Determining solar characteristics using planetary data

Transcription

1 Detemining sola chaacteistics using planetay data Intoduction The Sun is a G-type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this investigation I will be examining the Sun and its physical chaacteistics. I will use a database povided by the Euopean Space Agency, found at to acquie vaious pieces of infomation about the planets in the Sola System and then use that to detemine some of the Sun s chaacteistics though the laws of astophysics. Featue 1: Mass The most basic chaacteistic about the Sun that I can find is its mass. The mass of the Sun must fist be found befoe it is possible to detemine chaacteistics based on gavitational foce. I plan to detemine the mass of the Sun using data fom the planets. This can be done though the application of Johannes Keple s laws of obital motion. Keple s thid law states that: EX A moe focused (and singula) eseach question would have helped the student poduce a moe inteesting investigation. C A clea and diect intoduction helps the eade undestand what is to follow. The student s language is clea and diect in most cases. EX This database also gives the mass of the Sun. A The student has indeed selected appopiate data given thei eseach questions. EX The topic is clealy identified, a seies of basic eseach questions will be answeed, and appopiate concepts and techniques ae to be used hee. This investigation is not of sufficient complexity to be commensuate with the level of the couse. EX A bette physics IA would have been one that focused on a single eseach question and then went into moe depth. This investigation is moe like a homewok poblem than an expeiment. The squae of a planet s obital peiod is diectly popotional to the cube of its semi-majo axis. This law can be demonstated using the planets in ou Sola System and thei obits aound the Sun. I found a gaph on the intenet which shows the accuacy of Keple s thid law in ou Sola System. C The gaph shows this to us only if we appeciate the gadient of the log-log gaph. But we know what the student means hee. Page 1 of 8 Physics teache suppot mateial 1

2 The obital peiod of a body is the time it takes to complete one full obit. The semi-majo axis is half of the longe diamete of an obit s elliptical path. Any popotionality statement can be expessed in an equation though the addition of a constant. In this case, the constant must elate to the gavitational foce which guides the obits and thei cicula paths. The full equation fo Keple s thid law is given as: P 4π = a GM ( + M) 3 1 EX The method is appopiate. Equations ae explained but backgound and context ae vey limited hee. Whee P is the obital peiod, G is the univesal gavitational constant (6.67x10-11 m 3 kg -1 s - ), M 1 and M ae the masses of the two celestial bodies and a is the semi-majo axis of the obit. This equation can then be eaanged to find the sola mass, M 1 : Page of 8 Physics teache suppot mateial

3 Now, using data fom the planetay database, I can calculate the mass of the Sun. To impove the accuacy of the esult, I did this calculation fo each of the eight planets. Sample calculation using data fom Mecuy: EX This appoach gives cedit to the student fo using an appopiate method. Howeve, the student is not awae of any uncetainties in the database o of significant figues in thei calculations. M M π ( ) = ( ) ( ) = kg 3 These ae the esults I obtained fo the sola mass using data fom each of the planets: Planet Sola Mass (kg) Mecuy x10 30 Venus x10 30 Eath x10 30 Mas x10 30 Jupite x10 30 Satun x10 30 Uanus x10 30 Neptune x10 30 A Fo the fist eseach question, the amount of data is sufficient. Howeve, thee is no appeciation of pecision o accuacy in the data that is consideed hee. All the esults ae vey simila when ounded. The main diffeence occued when going fom the smalle and lighte inne planets to the lage and heavie oute ones. The geate mass of these planets changed the value calculated slightly. I decided to take an aveage mass fom these esults and got my final value fo the sola mass as x10 30 kg. C and A The language hee is vague and not scientific. PE This peception might be consideed pesonal input and initiative but given the oveall epot, Pesonal Engagement is had to find (until thee is a hint of PE at the end of the epot). EV Yes, but what is the pecision of this value? Page 3 of 8 Physics teache suppot mateial 3

4 Featue : Suface Gavity Afte successfully detemining the mass of the Sun though Kepleian calculations, the Sun s gavitational foce can be calculated. The suface gavity of a body is the acceleation due EV How does the student know this? Moe explanation is expected. EX This is eally a second eseach question. to the foce of its gavity when at its suface. The mathematical fomula fo acceleation due to gavity is deived fom Newton s law of univesal gavitation. Newton s law is shown in the pictue below. C The souce of this image is needed hee. The teache should have caught this omission. Then, taking Newton s second law, F get: = mg and setting the two foces equal to each othe we GMm mg = The masses then cancel out allowing one to solve fo the acceleation due to gavity using the following fomula: GM g = Whee g is the suface gavity, G is the gavitational constant, M is the mass of the body and the distance fom the body s cente of gavity. To calculate the suface gavity, the value fo must be set equal to the body s adius. In the last section I detemined the mass of the Sun. Its Page 4 of 8 Physics teache suppot mateial 4

