The mass of the sun
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In the morning post we measured the mass of the earth.
Now we will measure the mass of the sun.
We can use the following formula to measure the mass of the sun:
M = v ^ 2r / G
Here M is the mass of the sun, v is the speed of rotation of the earth around the sun, r is the radius of the circle around which the earth revolves around the sun (actually in the elliptical circle, we take it as a circle for the convenience of calculation), and G is the gravitational constant.
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So the formula means: the mass of the sun = the square of the speed of the earth, the radius of the circle of the earth's orbit is the gravitational constant.
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According to the above formula, we only need to know the distance of the earth from the sun to find the mass of the sun. This distance was estimated by Greek philosophers about two thousand years ago. Now we know more precisely, about 150 million km. (15 * 10 ^ 11 meters if written in meters). This is what we can take as the radius of the circle of the Earth's orbit.
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Then came the motion of the earth. To find out the speed, we first need to find the circumference of the orbit. If you know the radius of the circle, you can easily find the circumference. That's why the formula is,
C = 2πr
That is, circumference = 2 times pi (3.14159) times radius.
The circumference is 942,000,000 km. If we divide this circumference (converted to meters) by dividing 365 days and 6 hours into seconds, then how many kilometers the earth travels per second. I will get it quickly. And that is, 30 km. If you take it in meters, it is 30,000 meters per second.
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So far we have got the values of v and r to use in our formula. And the value of G remains. It is a gravitational constant. Its value is 6.67 * 10 ^ -11,.
Now we can set the value to the formula:
The mass of the sun = 30000 ^ 2 times 15 * 10 ^ 11 divided by 6.67 * 10 ^ -11. If you calculate it with a calculator, the mass of the Sun is the same as the weight of the Sun. And that number is 1.989 × 10 ^ 30 kg (26 zero kg as per 1979).
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He also wanted to explain how the formula came about. But I did not explain for fear of growing up. Suffice it to say that the earth's orbit around the sun is largely due to the sun's gravitational force. Otherwise the earth would move in a straight path at its own pace and go somewhere else.
And the gravitational force of the sun is proportional to its mass. So if we can determine how much gravitational force of the sun is being applied to the earth, we can also determine the mass of the sun. Our formula is based on the determination of the force of the sun.
