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(II) The asteroid belt between Mars and Jupiter consists ofmany fragments (which some space scientists think camefrom a planet that once orbited the Sun but was destroyed).(a) If the mean orbital radius of the asteroid belt (where theplanet would have been $)$ is about three times farther fromthe Sun than the Earth is, how long would it have taken thishypothetical planet to orbit the Sun? (b) Can we use thesedata to deduce the mass of this planet?

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a) 5$y$b) No, mass of the planet can not be calculated from the available data as the relationship is mass independent Any object at orbit radius of 3 times than Earth's will take 5 years to complete, regardless of its mass.

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

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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(II) The asteroid belt bet…

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The asteroid belt that lie…

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Jupiter's four large …

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Io, one of Jupiter's …

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A newly discovered asteroi…

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The asteroid belt circles …

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Orbits of the planets. Acc…

In 2004 astronomers report…

going to use Kepler's Third Law s. So we can say that the period of the planet, okay, divided by the period of Earth, squared well equal the radius of the planet divided by the radius of Earth cubed. So we can say that the period of the planet will equal the period of Paris times the radius of the planet divided by the radius of earth, cubed rather to the three halves power. And so we can say that this will equal one year the period of Earth times three to the three halves power. And this is giving us 5.20 years. So this would be the period of the unknown planet. And that would be for party for part B. They're asking if we can calculate mass. So no mass can be calculated because thie relationship is mass independence. That is the end of the solution. Thank you for watching

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