A lobe in a visible jet from galaxy \(\mathrm{M} 87\) is observed at a distance of 1,530 pc \((5,000\) light-years) from the galaxy's center moving outward at a speed of 0.99 times the speed of light \((0.99 c) .\) Assuming constant speed, how long ago was the lobe expelled from the supermassive black hole at the galaxy's center?

The speed of light, commonly denoted as \( c \), is an incredibly important constant in physics. Light moves through a vacuum at roughly 299,792 kilometers per second (km/s). This speed is so fundamental it features in Einstein's theory of relativity. In many calculations, scientists often express light speed in units of light-years, which is the distance that light travels in one year.

For example, in our problem, the lobe from galaxy M87 is traveling at 0.99c, meaning 99% of the speed of light. High speeds near the speed of light require specific formulas used in the field of relativity, illustrating why this concept is critical to solving the given problem. Imagine how distant and ancient phenomena can be analyzed through these calculations!

Galaxy M87, also known as Messier 87, is an enormous galaxy situated approximately 53 million light-years away in the Virgo cluster. Famous for its very energetic jet that shoots out from its center, this jet is believed to originate from the supermassive black hole residing at M87's core.

The supermassive black hole in M87 is one of the most massive known, weighing in at several billion times the mass of our sun. The jet visible from M87 is composed of accelerated particles ejected at nearly the speed of light, making it an excellent subject for relativity studies and astronomical observations.

A light-year is a measure of distance, not time. It signifies how far light travels in one year—about 9.461 trillion kilometers (or roughly 5.88 trillion miles). Astronomers use light-years to describe vast distances in the universe.

In the problem, the lobe from M87 is 5,000 light-years away from the galaxy's center. This measurement helps us understand just how incredibly vast the distances are in space. Calculating how long it took for the lobe to travel those 5,000 light-years at 0.99 times the speed of light gives us insight into the age of cosmic events, like the ejection event we're studying. Estimating these timings helps pinpoint the history and behaviors of celestial objects.

Astrophysics often involves solving complex problems using fundamental principles. In our example, we're given the distance in light-years and the speed of the lobe in terms of light speed. We use the formula Time = Distance / Speed to find out how long it took for the lobe to travel that distance.

Calculating: Time = \( \frac{5,000 \text{ light-years}}{0.99c} \). Solving this gives us approximately 5,050.51 years. This means that about 5,050 years ago, the lobe was expelled from the supermassive black hole in M87's center. This kind of problem-solving integrates knowledge of physics, mathematics, and astronomy.

• Identifying units and converting them as necessary
• Using fundamental formulas to solve for unknowns
• Interpreting results to understand cosmic events