Concept explainers
(a)
The initial speed of the satellite.
(a)
Answer to Problem 40AP
The initial speed of the satellite is
Explanation of Solution
The mass of the satellite is
Formula to calculate the initial speed of the satellite is,
Here,
Substitute
Conclusion:
Therefore, the initial speed of the satellite is
(b)
The final speed of the satellite.
(b)
Answer to Problem 40AP
The final speed of the satellite is
Explanation of Solution
Formula to calculate the final speed of the satellite is,
Here,
Substitute
Conclusion:
Therefore, the final speed of the satellite is
(c)
The initial energy of the satellite-Earth system.
(c)
Answer to Problem 40AP
The initial energy of the satellite-Earth system is
Explanation of Solution
Formula to calculate the initial energy of the satellite-Earth system is,
Here,
Substitute
Conclusion:
Therefore, the initial energy of the satellite-Earth system is
(d)
The final energy of the satellite-Earth system.
(d)
Answer to Problem 40AP
The final energy of the satellite-Earth system is
Explanation of Solution
Formula to calculate the final energy of the satellite-Earth system is,
Substitute
Conclusion:
Therefore, the final energy of the satellite-Earth system is
(e)
The mechanical energy of the system has decreased and estimates the amount of decrease mechanical energy of the system.
(e)
Answer to Problem 40AP
The amount of decrease mechanical energy of the system is
Explanation of Solution
Formula to calculate the mechanical energy of the system is,
Substitute
Conclusion:
Therefore, the amount of decrease mechanical energy of the system is
(f)
What force makes the satellite’s speed increases.
(f)
Answer to Problem 40AP
The component of the gravitational force pulls forward on the satellite and increases the speed of satellite.
Explanation of Solution
The only forces act on the satellite is the backward force of air resistance comparatively very small in magnitude to the force of gravity. Because the spiral path of the satellite is not perpendicular to the gravitational force, one component of the gravitational force pulls forward on the satellite to do positive work and makes speed increases.
Conclusion:
Therefore, component of the gravitational force pulls forward on the satellite and increases the speed of satellite.
Want to see more full solutions like this?
Chapter 13 Solutions
Physics for Scientists and Engineers
- If a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.arrow_forwardFind the escape speed of a projectile from the surface of Jupiter.arrow_forwardWhat is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forward
- The astronaut orbiting the Earth in Figure P3.27 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 600 km above the Earth’s surface, where the free-fall acceleration is 8.21 m/s2. Take the radius of the Earth as 6 400 km. Determine the speed of the satellite and the time interval required to complete one orbit around the Earth, which is the period of the satellite. Figure P3.27arrow_forwardShow that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your expression give the correct value for Earth’s areal vilocity about the Sun?arrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forward
- An Earth satellite has an elliptical orbit described by (as shown in the pic.) (All units are in miles). The coordinates of the center of Earth are (16,0). Solve, a. The perigee of the satellite’s orbit is the point that is nearest Earth's center. If the radius of Earth is approximately 4000 miles. Find the distance of perigee above Earth’s surface. b. The apogee of the satellite’s orbit is the point that is the greatest distance from Earth’s center. Find the distance ofthe apogee above Earth’s surface.arrow_forwardA satellite has a mass of 5850 kg and is in a circular orbit 4.10 × 105 m above the surface of a planet. The period of the orbit is 2.00 hours. The radius of the planet is 4.15 × 106 m. (a) Find the mass of the planet,(b) the energy of the orbit, and (c) the escape velocity from this orbit. If the speed of the satellite is increased by 20% what would be the maximum distance above the planet? Needs Complete typed solution with 100% accuracy.arrow_forwardWhat are (a) the speed and (b) the period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.4 * 105 J per orbital revolution. Adopting the reasonable approximation that the satellite’s orbit becomes a “circle of slowly diminishing radius,” determine the satellite’s (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f ) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth’s center conserved for (g) the satellite and (h) the satellite–Earth system (assuming that system is isolated)?arrow_forward
- A satellite is in a circular low Earth orbit at an altitude of 390 km above the equator's surface. For Earth's radius at the equator, use RE, eq = 6.38 ✕ 106 m. Assuming only the force of Earth's gravity acts on the satellite, determine the smallest required change in the satellite's speed if it is to escape Earth's gravity and never return.arrow_forwardA satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R = 1.8 × 107 m. The mass of the planet is M = 4.8 × 1024 kg. a)Express the speed v in terms of G, M and R. b)Express the magnitude of the centripetal acceleration ac of the satellite in terms of the speed of the satellite v, and R. c)Calculate the numerical value of v, in m/s.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningFoundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage LearningStars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage Learning