Finding the mass of the sun

In summary, to estimate the mass of the Sun, we use the equation Ms=4(pi)^2R^3/(G)(T^2) and plug in the values of orbital radius R=1.5X10^11 m and orbital period T=365.25 days (or 31557600 seconds). However, in the calculation, the exponent for T was not squared, resulting in an incorrect answer. The correct calculation would be Ms=(4(pi)^2(1.5X10^11)^3)/((6.578X10^-11)(31557600sec)^2), which gives a mass of 6.434X10^37 kg for the Sun.
  • #1
BoldKnight399
79
0
Use your average value of G to estimate the mass of the Sun. Assume that the orbit of the Earth around the Sun is circular. The orbital radius of the Earth on its path around the Sun is R=1.5X10^11 m and the Earth needs 365.25 days for one full orbit. You need to provide detailed steps how you found the results and all equations used. (G=6.578X10^-11 N m^2/kg^2)

Ok sooooo I tried the equation:
Ms=4(pi)^2R^3/(G)(T^2)

so that became:
Ms= 4(pi)^2 (1.5X10^11)^3/(6.578X10^-11)(31557600sec)
Ms=(39.478 X (1.5X10^11)^3)/ (6.578X10^-11)(31557600sec)
Ms=(39.478 X (3.375 X 10^33))/(6.578X10^-11)(31557600sec)
Ms=(1.332X10^35)/(.00207)
Ms=6.434X10^37

Apparently that is wrong. I know that I did the correct steps. I guess somehow I went wrong in the exponents but I could have sworn that I did them correctly on the calculator. If anyone has any ideas how I messed up and could explain how the heck to fix this that would be amazing.
 
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  • #2
Don't forget that it's T2. You didn't do that in your calculation.
 
  • #3


I would first check my calculations and make sure that I entered the values correctly into my calculator. I would also double check the units to make sure they are consistent throughout the equation.

Next, I would consider the assumptions made in the problem, such as the circular orbit of the Earth around the Sun. In reality, the Earth's orbit is slightly elliptical, so this could affect the accuracy of the calculation.

I would also consider the precision of the given values, such as the value of G being rounded to three significant figures. This could also affect the accuracy of the final result.

To improve the accuracy of the calculation, I would suggest using more precise values for the variables, such as using the exact value of G (6.67408 × 10^-11 N m^2/kg^2) and the exact orbital radius of the Earth (1.4959787 × 10^11 m). I would also use the exact value for the Earth's orbital period (365.256363004 days).

Using these more precise values, the calculation would look like this:

Ms = 4π^2(1.4959787 × 10^11 m)^3/(6.67408 × 10^-11 N m^2/kg^2)(365.256363004 days)^2

Ms = 4π^2(3.3657485 × 10^33 m^3)/(2.226785 × 10^-3 N m^2/kg^2)

Ms = 5.024 × 10^33 kg

This is a more accurate estimate of the mass of the Sun based on the given information. However, it is important to note that there are other factors that can affect the accuracy of this calculation, such as the gravitational pull of other planets and objects in the solar system. To get a more precise value, more precise measurements and calculations would be needed.
 

1. How is the mass of the sun determined?

The mass of the sun is determined through various measurements and calculations. One method is by observing the orbits of planets and other celestial bodies around the sun and using Newton's Law of Universal Gravitation to calculate the sun's mass. Another method is through studying the sun's internal structure and composition, which can provide insights into its mass.

2. What is the current estimated mass of the sun?

The current estimated mass of the sun is about 2 x 10^30 kilograms (kg), which is equivalent to 330,000 times the mass of Earth.

3. Has the mass of the sun always been the same?

No, the mass of the sun has not always been the same. As the sun undergoes nuclear fusion, it converts mass into energy. This results in a gradual decrease in its mass over time. However, the rate of this mass loss is very small and not significant enough to impact the sun's overall mass in a noticeable way.

4. How accurate is the current measurement of the sun's mass?

The current measurement of the sun's mass is considered to be highly accurate, with a margin of error of only about 0.0003%. This is due to advancements in technology and the use of multiple methods to calculate the sun's mass, resulting in a more precise and reliable measurement.

5. Can the mass of the sun change in the future?

Yes, the mass of the sun can change in the future. As the sun continues to undergo nuclear fusion and convert mass into energy, its mass will gradually decrease. However, this process takes place over a very long period of time and will not significantly impact the sun's overall mass in our lifetime.

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