Week 10 - Smaller Objects in the Solar System

Name: Key Smaller Objects in the Solar System The Kuiper Belt In the table below you will find orbital values for Pluto, Eris, selected Kuiper Belt objects, and selected planets. Object Type Average Distance to Sun (AU) Eccentricity Time to Orbit (yrs) Inclination of Orbit Saturn Planet 9.6 0.06 29 2.5 o Uranus Planet 19.2 0.05 84 0.8 o Neptune Planet 30.0 0.01 165 1.8 o 2005 FY9 Kuiper Belt 45.6 0.16 308 29.0 o 2003 EL61 Kuiper Belt 43.3 0.19 285 28.2 o 2002 AW197 Kuiper Belt 47.3 0.13 325 24.4 o 2004 XR190 Kuiper Belt 57.0 0.08 430 47.0 o Pluto ---------- 39.5 0.25 248 17.16 o Eris ---------- 67.7 0.44 557 44.19 o 1) Which type of object (Kuiper Belt or planet) has higher eccentricity on average? Kuiper Belt object 2) Which type of object (Kuiper Belt or planet) will have the biggest change in its distance from the Sun during its orbit? Explain your answer. Kuiper Belt objects – the larger the eccentricity the bigger the change in distance from the Sun. 3) Which type of object (Kuiper Belt or planet) has higher inclination on average? Which individual object is the most tilted? Kuiper Belt objects – 2004 XR190 is the most tilted object in the table. 4) Draw a diagram showing the inclination of Eris. I have drawn the inclination of Pluto as an example. 5) Which object in the table takes the most time to orbit the Sun? Which object in the table is the farthest from the Sun? What famous law is shown by this result? Eris takes the most time to orbit and is the farthest from the Sun. This is Kepler’s 3 rd law! 6) Using the data on the table, determine whether Pluto and Eris better fit as Kuiper Belt objects or planets. Give at least 2 reasons why. Pluto and Eris both have higher eccentricity and higher inclination. This makes them much more like the Kuiper Belt objects than like planets. Name: Key Eris’s Orbit Pluto’s Orbit Orbit of Planets around Sun Orbit of Planets around Sun Sun Sun Inclination

Comets In the table below, we have the orbital values for a selection of comets. Object Closest Approach to Sun (AU) Average Distance to Sun (AU) Eccentricity Time to Orbit (yrs) Inclination of Orbit Encke 0.85 2.2 0.33 3.3 12 o Tempel 1 1.5 3.1 0.52 5.5 11 o Stephan- Oterma 1.57 11.2 0.86 38 18 o Gibbs 4.43 12 0.63 42 7 o Halley 0.59 18 0.967 76 18 o Hale-Bopp 0.93 185 0.995 2,500 89 o Hyakutake II 0.23 950 0.999 29,300 56 o McNaught 5.85 5679 0.999 428,000 73 o Neat 7.03 7126 0.999 602,000 68 o 1) For each comet in the list above, tell whether it is a long-period or short-period comet. Explain how you decided. Long-Period (Time to Orbit>200 years): Hale-Bopp, Hyakutake II, McNaught, Neat Short-Period (Time to Orbit < 200 years): Encke, Tempel 1, Stephan-Oterma, Gibbs, Halley 2) Which type of comet (long-period or short-period) typically has the highest inclination? Long-Period 3) Draw a diagram showing the typical inclination of a short-period comet and the typical inclination of a long-period comet. 4) Where do short-period comets come from? Where do long-period comets come from? Short-Period from Kuiper Belt; Long-Period from Oort Cloud 5) Using your answers to question 4, explain why long-period and short-period comets have the typical inclinations that they do. Kuiper Belt is shaped like a donut so you can only have smaller inclinations. Short- period comets come from Kuiper Belt so they must also have smaller inclinations. Oort Cloud is round, so you can have high inclinations. Long-period comets come from the Oort Cloud so they can have high inclinations. 6) Comets McNaught and Neat never get closer than 5.85 AU from the Sun. What does this say about the appearance of these comets even at their closest approach? These comets never get close enough to the Sun for the ice in the nucleus to evaporate and form a coma or tail. So these will not look like your “normal” comets – just nuclei of rocks and ice. Long- Short-Period Orbit of Planets around Sun Sun

f) Finally, we can use Kepler’s Laws and the moons’ orbits around Jupiter to calculate the mass of Jupiter. In general, the equation is: Mass = 4 π 2 ( Distance ) 2 G× ( Period ) 2 , where G is a constant. For Jupiter and its moons we can make the equation a little easier to work with: compared Distance ∈ km of Moon Mass ( ¿ Earth ) = 1.33 × 10 − 14 × ( ¿ planet ) 3 ( Period of Moon ' s orbit ∈ days ) 2 Using the distance and period of Io on the previous page, calculate the mass of Jupiter compared to the Earth. compared Mass ( ¿ Earth ) = 1.33 × 10 − 14 × 421,700 3 1.77 2 = 318.4 g) Does the mass you calculated for Jupiter make sense? Explain. Remember that the mass you calculated is the mass compared to Earth. Yes – it makes sense that Jupiter would be quite a bit heavier than the Earth. h) How would your answer be different if you Ganymede (the heaviest moon of Jupiter) to calculate Jupiter’s mass? Explain. It would be the same – we are measuring the mass of Jupiter, so it should not matter which moon we use to measure it. i) The equation above works for any time one object is orbiting another object due to gravity. The object that is orbiting counts as the moon in the equation and the mass that is calculated is for the object that is in the middle. Use the equation to calculate the mass of the Sun compared to Earth. Hints: 1 AU = 1.5 x 10 8 km, 1 year = 365.24 days. compared Mass ( ¿ Earth ) = 1.33 × 10 − 14 × ( 1.5 × 10 8 ) 3 365.24 2 = 336,487 j) Does the mass of the Sun that you calculated make sense based on the mass you calculated for Jupiter and the mass of the Earth? Explain. Yes, the mass of the Sun is much higher than the mass of the Earth or the mass of Jupiter.