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How is the Mass of the Sun Calculated?

Measuring an object's mass on Earth is fairly simple. Put an object with a known mass on a balance and compare it to an object with unknown mass. But objects that are too large can't fit on a balance, and objects in space can't get put on a balance. So the mass of an object like the sun has to be measured in different ways. Scientists use what they know about gravity and Earth's orbit to measure the mass of the sun.

The Basic Concept
- Since the force of gravity is constant on every object, scientists can use a formula to find out the mass of a central object according to how fast another object orbits it, combined with the distance between the two objects. Scientists can calculate the mass of the sun like this, since all this information is readily available.
Velocity
- Gravity determines the velocity ("v") of an orbiting object. Scientists know exactly how much gravity acts on any object. This constant is called the "universal constant of gravity." Since this constant, expressed as "G," never changes, celestial objects orbit other objects at different velocities because their masses vary. Find the velocity of Earth by dividing the total distance Earth travels in one orbit by the time it takes for Earth to complete an orbit. You must measure the distance in meters and measure the orbital time in seconds.
Distance of Earth's Orbit
- Use the formula to find the circumference of a circle to calculate the total distance the earth travels in one orbit. Earth's average distance form the sun is 150,000,000 kilometers. Express this distance in meters and multiply it times pi, then times two. The product is the total distance of one Earth orbit, in meters. Use this measurement to calculate Earth's velocity.
Plug in the Numbers
- Earth's velocity, its orbital radius and the universal constant of gravity are all that a scientist needs to calculate the mass of the sun. Square "v," then multiply it times "r." Divide the resulting product by the universal constant of gravity. The quotient represents the sun's mass.
Scientific Notation
- The numbers to plug into this equation are either very small or very large. Express these numbers in scientific notation, or you will have numbers that contain far too many digits to work with. Large numbers, such as "v," will use positive exponents, while tiny numbers, such as the universal constant of gravity, need to be expressed with negative exponents.
Units of Measure
- Mass measurements are based on the gram. It would be impractical to measure the mass of the sun in grams, so use kilograms. Also remember scientific notation. Even when the sun's mass is measured in kilograms, without scientific notation, the figure would contain 24 zeros.

Astronomy