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Orbital Radius and orbital period data for the four biggest moons of Jupiter are listed in the table below. The mass of the planet Jupiter is 1.9 × 1027 kg.
Jupiter's Moon | Period (s) | Radius (m) | T2/r3 |
Io | 1.53×105 | 4.2×108 | ? |
Europa | 3.07×105 | 6.7×108 | ? |
Ganymede | 6.18×105 | 1.1×109 | ? |
Callisto | 1.44×106 | 1.9×109 | ? |
What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?
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- 7. The brightest four moons of Jupiter were discovered by Galileo with one of his earliest telescopes. These moons, lo, Europa, Ganymede, and Callisto, are called the Galilean moons in his honour. Some of the available data about these moons are given below. MOON r (km) V T (earthyears) 0.004837 lo a. Europa Ganymede Callisto 4.219 x 105 6.712 x 105 1.853 x 106 0.0195884 The radii are from the centre of Jupiter to the centre of the moon in question. One earth year has 365 days. Using the data for above, find the mass of Jupiter. Be specific as to which line of data was used and why. Show all work.Given the following information on Jupiter's Galilean moons, (a) determine the average mass of Jupiter and (b) compare to the known value of 1.898 × 1027 kg. Jupiter's diameter is 1.40 × 105 km. Assume the diameter of Jupiter is 139,820 km. Period in Orbital Diameter in Name Days Jupiter Diameters lo 1.77 6.03 Europa 3.55 9.60 anymede 7.16 15.3 Callisto 16.7 26.9Until recently, the term "planet" had no clear-cut definition. In August of 2006, leading astronomers established new guidelines and declared that Pluto is no longer a planet. Which of the following is either false or least consistent with the new guidelines? Group of answer choices Pluto is by far the largest known object in the Kuiper belt, while Eris is the largest known object in the asteroid belt. A planet must have cleared the neighborhood around its orbit. Pluto is automatically disqualified from being a planet because its oblong orbit overlaps with Neptune's. A planet must have sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a nearly round shape. Pluto and the asteroid Ceres are both now classified as dwarf planets.
- Question 3. Astronomers are consistently finding new moons of Jupiter, both big and small. Suppose astronomers discovered a new moon called Yelruh that orbits a distance of 5.63x108 m from the surface of Jupiter. Using the information for another moon of Jupiter, calculate Yelruh's orbital period.A newly discovered planet, Eagal, has two known moons, Dorainn and Bron. The table below gives some of the known information about Dorainn and Bron. Dorainn Bron Mass 1.427 x 1015 kg 1.427 x 1015 kg Radius 6.142 km Orbital Period 1.091 x 105 s Orbital Radius 23,640 km 27,650 km a. Determine the gravitational field strength at the surface of Dorainn. b. Using only the information provided for each moon and proportionality, determine Bron's orbital period. Clearly show or explain all workings. c. Use the data provided for Dorainn to determine the mass of Eagal. d. Determine the orbital speed of Bron.I. Directions: Complete the given table by finding the ratio of the planet's time of revolution to its radius. Average Radius of Orbit Times of Planet R3 T2 T?/R3 Revolution Mercury 5.7869 x 1010 7.605 x 106 Venus 1.081 x 1011 1.941 x 107 Earth 1.496 x 1011 3.156 x 107 1. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support? II. Solve the given problems. Write your solution on the space provided before each number. 1. You wish to put a 1000-kg satellite into a circular orbit 300 km above the earth's surface. Find the following: a) Speed b) Period c) Radial Acceleration Given: Unknown: Formula: Solution: Answer: Given: Unknown: Formula: Solution: Answer: Given: Unknown: Formula: Solution: Answer:
- Given the following information on Jupiter's Galilean moons, (a) determine the average mass of Jupiter and (b) compare to the known value of 1.898 × 1027 kg. Jupiter's diameter is 1.40 × 105 km. Assume the diameter of Jupiter is 139,820 km. Period in Orbital Diameter in Name Days Jupiter Diameters lo 1.77 6.03 Europa 3.55 9.60 Ganymede 7.16 15.3 Callisto 16.7 26.9Comet Halley has a semi-major axis of 17.7 AU. (The AU, or Astronomical Unit, is the distance from the Sun to the Earth. 1 AU = 1.50x1011 m.) The eccentricity of Comet Halley is 0.967. a. How far is Comet Halley from the sun at Aphelion, the farthest position from the sun? (Give your answer in AU.)? b. What is comet Halley's orbital time? (Give your answer in years.) Note: Using Kepler's third law in the form: P2 = a3 is convenient. This equation works for any object orbiting the sun when the orbital period is in years and the semi major axis is in AU. The reason this works is because this equation is normalized to earth. The AU and year are both 1 for Earth. c. In what year will Comet Halley start to move back toward the sun?1. The diameter of the Sun is equal to 1.392*10^9 m, and the distance from the Sun to Saturnis equal to 9.5 AU. Suppose you want to build an exact scale model of the solar system,and you are using a volleyball with average diameter of 21 cm to represent the Sun. a) In your scale model, how far away would Saturn be from the Sun? Give your answer inmeters.b) The actual diameter of Saturn is 116,460 km. What would be Saturn’s diameter in yourscale model? Give your answer in centimeters.
- 2. Are there any known satellites of Jupiter that are beyond the Hill sphere of Jupiter? If not, what is the largest ratio r(satellite)/r(Hill), among its satellites? 1/3 Hill Sphere Radius: RHill Rна M2 ЗМ110 Jup Europa Figure I Ganymede2. Comet 1943 I has a period of 512 years and an eccentricity of 0.999914 and an inclination of 22 degrees. a. What is the comet's semi major axis? b. What are its perihelion and aphelion distances? c. What is the most likely source region of this object? d. What is its tisserand parameter and what does that tell you?