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(I) Determine the mass of the Earth from the known periodand distance of the Moon.

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$5.98 \times 10^{24} k g$

00:04

Averell Hause

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Cornell University

University of Washington

University of Sheffield

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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for this problem. On the topic of gravitation, we are asked to determine the mass of the earth if we know the period any distance off the moon from the Earth. So we know the period off the moon and we know the distance off the moon and we can calculate the speed off the moon's orbit as V is equal to two pi r where r d radius of it's all but divided by t where t is the period of its orbit. But we also know that the speed can be calculated for any Earth. Satellite by V is equal to he square root off the universal gravitational constant constant g times the mass off the earth e divided by the radius of the orbit of the distance for the satellite from the center of the Earth are now equating these two equations as we've done means we can rearrange and make the mass of the earth the subject of the formula. So m e becomes for pi. Squid are cute off g times t squared. So here are is the distance off the moon from the earth. Now, since we know these venues, we substitute them in and we can find an estimation for the mass of the earth. So this is four pi squared and are history. Quite 84 comes tend to be eight in meters and that's cute, divided by the gravitational constant G, which is six 0.67 claims 10 to the minus 11. And that's Newton Meter squared for K G squared, multiplied by the period. And we know the period off the moon is one. Roughly one month, which is 27.4 days, will convert three days into seconds to keep everything in S I units. And they're 86,000 400 seconds today in this period is all squared. And so now if we calculate if you compute this value, we get an estimation for the mass off the earth to be five 0.98 times 10 to the power 24 k g mhm.

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