Explanation The normal component of acceleration of the satellite is given as, a n = g ( R r ) 2 Where, g - Acceleration of gravity at the surface of the planet R - Radius of planet r - Distance from the center of the planet to satellite Diameter of the sun is 1.39 G m Acceleration of gravity is 274 m / s 2 Assume the orbit is circular For planet Earth ( v m e a n ) o r b i t = 107 M m / h For a circular orbit, The normal component of acceleration is defined as, a n = v 2 r Calculation: According to given information, a n = g ( R r ) 2 But we know that, a n = v 2 r Theref

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.5, Problem 11.153P

To determine

The radius of orbit of planet Earth around the Sun.

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Chapter 11.5, Problem 11.152P

Chapter 11.5, Problem 11.154P

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A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)2, where g is the acceleration of gravity at the surface of the planet, R is the radius of the planet, and r is the distance from the center of the planet to the satellite. Knowing that the diameter of the sun is 1.39 Gm and that the acceleration of gravity at its surface is 274 m/s2, determine the radius of the orbit of the indicated planet around the sun assuming that the orbit is circular.

Human centrifuges are often used to simulate different acceleration levels for pilots. When aerospace physiologists say that a pilot is pulling 9 g,s , they mean that the resultant normal force on the pilot from the bottom of the seat is nine times their weight. Knowing that the centrifuge starts from rest and has a constant angular acceleration of 1.5 RPM per second until the pilot is pulling 9 g's and then continues with a constant angular velocity, determine (a) how long it will take for the pilot to reach 9 g's (b) the angle 0 of the normal force once the pilot reaches 9 g’s. Assume that the force parallel to the seat is zero.

Consider a satellite around Earth in an elliptic orbit. At a point in its orbit, the radius (in km) from the center of the Earth is varying with time as r(t) = 7000 - 0.54 t (with t in seconds). The angular rate is 0 (t) = 1.02 x 10³ rad/s. What is the magnitude of acceleration (in m/s²) at t = 0.

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Vector Mechanics for Engineers: Dynamics

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