Formation of the Solar System

F ORMATION OF THE S OLAR S YSTEM P ART I. T HE S UN ' S S OURCE OF E NERGY The source of all energy in the Sun is the fusion of 4 hydrogen atoms into 1 helium atom, which releases energy. The amount of energy released per reaction can be calculated by using Einstein's very famous equation which relates matter and energy: E = mc 2 . The c in this equation is simply the speed of light (a constant). The m is the mass of matter which was converted to energy in the reaction. You will find that the mass of 4 hydrogen atoms is slightly larger than the mass of one helium atom; the difference in mass is the amount of mass converted to energy in the reaction. Calculate it. Show your work, not just the results. There is a video tutorial posted if you need help with the equations. Mass of one hydrogen atom: 1.6737 × 10 − 27 kg Mass of one helium atom: 6.6465 × 10 − 27 kg 1. Calculate the difference in mass between 4 hydrogen atoms and one helium atom. 4 hydrogen = 6.6948 x 10 -27 – 6.6465 x 10 -27 0.0483 x 10 ^-27 2. Now, plug the difference in mass into Einstein's equation, and solve for the Energy ( E ) released during one reaction. ( c 2 = 9 × 10 16 meters 2 second 2 ) (0.0483 x 10^-27) (9x 10^16) = 4.347×10^-12 joules 3. All of the Sun's energy comes from hydrogen fusion in the core. The total amount of energy the Sun releases is called its Luminosity, which is: 3.846 × 10 26 Watts (A Watt is a Joule/second). a. Find out the total number of reactions which must take place every second in order for the sun to maintain this Luminosity (simply divide the Sun's luminosity by your answer from #2). 8.848 x 10^37 b. Now find out how much mass is converted to energy every second in the core of our Sun by dividing the luminosity of the Sun by c 2 . Your result is in units of kg. 4.273 x 10^9 kg c. Find how much mass is converted to energy every second in the core of our Sun by taking your mass answer to question 1 and multiplying by the number of reactions per second from 3.a. You should have the same answer as the above question. 4.273 x 10^9 kg P ART II: W HY ARE T HERE T WO T YPES OF P LANETS ? For this section, I want you to find out the physics behind the separation of Terrestrial planets (Mercury, Venus, Earth, and Mars) and the Jovian planets (Jupiter, Saturn, Uranus, Neptune). In (2) (2) (2) (2) (2)

other words, why did the planets closest to the Sun form as low mass, rocky bodies while planets further out formed massive, gas giants? To do this, let us first map out the solar system based on the planets' distances from the Sun. However, instead of looking up these values, I want you to extrapolate through observation the distance of the outer planets from the Sun by simple observation using Stellarium and Kepler's 3 rd Law of planetary motion (which you will explore in a future lab). Kepler’s 3 rd Law tell us that the square of a planet’s orbital period is proportional to the cube of the semimajor axis of its orbit, or in other words, the time it takes a planet to orbit the Sun depends on the planet’s distance from the Sun. If we use units of years and Astronomical Units, then the relationship is equal: Period 2 (years) = semi-major axis 3 (AU), or P 2 = a 3 . Therefore, the distance from the Sun is a = P 0.66 If you watched long enough, you could get the value for P by simple observation from Earth. Perform your observations in Stellarium for the Jovian planets and record all pertinent information in the space below. Once you have your final values, complete the table on the following page. I must see that you calculated them (not just looked them up). Open Stellarium. Turn off the atmosphere and ground by hitting “A” and “G”. Open the Date/time window [F5] and move it to the lower right corner of the screen to keep it out of the way. Open the Search window [F3] to find each planet. Once you have the planet selected, press the spacebar to keep the planet centered. When a planet is selected, the info pane shows to the left. Previously this semester, we learned that Azimuth tells us how far around in the sky an object is located. Find the row with Az./Alt. to find the Azimuth and Altitude. We only need the Azimuth for this activity. Record the current Azimuth in degrees. Then, forward the time by years until the planet reaches close to this Azimuth again. Only make one orbit! Using Kepler’s 3 rd Law, calculate the distances and copy them into the table on the next page. Planet Azimuth (degrees) Period (years) – the time for the planet to return/make one orbit Distance (AU) calculated from a = P 0.66 Jupiter 349 12 5.16 Saturn 80 29 9.23 Uranus 222 86 18.91 Neptune 330 164 28.96 T ABLE : D ISTANCES FROM THE S UN IN AU Mercur y 0.387 Venus 0.723 Earth 1.000 (4) (4)

With this information, describe the process by which planets are formed from the surrounding material, and explain the reason why the Jovian planets were able to obtain so much more mass than the Terrestrials. Remember: (1) Gas moves quickly since each particle has very little mass and is therefore harder to trap and hold on to compared to the slow moving, more massive dust particles. (2) To trap gas, what do you need at the beginning. Look at the reading pages of this week’s module if you need help with the explanation. _Planets are formed with surrounding dust. To trap gas, you need gravitational pull to capture it. The terrestrial planets are closer to the sun and have higher temperatures making it harder to capture since there is only rocky dust surrounding it. Jovian planets are farther from the sun and have lower temperatures. They have a higher mass because there is a lot of ice and rocks surrounding that clump together. ______________________________________________________________________________ _______ ______________________________________________________________________________ _______ ______________________________________________________________________________ _______ ______________________________________________________________________________ _______ ______________________________________________________________________________ _______ ______________________________________________________________________________ _______ ______________________________________________________________________________ _______