Hi everyone! I’ve always been fascinated by how scientists figure out the mass, radius, and age of stars and planets, especially when they’re so far away. Can someone explain in simple terms how they do this? What tools and methods do they use to gather and interpret this information? Thanks in advance for satisfying my curiosity!
In: Planetary Science
A lot of what we originally knew about stars comes from lots of observation.
In the 1830s, telescopes became sensitive enough that you could use the parallax method to see the distance to the nearest stars. By looking at them when the Earth was at two different points in its orbit around the sun, they could see that they were slightly shifted, compared to the background. The farther away a star is, the less its position appears to shift between those two points.
Astronomers began to notice in the late 19th century that there was a relationship between the colour of a star and how bright it is, with many of the brighter stars generally being bluer. At this point, they turned to another recent scientific discovery, known as black body radiation, where a mathematical relationship was found between how hot something is and what colours it glows at. There’s also a relationship between how brightly it glows and its temperature. If you heat up an inch-diameter sphere, it will be dimmer and redder at a lower temperature than at a higher temperature, and that relationship is independent of what it’s made of. So, if you know how bright something is and what colour it’s glowing at, you can figure out how big it is.
Now, combine these discoveries together. Astronomers knew how far away the nearest stars are. By knowing how bright they appeared, they could calculate how bright the stars would be up close. Using the relationship between brightness and colour, they could use another calculation to determine how large those stars are. Since most of the nearby stars seem to follow this relationship, the astronomers could extrapolate that farther ones followed the same rules. If it’s a particular colour, it’s probably a certain size. What’s more, since we know that brightness is related to colour, we could determine how far away the more distant stars are without having to use the parallax method.
Now for the mass. Lucky for us, a good half of the stars in the galaxy are bound in binary systems. By looking at them regularly, you can see these stars orbit each other. Since we know how far away all of these stars are, we can also see how far they are from each other.
In the 17th century, Isaac Newton developed calculus. While causing nervous breakdowns for a lot of math students since then, it proved to be very resilient. One of the big successes of this type of mathematics was Newtons Law of Universal Gravitation which provided a direct relationship between the masses of two objects, their distance from each other, and the period of their orbits around each other. Astronomers knew how long those binary stars too to orbit each other. They knew how far apart they were. So they could plug those numbers in to get their masses.
Now you have the sizes and masses of both stars, with the exception of those few weird outliers. Two out of three! Hell yeah!
Age is a lot more tricky, and astronomers couldn’t figure that out until the 1970s when computers were powerful enough to do some intricate stuff. Everyone knew that the stars had to follow the laws of physics but the amount of brute force calculations needed to tell us how all those laws interact were beyond what a human being could do. But the computers of that era could do just that. They were able to produce models of stars of varying masses to see how they develop over millions, or even billions of years. These models consistently showed that the lighter redder stars burned their hydrogen fuel so slowly that they could keep going for trillions of years, while the heavier bluer stars could burn through their fuel in a matter of millions of years. As stars between those extremes aged, they turned into red giants, accounting for those outliers that were such a mystery for the last century.
Size, mass, and age. It was a long strange trip but we eventually got there.
You also mentioned planets, by which I’m assuming you mean those around other stars. According to all theories about how solar systems form, it’s generally agreed that the planets that orbit a star are roughly the same age as the star itself. They formed alongside each other, so they will generally have that relationship. You can find the size of an exoplanet by seeing how much of their star’s light is blocked when it passes between it and Earth. A very fiddly observation but it can be done.
You can also see how massive the planet is by seeing how much its star shifts back and forth during its orbit. But this shift in position is way too minute to see, so you have to use another little trick of physics. It’s been known since the mid-19th century that waves appear squeezed together if they’re emitted by something moving toward you and appear spread apart if it’s moving away. It’s also well known among physicists that light is a wave. By looking at how the light sent by a star is squeezed and spread during the planet’s orbit, you can see how much the star wobbles to compensate for it. We know how massive the star is, the period of the orbit, and the planet’s distance from the star. Plug those into Newton’s formula for gravitation and you have the planet’s mass.
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