Black holes are among the most difficult objects in the universe to study. Their gravitational pull is so strong that nothing, not even light, can escape from within their event horizon, the boundary beyond which escape is impossible. As a result, scientists cannot observe a black hole’s interior or place it on a scale to determine its weight.
Yet astronomers can measure the mass of black holes with remarkable precision. They do so by studying how black holes influence the matter, light, stars, and gas around them. Because gravity depends on mass, a black hole leaves measurable effects on its surroundings. By observing those effects and applying the laws of physics, scientists can calculate how much mass the black hole contains.
The methods vary depending on the black hole’s size, location, and environment. Some measurements rely on the orbits of nearby stars, while others use the motion of hot gas, the behavior of matter falling toward the black hole, or the gravitational waves produced when two black holes merge. Together, these techniques allow astronomers to investigate black holes ranging from a few times the mass of the Sun to billions of times its mass.
Why a black hole’s mass can be measured without seeing it
A black hole is a region of spacetime where gravity is so intense that an event horizon forms. Its mass determines much of its gravitational influence on the surrounding universe.
Although a black hole cannot emit light from inside its event horizon, its gravitational field extends beyond that boundary. Nearby objects respond to this gravity just as they respond to the gravity of any other massive body.
For example, Earth orbits the Sun because of the Sun’s gravitational attraction. Astronomers can determine the Sun’s mass by measuring Earth’s orbital motion and applying Newton’s laws of gravity. The same principle works for black holes. If scientists can measure how stars or gas move around an unseen object, they can estimate the mass responsible for that motion.
This approach is particularly useful because gravity does not depend on whether an object produces visible light. A dark object can still exert a measurable gravitational pull.
There is also an important distinction between mass and weight. Mass describes how much matter an object contains and is an intrinsic property of the object. Weight is the force gravity exerts on that mass and depends on the surrounding gravitational field. When astronomers discuss the mass of a black hole, they mean its mass, usually expressed in units of solar masses. One solar mass is approximately the mass of the Sun.
The central challenge is therefore not detecting gravity but identifying its source and measuring its effects accurately enough to determine the mass.
Measuring mass by tracking the orbits of nearby stars
One of the most direct and reliable ways to measure a black hole’s mass is to observe the movement of stars orbiting it.
A star traveling around a black hole follows an orbit shaped by the black hole’s gravitational field. By tracking the star’s position over time, astronomers can determine the size and shape of its orbit and how long it takes to complete one revolution.
These observations provide information about the mass of the central object. A more massive object produces a stronger gravitational influence, affecting the speed and orbital period of nearby stars.
The underlying principle comes from Newton’s law of universal gravitation and his laws of motion. For an object orbiting a much more massive central body, the orbital period and the size of the orbit can be used to calculate the central body’s mass.
This is an application of Kepler’s laws of planetary motion, which describe the relationship between an orbiting object’s distance, orbital period, and the mass of the body it orbits.
In practice, astronomers need more than a single observation. They collect measurements over months or years, sometimes much longer, to reconstruct the star’s complete orbit. The longer and more accurately they observe the motion, the better they can constrain the mass.
A particularly important example is Sagittarius A*, the supermassive black hole at the center of the Milky Way. It is surrounded by stars that astronomers have tracked for decades.
One especially useful star, known as S2, follows a highly elliptical orbit around the galactic center. It completes an orbit in approximately 16 years and passes relatively close to the central black hole. By measuring its changing position and speed, astronomers have determined that Sagittarius A* has a mass of approximately 4 million solar masses.
These measurements provide compelling evidence for a supermassive black hole at the center of our galaxy. They also demonstrate how astronomers can determine the mass of an object that cannot be observed directly.
Using a star’s speed to estimate a black hole’s mass
Sometimes astronomers cannot observe an entire stellar orbit. In those situations, measuring a star’s speed can still provide important information about the mass of an unseen object.
A star moving near a massive black hole can travel at extraordinary speeds because of the strong gravitational attraction. The closer it gets to the black hole, the more strongly gravity affects its motion.
Astronomers measure these speeds using a technique called spectroscopy. This method involves separating light into its component wavelengths to study the properties of the object producing it.
When a star moves toward Earth, its light is shifted toward shorter wavelengths, a phenomenon known as blueshift. When it moves away, its light shifts toward longer wavelengths, known as redshift. These changes are examples of the Doppler effect.
By examining the shifts in a star’s spectral lines, astronomers can determine its velocity along the line of sight, meaning its motion toward or away from Earth.
Combining this information with measurements of the star’s position and orbital geometry helps scientists reconstruct its motion and estimate the mass of the object influencing it.
