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A satellite circles a spherical planet of unknown mass in acircular orbit of radius $2.0 \times 10^{7} \mathrm{m} .$ The magnitude of thegravitational force exerted on the satellite by the planet is120 $\mathrm{N} .(a)$ What would be the magnitude of the gravitationalforce exerted on the satellite by the planet if the radius ofthe orbit were increased to $3.0 \times 10^{7} \mathrm{m} ?$ (b) If the satellitecircles the planet once every 2.0 $\mathrm{h}$ in the larger orbit, what isthe mass of the planet?

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a) 53$N$b) $3.1 \times 10^{26} k g$

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

McMaster University

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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6.73. So we have a satellite circling the planet was mess, we do not know, but we are told that its orbital radius is two times 10 to the seventh meters and the magnitude of the gravitational force it feels is 100 and 20 movements. So first we want to find out what the gravitational forces if we increase the, uh orbit radius by 50% and then if the satellite has a period of two hours of its orbit, that was the mass of the planet. So for part eight here, our new force a crime going G times the mass of the planet provided by are fine square, which we know is one and 1/2 times the original radius. So we have a 1.5 squared R squared. So this is one over two and 1/4 times g times the mass of the planet divided by the original radius square. And this, we know is 120 Newton's without having to know, uh, actually anything else at all about the set up here. We don't need to know the mass of the planet or the distance because we've expressed the change in the distance as being a multiple of the original. And so the new forest of this greater distances 53 notes. So now, at this, uh, larger radius, we're told the the period is two hours, which is 72. No, I'm sorry. 7000 200 seconds. Just 3600 seconds. And on our so we know that speed is GM over the square root of GM over our it's seen before We know is also equal to pi are divided, divided by the period. So now we just solve this equation for the mass. So this would be four pi squared r squared over. No, All right are cute because we haven't extra are from over here After we square everything over the period squared. So this is basically just time periods where this is basically you know what it is Kepler's third law. And so this works out to be 3.1 times into the 26 kilograms, and there we go

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