4. Lifespan: The lifespan of a main sequence star depends on its mass. Massive stars burn through their hydrogen fuel much faster and therefore have shorter lifespans, typically millions of years. Smaller stars, like red dwarfs, can remain on the main sequence for tens to hundreds of billions of years.
5. Hertzsprung-Russell Diagram: Main sequence stars can be found along a continuous band on the Hertzsprung-Russell (H-R) diagram, which plots stars according to their luminosity and temperature. The position of a star on the main sequence is determined by its mass.
6. Evolution: Once a star exhausts the hydrogen in its core, it leaves the main sequence and undergoes further stages of evolution, which can lead to it becoming a red giant, a white dwarf, a neutron star, or a black hole, depending on its initial mass.

Our Sun is a typical example of a main sequence star, currently in the middle of its life cycle. It has been in this stable phase for about 4.6 billion years and is expected to remain so for another 5 billion years.

Astronomy Calculators

Astronomical Units

Because of the enormity of space and the size of the objects studied, the field of astronomy employs units not commonly used in everyday life.  Nonetheless, these units do translate into common units at a grand scale, and vCalc provides automatic conversions between units for calculator inputs and answers via the pull-down menus.  The following is a brief description on the distance, mass and time units employed in the field of astronomy

Astronomy Distance Units

Astronomical Unit (au): Within our solar system, a common measure of distance is au, which stands for astronomical units.  A single astronomical unit is the mean distance from the Sun's center to the center of the Earth.

Light Travel in Time: Light is a primary observable when studying celestial bodies.  For this reason, the distance to these objects are measured in the amount of time it would take light to travel from there to the Earth.  We can say that an object is one light-year away, and that means that the object is at a distance where it took an entire year for light from the object to travel to Earth.  Since the speed of light is 299,792,458.0 meters per second, one can compute the distance equal to a light year as follows:

1 light year = 299,792,458.0 (meters / second) x 31,536,000 (seconds / year) = 9,460,528,405,000,000 meters

The same exercise can be used for light traveling shorter periods of times, light seconds, light minutes, light hours and light days.  Since even these units are not enough when computing distances across the universe, there is also a light relative distance of kilo-light years (1000 light years), or the distance light travels in a thousand years!

Angle Shift Seen from Earth: Because the Earth goes around the Sun, our observation of distant objects such as stars results in an angular shift when observed at opposite sides of the elliptical orbit.  This shift is used as the basis of a unit knows as a parsec.  A parsec was traditionally defined as the distance where one astronomical unit subtends an angle of one arcsecond.  A parsec was redefined in 2015 to 648000/π astronomical units.  Proxima Centauri, is the nearest star to the Sun and is approximately 1.3 parsecs (4.2 light-years) from the Sun. A mega-parsec is a million parsecs.

Astronomy Mass Units

Astronomical units also apply to the mass of enormous objects such as moons, planets and stars.  For this reason, astronomy also employs mass units that compare other objects to ones familiar to us.  For example, stars are often measured in mass units of solar masses. This is a comparison of their mass to the mass of our sun (one solar_mass).   For planets, astronomers use Earth masses and Jupiter masses for understanding the relative size of rocky planets and gas giants.

Astronomy Time Units

Astronomers use the same time units as everyone else, from the very small nanoseconds, to seconds, minutes, hours, days and years.  This is true with two exceptions known as sidereal days and sidereal years.  These refer to time relative to the celestial objects (the fixed stars).  The Earth rotates every 24 hours relative to the Sun. But we are moving in a circle around the Sun.  In comparison, the Earth rotates every 23 hours, 56 minutes and 4.0905 seconds (23.9344696 hours) compared to the stars in the celestial sphere.  This is known as a sidereal day.

In the same vein, a sidereal year is the time it takes the Earth to complete one orbit around the Sun relative to the celestial sphere.  Where a year is 365 days, a sidereal year is 365.256363004 days, or 1,224.5 seconds more than a calendar year.