However, velocity measurements alone do not always provide a unique mass estimate. Astronomers also need information about the star’s distance from the black hole and the orientation and shape of its orbit. Additional observations help reduce these uncertainties.
Measuring black holes through the motion of surrounding gas
Not all black holes have nearby stars that astronomers can track. Some are surrounded by large amounts of gas, which provides another way to measure their mass.
When gas approaches a black hole, gravity can pull it into a rotating structure called an accretion disk. As the material spirals inward, friction and other processes heat it to extremely high temperatures. The hot gas can produce intense radiation, particularly in X-rays and ultraviolet light.
The gas also moves at high speeds under the influence of gravity. By studying its motion, astronomers can estimate the mass of the central black hole.
One useful method involves measuring the Doppler shifts of emission lines produced by gas in the accretion disk. Different parts of the rotating disk move in different directions relative to Earth. Gas moving toward us produces blueshifted spectral lines, while gas moving away produces redshifted lines.
The size of these shifts reveals the gas’s speed. If astronomers can also estimate the distance of the gas from the black hole, they can use gravitational physics to infer the black hole’s mass.
This method is especially important for studying supermassive black holes in distant galaxies, where individual stars near the central object may be too faint or too closely packed to observe separately.
However, gas does not always move in simple circular orbits. Magnetic fields, radiation pressure, turbulence, and powerful outflows can influence its motion. These effects can complicate measurements, so astronomers must use detailed physical models to distinguish gravitational motion from other processes.
Using the brightness of active galaxies to estimate black hole mass
Some galaxies contain exceptionally bright central regions powered by material falling toward a supermassive black hole. These systems are called active galactic nuclei, or AGNs.
The brightest examples are known as quasars. They can outshine the combined light of all the stars in their host galaxies, even though much of their radiation comes from a relatively small region surrounding the central black hole.
Astronomers can estimate the mass of these distant black holes by combining measurements of the radiation produced by their accretion disks with observations of gas moving around them.
One widely used approach is called the reverberation mapping technique.
The basic idea is that changes in brightness near the black hole can affect the surrounding gas after a measurable delay. When the central source becomes brighter, its radiation travels outward and illuminates clouds of gas farther away. Those clouds respond by producing emission lines.
Because light takes time to travel, the emission-line response occurs after the initial brightness change. By measuring this time delay, astronomers can estimate the distance between the central source and the gas clouds.
They then measure the speed of the gas using Doppler shifts in its emission lines. Combining the gas’s distance with its velocity provides an estimate of the gravitational mass enclosed within its orbit.
This method is particularly valuable because it allows astronomers to estimate the masses of supermassive black holes in galaxies billions of light-years away.
Reverberation mapping does not require scientists to resolve the black hole’s immediate surroundings into separate visible objects. Instead, it uses changes in light as a kind of natural timing signal.
Nevertheless, the method involves assumptions about the geometry and motion of the gas. Astronomers account for these uncertainties when interpreting the results.
Detecting black hole mass through gravitational waves
A different approach became possible with the development of gravitational-wave astronomy.
According to Albert Einstein’s general theory of relativity, massive objects distort spacetime. When massive objects accelerate in certain ways, particularly when compact objects orbit one another, they can produce disturbances that travel outward through spacetime. These disturbances are called gravitational waves.
When two black holes orbit each other, they gradually lose orbital energy through gravitational radiation. As a result, their separation decreases, and they spiral toward one another. Eventually, they merge into a single black hole.
During the final stages of this process, the black holes move at enormous speeds and generate strong gravitational waves. These waves carry information about the masses and spins of the merging objects.
Scientists detect gravitational waves using highly sensitive instruments such as the Laser Interferometer Gravitational-Wave Observatory, or LIGO.
LIGO uses two long, perpendicular arms containing laser light. A passing gravitational wave slightly changes the relative lengths of these arms. This produces a tiny, measurable change in the interference pattern of the laser beams.
The resulting signal is analyzed using predictions from general relativity. The frequency and changing strength of the gravitational waves reveal how the black holes moved during their final orbits.
The waveform also contains information about the masses of the two black holes and the mass and spin of the final object.
An especially important feature is the gravitational-wave signal’s frequency evolution, often called its chirp. As the black holes spiral closer together, they orbit each other faster, causing the gravitational-wave frequency to increase. The pattern of this increase depends strongly on the masses of the objects.
Scientists compare the observed signal with theoretical waveforms calculated from Einstein’s equations. The best-fitting models provide estimates of the black holes’ properties.
