Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 54Q
To determine
To analyze: That Jupiter’s three large moons (Europa, Ganymede and Callisto) are in agreement with Newton’s form of Kepler’s third law, from the data given in Appendix 3.
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Comet 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?
The mass of Jupiter is 1/1047 of the Sun's mass (that's 0.000955). We want to confirm this using Newton's version of Kepler's Third Law, following the examples in Lecture 7. We'll use the approximate data for two different moons of Jupiter to see how close the results are. Pick the closest answer in each case:
(a) Ganymede is the third moon from the inside. It has an orbital period around Jupiter of approximately 0.0194 Earth years. Its semimajor axis is 0.0071 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data?
(b) Europa is the second moon from the inside. It has an orbital period around Jupiter of approximately 0.0096 Earth years. Its semimajor axis is 0.0045 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data?
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:
Chapter 4 Solutions
Universe
Ch. 4 - Prob. 1CCCh. 4 - Prob. 2CCCh. 4 - Prob. 3CCCh. 4 - Prob. 4CCCh. 4 - Prob. 5CCCh. 4 - Prob. 6CCCh. 4 - Prob. 7CCCh. 4 - Prob. 8CCCh. 4 - Prob. 9CCCh. 4 - Prob. 10CC
Ch. 4 - Prob. 11CCCh. 4 - Prob. 12CCCh. 4 - Prob. 13CCCh. 4 - Prob. 14CCCh. 4 - Prob. 15CCCh. 4 - Prob. 16CCCh. 4 - Prob. 17CCCh. 4 - Prob. 18CCCh. 4 - Prob. 19CCCh. 4 - Prob. 20CCCh. 4 - Prob. 21CCCh. 4 - Prob. 22CCCh. 4 - Prob. 23CCCh. 4 - Prob. 24CCCh. 4 - Prob. 1CLCCh. 4 - Prob. 2CLCCh. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10QCh. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 14QCh. 4 - Prob. 15QCh. 4 - Prob. 16QCh. 4 - Prob. 17QCh. 4 - Prob. 18QCh. 4 - Prob. 19QCh. 4 - Prob. 20QCh. 4 - Prob. 21QCh. 4 - Prob. 22QCh. 4 - Prob. 23QCh. 4 - Prob. 24QCh. 4 - Prob. 25QCh. 4 - Prob. 26QCh. 4 - Prob. 27QCh. 4 - Prob. 28QCh. 4 - Prob. 29QCh. 4 - Prob. 30QCh. 4 - Prob. 31QCh. 4 - Prob. 32QCh. 4 - Prob. 33QCh. 4 - Prob. 34QCh. 4 - Prob. 35QCh. 4 - Prob. 36QCh. 4 - Prob. 37QCh. 4 - Prob. 38QCh. 4 - Prob. 39QCh. 4 - Prob. 40QCh. 4 - Prob. 41QCh. 4 - Prob. 42QCh. 4 - Prob. 43QCh. 4 - Prob. 44QCh. 4 - Prob. 45QCh. 4 - Prob. 46QCh. 4 - Prob. 47QCh. 4 - Prob. 48QCh. 4 - Prob. 49QCh. 4 - Prob. 50QCh. 4 - Prob. 51QCh. 4 - Prob. 52QCh. 4 - Prob. 53QCh. 4 - Prob. 54QCh. 4 - Prob. 55QCh. 4 - Prob. 56QCh. 4 - Prob. 57QCh. 4 - Prob. 58Q
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- Part B. 1. The table below shows the gravitational force between Saturn and some ring particles that are at different distance from the planet. All of the particles have a mass of 1 kg. Table 1. Distance and Gravitational Force Data Distance of 1- Gravitational kg Ring Particle from Force between Saturn and 1-kg ring particle (in | 10,000 N) 2. Use the data in the table to make a graph of the relationship between distance and gravitational force. Label your graph "Gravitational Force and distance". Center of Saturn (in | 1,000 km) 100 38 Hint: Put the data for distance on the horizontal axis and the data for gravitational force on the vertical axis. 120 26 130 22 150 17 3. Look at your graphed data, and record in your answering sheet any relationship you notice. 180 12 200 9. 220 8 250 280 O 5arrow_forwardOrbital 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?arrow_forwardf the semi-major axis, a, is measured in AU and the orbital period, p, is measured in years, then Kepler's 3rd law allows us to calculate the mass of the object they are orbiting using the following equation: M = a3/p2 Furthermore, the mass that is calculated by this equation is given in solar masses (MSun) where, by definition, the Sun's mass is 1 MSun. Now, suppose I were to tell you that the mass of Jupiter is equal to 4.5e7 MSun. Does the stated mass of Jupiter make sense? Group of answer choices Yes No, it's too big. No, it's too smallarrow_forward
- a) The asteroid Ida has a small satellite orbiting it called Dactyl. Dactyl orbits Ida at a distance of about 90 km, with a period of about 8 hours. Calculate the mass of Ida. b) Mars has two moons, Phobos and Deimos. Phobos orbits Mars with an orbital period of 8 hours while Deimos orbits every 30.3 hours. What are the semi-major axes of each satellite? c) On the night side of Venus, we find that the brightest wavelength, that is the wavelength this region of the planet is emitting the most energy, is about 3.9 micrometers (3.9x10-6 meters). Approximately how warm is the planet in this region?arrow_forward2GM The asteroid Pallas has a mass of 2.11 x 1020 kg and an average radius of about 256 km (2.56 x 102 km). What is its escape velocity (in m/s)? (Hints: Use the formula for escape velocity, V. = remember to convert units to m, kg, and s.) m/s Could you jump off the asteroid? O Yes O Noarrow_forwardMeasure the periods for each planet. Measure the orbital radius of each planet. Calculate the ratios of square of the periods and cubed of the radii for the planets. Compare the results and comment if your result confirms Kepler's Third Law. (Pic1 has the yellow and bluw planets points plotted. Pic2 has the grey and red planet plots listed.)arrow_forward
- Tutorial Based on the orbital properties of Uranus, how far across the sky in arc seconds does it travel in one Earth day? The average orbital radius is 2.88 x 109 km and the period is 84.0 years. (Assume Uranus and the Earth are at the closest point to one another in their orbits.) How many full Moons does this distance cover if the Moon has an angular diameter of 0.5 degrees? Part 1 of 4 We first need to determine how fast the planet is moving across the sky. If we know the period and the distance between the Sun and the planet we can calculate the velocity using: 2ar which will tell us how many kilometers the planet travels in a day if we convert the period into days. days = (P years' |days/year Pdays days Submit Skip (you cannot come back)arrow_forwardSaturn’s A, B, and C Rings extend 75,000 to 137,000 km from the center of the planet. Use Kepler’s third law to calculate the difference between how long a particle at the inner edge and a particle at the outer edge of the three-ring system would take to revolve about the planet. Enter the value you get from the ratio of the period of the inner edge to the outer edge of the rings.arrow_forwardGalileo's telescopes were not of high quality by modern standards. He was able to see the moons of Jupiter, but he never reported seeing features on Mars. Use the small-angle formula to find the angular diameter of Mars when it is closest to Earth. How does that compare with the maximum angular diameter of Jupiter? (Assume circular orbits with radii equal to the average distance from the Sun. Using the following distances from the Sun: Mars is 228 million km, Jupiter is 778 million km, and Earth is 150 million km. The radius of Mars is 3396 km. The radius of Jupiter is 71,492 km.) angular diameter of Mars = ( )seconds of arc angular diameter of Jupiter =( )seconds of arc ratio of angular diameters (Jupiter/Mars) = ( )arrow_forward
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