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The Navstar Global Positioning System (GPS) utilizes a groupof 24 satellites orbiting the Earth. Using "triangulation" andsignals transmitted by these satellites, the position of a receiveron the Earth can be determined to within an accuracy of a fewcentimeters. The satellite orbits are distributed evenly aroundthe Earth, with four satellites in each of six orbits, allowingcontinuous navigational "fixes" The satellites orbit at an altitude of approximately $11,000$ nautical miles $[1$ nautical mile $=$ $1.852 \mathrm{km}=6076 \mathrm{ft} \mathrm{t}$ . $(a)$ Determine the speed of each satellite. (b) Determine the period of each satellite.

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a) $3.9 \times 10^{3} \mathrm{m} / \mathrm{s}$b) $4.4 \times 10^{4} \mathrm{sec} \sim 12 \mathrm{h}$

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Cornell University

Simon Fraser University

Hope College

Lectures

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

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The Navstar Global Positio…

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The $\textbf{Navstar Globa…

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The Global Positioning Sys…

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A typical GPS (Global Posi…

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GPS Satellites GPS (Global…

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The GPS satellites describ…

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A global positioning syste…

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Predict/Calculate A satell…

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The satellites that compri…

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Global Positioning System …

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So we have to find the radius here. It's going to be the radius of the earth, plus 11,000 nautical miles. So 11,000 times 1.852 kilometers and we have that are is equaling 2.68 times, 10 to the seventh meters. So at this point for party, when they they want the velocity we consider the velocity is going to be the gravitational, constant times the mass of the earth divided by our to the 1/2 power. So this would be 6.67 times 10 to the negative, 11th times the mass of the earth, 5.97 times, 10 to the 24th kilograms. And then this will be divided by 2.68 times, 10 to the seventh meters and all to the 1/2 power. And we find that V is equaling 3.86 times 10 to the third meters per second. So this would be your answer for party and then for part B, we want to find the period. So we know that vegan equal to pi r over t. This would be applied for any object in uniform Circular motion so the period will simply be to pie are divided by the so two pi times. Thie are 2.68 times 10 to the seventh meters and then this would be divided by 3.68 times, 10 to the third meters per second. And we find that the period is 4.4 times 10 to the fourth seconds. So severe answered for part B. That is the end of the solution. Thank you for watching.

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