Unlike methods based on visible stars or gas, gravitational-wave measurements do not require the black holes to produce electromagnetic radiation. They can reveal mergers involving black holes that might otherwise be difficult or impossible to observe.
How astronomers combine different measurements
No single method works equally well for every black hole. The best approach depends on the surrounding environment, the distance to the object, and the quality of available observations.
For black holes in our galaxy, astronomers can sometimes track individual stars and reconstruct their orbits. For supermassive black holes in distant galaxies, measurements of gas motion and reverberation mapping may be more practical. When two black holes merge, gravitational waves provide an independent way to determine their masses.
Scientists also compare different methods whenever possible. If separate techniques produce consistent results, confidence in the estimated mass increases.
For example, astronomers studying a nearby galaxy might measure the motion of stars near its center and compare the results with observations of gas in the same region. Differences between the estimates can reveal limitations in the assumptions used by either method.
Accurate measurements also require scientists to account for other sources of gravity. A black hole does not necessarily exist in isolation. Stars, gas, dark matter, and other matter contribute to the gravitational field around it.
If astronomers attribute all observed motion to the black hole when some of the gravitational influence comes from surrounding matter, they may overestimate its mass.
Distance measurements are also important. Errors in the estimated distance to a galaxy can affect the inferred physical size of stellar orbits and gas distributions, which in turn affects the calculated mass.
For these reasons, black hole mass estimates are generally reported with uncertainties rather than as perfectly exact numbers.
Why measuring black hole mass matters
Determining the mass of a black hole is more than an exercise in understanding an unusual astronomical object. It helps scientists investigate how galaxies form, evolve, and interact with their central regions.
Supermassive black holes are found at the centers of most large galaxies studied in detail. Their masses are often correlated with properties of the galaxies surrounding them, including the mass and motion of stars in the central regions.
These relationships suggest that galaxies and their central black holes influence one another during their evolution.
A growing black hole can release enormous amounts of energy as surrounding material falls inward. Radiation and powerful jets of particles can affect the surrounding gas, sometimes heating or pushing it away. This process, known as feedback, can influence how easily a galaxy forms new stars.
By measuring black hole masses across different galaxies, astronomers can test theories about how these objects grow and how their development relates to the evolution of their host galaxies.
Mass measurements also help scientists understand the different populations of black holes. Stellar-mass black holes form from the collapse of massive stars, while supermassive black holes contain millions or billions of solar masses. How the largest black holes formed and grew remains an active area of research.
Gravitational-wave observations add another important dimension. By measuring the masses of merging black holes, scientists can study how black holes form in different environments and how their populations change over cosmic time.
The more accurately astronomers measure black hole masses, the better they can test predictions from general relativity and investigate the extreme conditions created by gravity.
What scientists still cannot determine from mass alone
Although mass is one of the most important properties of a black hole, it does not describe everything about it.
In the framework of general relativity, an isolated black hole in a stable state can be described by three fundamental properties: mass, electric charge, and angular momentum, or spin.
Mass determines the overall gravitational scale of the black hole. Spin describes how rapidly it rotates and influences the structure of spacetime around it. Electric charge is theoretically possible, but astrophysical black holes are generally expected to have very little net charge because surrounding matter tends to neutralize it.
A black hole’s mass also determines the size of its event horizon, assuming its spin and charge are known. For a nonrotating, electrically neutral black hole, the event horizon’s radius is directly proportional to its mass.
However, knowing the mass does not reveal the detailed history of how the black hole formed. Two black holes with the same mass can have very different origins, environments, and rotational histories.
Nor does a mass measurement reveal what happens inside the event horizon. General relativity predicts the existence of a central singularity in the simplest classical descriptions of black holes, but physicists do not yet have a complete theory that combines gravity with quantum mechanics to explain the deepest interior regions.
Astronomers therefore distinguish between what observations establish and what physical theories predict. The mass of a black hole can be measured through its observable gravitational effects, even though many questions about its internal structure remain unresolved.
Measuring the invisible through its effects
Scientists do not need to see a black hole directly to determine its mass. They measure the influence it has on the universe around it.
The orbits of nearby stars, the motion of hot gas, changes in the brightness of active galaxies, and gravitational waves from merging black holes all provide measurable evidence of gravitational mass.
Each method uses a different physical signal, but the underlying principle is the same: mass shapes gravitational motion and the behavior of spacetime.
By combining precise observations with the laws of gravity, astronomers can weigh objects that emit no light from within their event horizons. In doing so, they turn one of the universe’s most elusive objects into something that can be studied quantitatively, tested against physical theories, and understood through observation.
