Solution Found!
In Section 9.8, we used a method of successive
Chapter 9, Problem 9.26(choose chapter or problem)
In Section 9.8, we used a method of successive aproximations to find the orbit of an object that is dropped from rest, correct to first order in the earth's angular velocity Q. Show in the same way that if an object is thrown with initial velocity vo from a point 0 on the earth's surface at colatitude 0, then to first order in Q its orbit is x = vxot Q (vvo cos 0 vzo sin 6)t2 4C2gt3 sin 0 y = vyot Q (vxo cos 0)t2 (9.73) z = vzot Zgt2+ (vxo sin 0)t2. [First solve the equations of motion (9.53) in zeroth order, that is, ignoring Q entirely. Substitute your zeroth-order solution for and z into the right side of equations (9.53) and integrate to give the next approximation. Assume that vo is small enough that air resistance is negligible and that g is a constant throughout the flight.]
Questions & Answers
QUESTION:
In Section 9.8, we used a method of successive aproximations to find the orbit of an object that is dropped from rest, correct to first order in the earth's angular velocity Q. Show in the same way that if an object is thrown with initial velocity vo from a point 0 on the earth's surface at colatitude 0, then to first order in Q its orbit is x = vxot Q (vvo cos 0 vzo sin 6)t2 4C2gt3 sin 0 y = vyot Q (vxo cos 0)t2 (9.73) z = vzot Zgt2+ (vxo sin 0)t2. [First solve the equations of motion (9.53) in zeroth order, that is, ignoring Q entirely. Substitute your zeroth-order solution for and z into the right side of equations (9.53) and integrate to give the next approximation. Assume that vo is small enough that air resistance is negligible and that g is a constant throughout the flight.]
ANSWER:Step 1 of 4
Let project the object from the origin O above the earth surface. Then the position of the object at any time,
The velocity of the object,
The angular velocity of earth about x axis,
Take cross product of 
