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A satellite is in a circular orbit about the earth $\left(M_{\mathrm{E}}=5.98 \times\right.$ $10^{24} \mathrm{kg} .$ The period of the satellite is $1.20 \times 10^{4} \mathrm{s}$ . What is the speed at which the satellite travels?

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$5.92 \times 10^{3} m / \mathrm{s}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

Hope College

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

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.

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A satellite is in a circul…

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02:56

02:27

A satellite is in a c…

01:37

A satellite is in elliptic…

01:55

A satellite moves in a cir…

01:16

02:48

The speed of a satellite l…

01:23

02:13

A satellite circles the ea…

here we have to find the velocity of a satellite going around Earth, given that we know it's period in seconds. So first, let's start by rewriting or period in terms of e the value we want to find. We know that T is equal to two pi over a mega and we can we write that as two pi r over. Hey, all right, so that's good, but we don't know what ours. So let's use another set of equations to find that we know that for a satellite within around a planet are centripetal force and B squared over R is going to be equal to our gravitational force, which is G times the mass of our satellite little M times the mass of our planet and e over r squared. Now we can use this to sulfur are were equal to m E times G over v squared. Now that we have a warrant for TV, we can plug it back in tour equation for tea that we just found over here and solve for V. So let's be right. We had earlier as V equals two pie or over tea, which, as we just found, is to pie Times and e d'oh, I realized that I switched between a big game in a little M. Let's keep that consistent. Weaver. Gee, Rita, But and so m e g comes to pi divided by tee times v squared. Now we can simplify that. Bring all our views to the same side and we get that V. It was gonna be equal to the cube root of g times, M E times to pike all over our period and those earlier constants or given quantities. So all that's left for us to do is plug in, Uh, G is aggressive nature, gravitational constant. It's kind of long, So I'm gonna write out down here instead. 6.67 times, 10 to the negative 11 Newton's times meters squared, kilograms squared And who's gonna be G times the mass of the earth? That's 5.98 times 10 to the 24 kilograms times to pie and that's all gonna be over 1.20 times tend to 1/4 seconds. That is our period that were given. I'm so plugging that all into our calculator. We find that the is equal to 5.92 times 10 cubed meters per second. The solution to our problem

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