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What Is Solar Mass?

A solar mass is the mass of the sun. Or, more precisely, it's 1.989 x 10^30 kilograms — about 333,000 Earths.

Astronomers use a solar mass as a basic unit of mass. Since most things in space are big and heavy — such as stars, galaxies and black holes — it makes more sense to talk about such cosmic objects in terms of solar masses as opposed to a much smaller unit, such as kilograms.

Thinking about objects in terms of solar masses also provides a more intuitive sense of the object's mass relative to the sun. The supermassive black hole at the center of the Milky Way galaxy, for example, is about 7.956 x 10^30 kg. Such a huge number is a bit harder to imagine than if you were to say the black hole is as massive as 4 million suns.

Thanks to Sir Isaac Newton, calculating the sun's mass isn't too hard, either. The sun's mass determines how strong its gravity is. And its gravity determines the orbital distance and speed of a planet like Earth.

For example, if the sun were more massive with a stronger gravitational pull, and if Earth were at the same distance from the sun, our planet would have to orbit faster or it would fall into the sun. If the sun were less massive with a weaker gravitational pull, Earth would have to orbit slower or it would be flung out of the solar system.

Newton's equations will calculate the sun's mass as long as we know the speed of Earth's orbit and the distance to the sun. Astronomers use basic geometry to calculate those two constants. Earth orbits the sun at about 67,000 mph (107,000 km/h), according to Cornell, and the distance from Earth to the sun (called an astronomical unit) is 92,955,807 miles (149,597,870 kilometers) according to the International Astronomers Union.

What Is Solar Mass?
Our active Sun.Credit: NASA/SDO

In the late 1600s, Newton computed the relative masses of the sun and other planets. His calculations were mostly correct, although his values for Earth's relative weight were off. He found the sun to be 169,282 times more massive than Earth, whereas the accurate value is 331,950. He miscalculated because his numbers for the Earth-sun distance relied on inaccurate measurements of the sun's parallax, which is the apparent shift of the sun in the sky as observed at different points in Earth's orbit. Researchers also found that he made an error in transcribing numbers when writing new editions of "Principia," his collection of texts that describe mathematical and physical concepts.

Today, instead of using parallax, astronomers can accurately measure distances between solar system objects with radar. By measuring the time it takes for a satellite's radar signal to bounce back from another planet, astronomers can determine the distance to that planet. But because the sun doesn't have a solid surface, radar signals don't bounce back. So, to measure the Earth-sun distance, astronomers first must measure distances to another object, such as Venus. Then, by triangulation, they can calculate the distance to the sun.

Plug that value and the measured speed of Earth's orbit into Newton's equations, and with some simple algebra, you can calculate the sun's mass. Assuming a circular orbit (Earth's orbit is close to a circle), M = (d/G)v^2, where d is the distance to the sun, v is Earth's orbital speed, and G is the gravitational constant.

Further reading:

  • An overview of facts about the sun, from NASA.
  • Sun/Earth comparison by the numbers, from NASA.
  • Find information about NASA's missions to study the sun.

Topic: #solar system
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