5 adius can be found though measuing its angula size in the sky and then, knowing the distance fom the Eath to the Sun, the adius can be calculated tigonometically. I was unable to do this myself, so I obtained the adius of the Sun fom my database, as km. Using this data, the suface gavity of the Sun can be calculated. g = ( ) ( )( ) g = 74.3ms A Technically, the student used the datum (a single value) fom the data base. This is hadly sufficient. Again, this appoach is moe like a homewok poblem. A Again, thee is no appeciation of eos, uncetainties, assumptions o significant figues. As a compaison, the suface gavity on Eath is 9.81ms -, almost 8 times less. Its vey lage gavitational foce is how the Sun manages to keep all the planets in obit. Featue 3: Escape Velocity The escape velocity of a celestial body is the velocity equied by an unpoweed object to escape that body s gavitational field. At escape velocity, the gavitational potential enegy of the object and its kinetic enegy will equal zeo when added. The fomula fo escape velocity can be deived though this. Kinetic enegy has the fomula E Ek g 1 = mv and gavitational potential enegy is given by GM M = When these two ae added, they must equal zeo, so: 1 mv 1 GM M + = 0 1. Page 5 of 8 Physics teache suppot mateial 5

6 This now allows us to eaange this fomula to solve fo v, the escape velocity. v = GM Now the values that we obtained can be inseted into the equation. v = ( )( ) v = ms 1 This value I obtained is the velocity an object fied fom the suface of the Sun to be fied in ode to escape its gavitational field about 617.7kms -1. Howeve, this value does not have many pactical applications as we do not fie objects fom the suface of the Sun. A much moe useful value to calculate would be the velocity equied to escape sola obit when launched fom the Eath. This allows us to launch pobes into the intestella medium. To calculate this value, the Eath s aveage distance fom the Sun, one astonomical unit, must be set as the value in the equation. EX and C Although the student is coect hee, they ae taking attention away fom the quality and natue of the IA, and as such this digession adds nothing. v = ( )( ) v = 4118ms In ode to escape the Sun s gavity when launched fom the Eath, a velocity of 4kms -1 is equied. This value can be used if pobes eve need to be sent on a sola escape tajectoy. Page 6 of 8 Physics teache suppot mateial 6

7 Conclusion Using data povided in an online database, I was able to detemine the mass, gavitational foce and escape velocity of the Sun. To check the accuacy of the esults I calculated, I compaed them to the actual accepted values. The mass of the Sun that I obtained was x10 30 kg. The actual accepted value is x10 30 kg. My esult was only 0.015% highe than the accepted value. This shows that though the application of Keple s thid law, celestial masses can be calculated with a vey good amount of accuacy. C Headings fo the thee investigations and the Conclusion and Evaluation sections help the eade appeciate content. The language is clea and diect, with only a few digessions. The oveall epot is focused and flows. EV and C This data needs a efeence. We only assume it came fom the same database. EV A complete evaluation would include the popagation of uncetainty given the data and pocessing, not just compaing the esult to the accepted value. Howeve, the student was wise to make this compaison. The next chaacteistic that I calculated was the suface gavity of the Sun. The value I obtained was 74.3ms -1. The accepted value is 74.0ms -1. My value is 0.15% highe which is once again vey close. The eason that my esult is highe is because I used the mass of the Sun that I calculated in the fist pat, which was also slightly highe than the actual mass. Howeve, my calculations wee still vey accuate. The final chaacteistics I calculated wee the escape velocities fom the suface of the Sun and also the sola escape velocity fom Eath. Fo the escape velocity fom the suface of the Sun, I got a value of 617.7kms -1. This is identical to the accepted value, which means that I was able to pefom my escape velocity calculation vey accuately. The esult that I calculated fo the sola escape velocity fom Eath was 4.1kms -1. This is also identical to the accepted value. My escape velocity calculations wee extemely accuate. Oveall, the values I obtained though my calculations in this investigation wee vey accuate with egads to the actual values and I am pleased with how it tuned out. I was able to apply Keple s and Newton s laws of astophysics to the planets and the Sun in ou Sola System well and though this I was able to confim the accuacy of these laws. EV Yes, the thee calculations ae exceptionally good as one would expect using a basic plug in the values method. Moe depth is expected hee, even with a database. Page 7 of 8 Physics teache suppot mateial 7

8 Evaluation I chose to do this investigation because of a pesonal inteest in the field of astophysics. I chose to do ou Sola System because it is the system that we ae most familia with and we have an abundance of data to do with the celestial bodies in it. The Sun, being the focal point of the Sola System, was the best choice fo me to conduct my investigation on. I knew that I could use the obital data of the planets to calculate vaious chaacteistics of the Sun. Fo my database, I chose the one povided by the Euopean Space Agency because it has vey accuate and pecise infomation with easy accessibility. The database poved vey useful thoughout my investigation and gave me vey accuate esults in the end. PE Stating one s inteest and demonstating that inteest ae not the same. PE Could this be a justification fo the eseach poject? Thoughout my investigation, I had to apply vaious physical laws. In ode to conduct the fist pat of my investigation I had to familiaize myself with Keple s thid law, a topic that we only studied biefly in class and I did not know too much of. I was able to use the law popely and accuately to calculate my data. Newton s laws of gavitation wee ones that we had studied moe extensively so I was also able to apply them in a pope manne and effectively. The accuacy of my esults shows a good application of these laws. I am pleased with how the investigation tuned out and the esults I managed to obtain. If I could add moe to this investigation I would pobably look into doing futhe calculations of diffeent factos, examining chaacteistics such as the Sun s suface tempeatue, luminosity and enegy output. I would also pobably do moe calculations fo my cuent factos, such as expanding my sola escape velocities to include those fom all the planets. In this investigation I only looked into a small faction of the sola chaacteistics available. Howeve, I think that what I did with my investigation went vey well. EV Although the student is awae of extensions of this study, none of them pove any moe inteesting than just plugging in numbes. Page 8 of 8 Physics teache suppot mateial 8