# Solar System: How Do We Calculate Mass Of Sun?

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It is too easy for you to measure the mass of everyday items, like a bread, an apple, a watermelon but how do you measure the mass of something much much larger, like the SUN?

To determine the mass of sun let’s use an approach called the orbital method. We can calculate the mass of the Sun by measuring the orbital speed and the radius of one of the planets, such is Jupiter. Jupiter orbits the sun at 13 km/s, the shape of Jupiter’s orbit is essentially circular with a radius of 780 million km. So how to use these two numbers to calculate the Sun’s mass?

Let’s start with Newton’s second law of motion which says: the net force acting on Jupiter is equal to its mass (times) its celebration, or: $\inline&space;F=m\times&space;a$.

The net force is a gravitational force the Sun’ exerts on Jupiter. The magnitude of this force is equal to the universal gravitational constant (times) the mass of Jupiter (times) the mass of the Sun (divided by) the square of the radius of Jupiter’s orbit, or: $\inline&space;F_{G}=\frac{G\times&space;m_{J}\times&space;M_{S}}{r^{2}}$

Now, because Jupiter moves around the Sun in uniform circular motion, we know that its acceleration is directed toward the sun (image above) and it is equal with speeds squared (divided by) the radius, or: $\inline&space;a=\frac{v^{2}}{r}$.

So we substitute the gravitational force and Jupiter’ acceleration in the second low we get the following formula: $\inline&space;\frac{G\times&space;m_{J}\times&space;M_{S}}{r^{2}}&space;=m_{J}\times&space;\frac{v^{2}}{r}$

If we want to know the mass of the Sun, we rearrange the formula … we obtain: $\inline&space;M_{S}&space;=\frac{v^{2}r}{G}$. Now, when we substitute in the speed and radius of Jupiter’s orbit we can complete our calculations of the Suns mass = $\inline&space;2\times&space;10^{30}$ kg.

So, what is this number really means? The Sun is 1000 times the mass of Jupiter and three hundred thousand times a mass of Earth… really huge.

Excellent! If this approach works, what would you like to do next?

Article by B. Own