Question

The best measurements of the mass of the black hole at the galactic center come from (a) the orbits of stars in the galactic center. (b) the orbits of gas clouds in the galactic center. (c) the amount of radiation coming from the galactic center.

Short answer

(a) the orbits of stars in the galactic center.

Step-by-step solution

Understanding the Problem

The problem asks which method provides the best measurement of the mass of the black hole at the center of a galaxy. We have three options: (a) the orbits of stars, (b) the orbits of gas clouds, and (c) the amount of radiation from the galactic center.

Analyzing Each Option

To determine the best answer, we need to analyze each method. The orbits of stars (option a) near the black hole are often used to measure mass since they directly respond to gravitational forces. The orbits of gas clouds (option b) can also be influenced by other factors like friction. Radiation (option c) does not directly indicate mass as it may come from various sources.

Evaluating Practical Use

In practice, observing the orbits of stars provides a precise way to calculate the black hole's mass using Kepler's laws of motion. Gas clouds involve uncertainties due to additional influences, and radiation measurements do not directly yield mass. Scientists prefer using star orbits as it provides precise, reliable results.

Conclusion

Based on understanding and practical evaluation, the orbits of stars in the galactic center provide the most accurate mass measurements. This method minimizes interference and directly relates to the gravitational pull of the black hole.

Key concepts

Galactic Center

The Galactic Center is the rotational hub of our Milky Way galaxy, packed with stars, gas, and dust. It is also the home of a supermassive black hole, known as Sagittarius A*. This dense and energetic area is about 26,000 light-years away from Earth. Though it is not visible to the naked eye due to thick interstellar dust and gas clouds, scientists have utilized radio, infrared, and X-ray telescopes to observe it.
The study of the Galactic Center is crucial because it helps us understand more about the dynamics of the Milky Way. As we peer into this bustling area, we can see the way stars and other celestial bodies move around, influenced by the massive gravitational pull of the black hole. This movement helps astronomers measure the black hole's mass more accurately.

Star Orbits

Star orbits around the Galactic Center are a key tool for measuring the mass of the central black hole. Stars move in predictable patterns that are dictated by the gravitational forces acting upon them. When a star orbits close to a black hole, its velocity and path reveal much about the black hole's mass and gravitational pull.
The closer the star is to the black hole, the more it accelerates due to the intense gravitational forces. Astronomers observe these speeding stars for extended periods to track their orbits accurately. By studying their trajectories, scientists can precisely measure the mass of Sagittarius A* and other similar cosmic entities across different galaxies. This method's precision makes it the preferred choice for astronomers seeking to understand giant black holes.

Kepler's Laws of Motion

Kepler's Laws of Motion serve as a foundation for understanding celestial movements. These laws describe how stars and planets orbit massive celestial bodies, such as stars orbiting a black hole in the Galactic Center.
According to Kepler:

• Planets (or stars) follow an elliptical orbit around a central mass, like a black hole.
• The line joining a planet to the central mass sweeps out equal areas in equal times, meaning that a star moves faster when it's closer to the black hole.
• The square of a planet's orbital period is directly proportional to the cube of the semi-major axis of its orbit.

By applying these laws, astronomers can predict the movement and speed of stars orbiting black holes, allowing them to calculate the mass and gravitational force exerted by these massive entities accurately.

Gravitational Forces

Gravitational forces are the invisible arms that govern the dance of celestial bodies, including stars orbiting around the Galactic Center. They are the key to understanding the interactions between massive objects like black holes and the surrounding stars.
Gravity works by pulling objects together, and its strength increases with the mass of the objects and decreases with the square of the distance between them. This means the closer the star is to a black hole, the stronger the gravitational attraction.
By observing how stars orbit the black hole, scientists can measure the gravitational forces involved. This data is essential for calculating the mass of the black hole using sophisticated mathematical models and allows scientists to draw broader conclusions about the dynamics at the core of the Milky Way.