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(III) The comet Hale-Bopp has a period of 2400 years.(a) What is its mean distance from the Sun? (b) At itsclosest approach, the comet is about 1.0 AU from the Sun$(1 \mathrm{AU}=$ distance from Earth to the Sun). What is thefarthest distance? (c) What is the ratio of the speed at theclosest point to the speed at the farthest point?

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a) 180$A U$b) 360$A U$c) 360$/ 1$

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

Simon Fraser University

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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45. So we're thinking about the Comet Hale box, which was a prominent comment that was discovered in the 20th century by unsurprisingly, Hale and Bob has a period of 2400 years. So I want to find its mean distance from the sun and given its minimum distance, is one astronomical unit. We want to find its maximum distance. And then we want to find the ratio of the speeds that the closest and uh far this point, which will be the ratio of the maximum and minimum to minimum speeds. Because it's going the fastest one. It's the closest to the sun. So our party here we use Kepler's third law. So the ratio of these Raby I cube is equal to the ratio of the periods squared. And because the heart be eyes in astronomical units, we're gonna go ahead and use use one astronomical unit as the Earth's distance from the sun because that would make our lives easier. The next part. So this is the distance for the Earth Times ratio of the two periods to the 2/3 power. This is 179.3 a u true round to 180 now for the second part? Yeah, The mean distance is the average of the maximum and minimum distances our next, plus our men over too. We're told that the minimum distance is one astronomical. You incident putting that and, uh, 180 in here. We find that it's maximum distance is 360 a u. So for this part, we're going to use Kepler's second law, which has to do with the equal areas and equal times. So 1/2 be men time some time that we don't care. What time is it? Just the same as the other one. Times are men. So this is an area of a triangle swept out in some smallish time t, which is why we're able to approximate it. It's a triangle. This has to be the same. Is the area of a triangle swept out in the same amount of time at the maximum, um, distance. And like I said, the maximum speed is of the closest distance. Sorry about that. Our max Here are the acts that be then our max and, um So the maximum speed divided by the minimums be is the ratio of their corresponding distances. So we know this is, um no. So sorry. There's going to be our Max over our men. And so we know that this is 360 this is one. And so astronomical units cancel out there and we're left with dimension less 360.

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