Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 6, Problem 24P
To determine
To Find: The orbital radius of a satellite having geosynchronous orbit.
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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.
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Problems
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rce
*24 Compute the orbital radius of an earth satellite that has
an equatorial orbit and always remains above a fixed
point P on the earth's surface. Communication satel-
lites have such "geosynchronous" orbits (Fig. 6-19).
These satellites are used to relay radio and television
signals around the world.
s if
un-
hate
Communication
satellite
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Fig. 6-19
25 The earth orbits the sun in an approximately circular
orbit of radius 1.496 X 10" m (about 93 million
15
A satellite describes a circular orbit at an altitude of 19 110 km above the surface of the earth. Determine (a) the increase in speed required at point A for the satellite to achieve the escape velocity and enter a parabolic orbit, (b) the decrease in speed required at point A for the satellite to enter an elliptic orbit with a minimum altitude of 6370 km, (c) the eccentricity ε of the elliptic orbit.
Chapter 6 Solutions
Physics Fundamentals
Ch. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5QCh. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 9QCh. 6 - Prob. 10Q
Ch. 6 - Prob. 11QCh. 6 - Prob. 12QCh. 6 - Prob. 13QCh. 6 - Prob. 14QCh. 6 - Prob. 15QCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 27PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 38PCh. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Prob. 44PCh. 6 - Prob. 45P
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- What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forwardThe “mean” orbital radius listed for astronomical objects orbiting the Sun is typically not an integrated average but is calculated such that it gives the correct period when applied to the equation for circular orbits. Given that, what is the mean orbital radius in terms of aphelion and perihelion?arrow_forwardIf 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_forward
- An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planetarrow_forwardFollowing the technique used in Gravitation Near Earth’s Surface, find the value of g as a function of the radius r from the center of a spherical shell planet of constant density with inner and outer radii Rin and Rout . Find g for both eq and for RinrRout . Assuming the inside of the shell is kept airless, describe travel inside the spherical shell planet.arrow_forwardThe mean diameter of the planet Mercury is 4.88106m , and the acceleration due to gravity at its surface is 3.78m/s2 . Estimate the mass of this planet.arrow_forward
- Find the speed needed to escape from the solar system starting from the surface of Earth. Assume there are no other bodies involved and do not account for the fact that Earth is moving in its orbit. [Hint: Equation 13.6 does not apply. Use Equation 13.5 and include the potential energy of both Earth and the Sun. Substituting the values for Earth’s mass and radius directly into Equation 13.6, we obtain vesc=2GMR=2(6.67 10 11Nm2/kg2)(5.96 10 24kg)(6.37 106m)=1.12104m/s That is about 11 km/s or 25,000 mph. To escape the Sun, starting from Earth’s orbit, we use R=RES=1.501011m and MSum=1.991030kg . The result is vesc=4.21104m/s or about 42 km/s. We have 12mvesc2GMmR=12m02GMm=0 Solving for the escape velocity,arrow_forward(a) Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass mE, radius RE) and place it in a circular low earth orbit—that is, an orbit whose altitude above the earth’s surface is much less than RE. (As an example, the International Space Station is in low earth orbit at an altitude of about 400 km, much less than RE = 6370 km.) Ignore the kinetic energy that the spacecraft has on the ground due to the earth’s rotation. (b) Calculate the minimum amount of additional work required to move the spacecraft from low earth orbit to a very great distance from the earth. Ignore the gravitational effects of the sun, the moon, and the other planets. (c) Justify the statement “In terms of energy, low earth orbit is halfway to the edge of the universe.”arrow_forwardQuestion 4 of 7 GMm where If the gravitational force between two objects of mass M and m, separated by a distancer, has magnitude G = 6.67 × 10-1" m°kg¬'s¯², then the work required to increase the separation from a distance r¡ to a distance r2 is GMm(r,' – r,'). Compute the work required to move a 1500-kg satellite from an orbit 1000 km above the surface of Earth to an orbit 1500 km above the surface of Earth. Assume that Earth is a sphere of radius R = 6.37 × 10° m and mass M. = 5.98 × 1024 kg. Treat the satellite as a point mass. (Write your answer in scientific notation with two decimal places.) 1.47 x107 J W = Incorrect Question Source: Rogawski 4e Calculus Early Transcendentals| Publisher: W.H. Fm 014 étv hulu MacBook PrOarrow_forward
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