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Lab Notebook: L1: Finding the Mass of the Sun P a g e 1 | 3 Name F inding the Mass of the Sun Station # 6 Lab Group Members Puurich Cameron Solomon Instructions: Please increase space as necessary. Make sure your notebook is legible, clear, and well organized. Objective The objective of this lab is to find the mass of the sun, using Kepler’s Third Law, and data given from the planets that orbit the sun, specifically the planets’ semimajor axis and their orbital periods. We will use what we know about Kepler’s Third Law, the g ivens, and what the data shows us, plug our information in, and calculate for the mass of the sun. Prediction My prediction for this lab is that the mass of the sun will be accurate and will agree with the established value. Here’s why: we aren’t doing any human based experimenting and will be using data that has been given to us. We will also be using direct calculations, meaning if there are any outliers/data that simply doesn’t ma ke sense, it will be based on the inaccurate given data, rather than human error. Unless of course I make a mistake while calculating the mass. Method The method for this lab is self-explanatory. Some of the data given from the table of each planet was used (semimajor axis, orbital period), along with the gravitational constant, G=6.67*10 −11 Nm 2 /kg 2 . With all this information given, we will use Kepler’s 3 rd Law, which states: 𝑇 = 2𝜋 ⋅ √ 𝑎 3 𝐺𝑀 . We rearrange this equation to solve for M, which is the mass of the sun. The rearranged equation looks like this: 𝑀 = 4𝜋 2 𝑎 3 𝐺𝑇 2 . Making sure every value is in SI Units, we just plug and chug to solve for the mass of the sun.

Lab Notebook: L1: Finding the Mass of the Sun P a g e 2 | 3 Data Plot / Data Analysis After direct calculations for the mass of the sun using values from each planet, we got an average value of 1.99385 ± 0.002 × 10 30 𝑘𝑔 . The uncertainty found with these masses was found to be 4.08 × 10 27 𝑘𝑔 . To the naked eye, that might seem like an enormously large number, but compared to the actual value, the uncertainty is 0.02%. The established value of the sun is 1.98847 ± 0.00007 × 10 30 𝑘𝑔 , which is very close to the mass we determined through direct calculation. The graph is inaccurate when it comes to trying to determine the mass of the sun. The graph shows a comparison of the semimajor axis of the planets to the orbital periods. This isn’t enough information to find the mass of the sun. To calculate the sun’s mass, we need to use Kepler’s equation to plug and chug. We chose to use all of planets’ data points, to make sure the data was consistent. The more data points we have, the more accurate the average would be. We did not find any outliers, which makes sense, because the mass of the sun does not change, regardless of what planet we use.

Lab Notebook: L1: Finding the Mass of the Sun P a g e 3 | 3 Conclusion After using Kepler’s 3 rd Law and the given date to directly calculate the mass of the sun, it was found that the average mass of the sun ~ 1.99385 ± 0.002 × 10 30 𝑘𝑔 . This mass found was extremely close to the established value of the sun, 1.98847 ± 0.00007 × 10 30 𝑘𝑔 . These two values agree with each other, because we used direct calculations and came up with no outliers. The linearized plot, however, did not agree with the established mass of the sun. The plot was created using only the semimajor axis and the orbital period, which was simply not enough information to calculate the mass of the sun. The graph didn’t tell us anything other than “the larger the axis, the longer the period, and they grow exponentially”. We needed to include the other values in Kepler’s 3 rd Law for the masses to make sense.

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