Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 4, Problem 49Q
To determine
The student who reaches the right conclusion about the relation between energy of a satellite and altitude.
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Suppose you're in a circular orbit around Saturn (M = 5.683 x 1026 kg) with a semi-major axis
of a = 237,948 km.
a. What is your orbital velocity?
b. Using the "Vis-viva" equation (which can be derived from the total energy)
v = GM
What is the delta-V you would need to get from your current orbit, into an elliptical orbit
that has an apoapsis near Titan (a = 1,221,870 km)?
Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion.
Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU.
Does this make physical sense? Explain why or why not.
why do we launch at a higher altitude to reduce the kinetic energy required to reach orbit?
Chapter 4 Solutions
Universe: Stars And Galaxies
Ch. 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. 10Q
Ch. 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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- . With the mass of earth as 5.9722×10 to the 24 kg. and the mass of the moon is 7.38 x10 to the 22kg.with a distance of 384790km a. what is the gravitational pull between the two objects? b. what happens to gravitational pull if you reduced the distance into 1/2?arrow_forward217% ab (See #4 for Earth mass and radus 5. A satellite has an orbital radius 100 km above the Earth's surface. a. What is the speed of the satellite? b. How many minutes does it take the sātellite to complete one orbit?arrow_forwardSince 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?arrow_forward
- Kepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun (Pa1.5) . For mean distances from 0.1 to 32 AU, calculate and plot a curve showing the expected Keplerian period. For each planet in our solar system, look up the mean distance from the Sun in AU and the orbital period in years and overplot these data on the theoretical Keplerian curve.arrow_forwardM M 1. What is the gravitational potential energy of the mass (m) in the picture? The mass is the same distance awayr from the centers of both of the other masses, and both of the other masses have the same mass, M. Give your answer in Joules. r= 400 million meters m = 7x1022 kg M = 2x1027 kg 2. What is the net gravitational force for the mass m at this location? Give your answer in Newtons.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
- r M M m 1. What is the gravitational potential energy of the mass (m) in the picture? The mass is the same distance away r from the centers of both of the other masses, and both of the other masses have the same mass, M. Give your answer in Joules. r = 400 million meters = 7x10²2 kg М - 2x1027 kgarrow_forwardQuestion 1. Calculate the speed of a satellite (mass of 1500kg) that orbits Mars at an altitude of 400 km.arrow_forwardSuppose humans are successful in living on the moon. They would need GPS just like on Earth to be able to navigate to “Moonmart”. They launch a 500 kg satellite in a geosynchronous orbit around the moon. Assume the Moon’s mass is 7.35x1022 kg.The moon takes 708.7 hours to make 1 rotation, or 2,551,320 seconds. What is the satellite’s orbit radius? What is the satellite’s orbit speed? After 20 years, a newer GPS satellite is built, and they want to get rid of the old one. How much energy is needed for the original satellite to escape its moon orbit?arrow_forward
- plain your answer. The formula for potential energy is PE = m g h. In this formula, PE stands for potential energy (in joules), m stands for mass (in kilograms), h stands for height (in meters), and g stands for acceleration caused by gravity. On Earth's surface, g is 9.8 m/s?. This means that every second, the speed of a falling object increases by 9.8 m/s. Calculate the potential energy of a 20 kg sled at 40 meters. Show your work. When you are done, use the Gizmo to check your answer.arrow_forwarda. What is a repeat ground-track orbit? b. Explain why repeat ground-track and Sun-synchronous orbits are typically used for Earth observation missions. = c. The constraint for a Sun-synchronous and repeat ground-track orbit is given by T 86, 400, where T is the orbital period in seconds, m the number of days and k the number of revolutions. Explain why this is, in fact, a constraint on the semi-major axis of the orbit. marrow_forward
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