Example in chapter: Gravitation

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Homework Help Overview

The discussion revolves around the motion of a comet in an elliptical orbit, specifically focusing on calculating the distances of nearest and farthest approaches (perihelion and aphelion) and determining the comet's speed at aphelion given its speed at perihelion. The problem involves concepts from gravitation and orbital mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to clarify the relationship between eccentricity, semi-major axis, and the distances of perihelion and aphelion. Questions are raised about specific calculations and definitions related to the orbit.

Discussion Status

Some participants are seeking clarification on specific parts of the problem, while others are providing insights into the definitions and relationships that govern the motion of the comet. There appears to be a productive exchange of ideas regarding the mathematical relationships involved.

Contextual Notes

There is mention of a solution that the original poster finds difficult to understand, indicating potential gaps in understanding the underlying concepts or calculations. The eccentricity and the distance between perihelion and aphelion are key parameters under discussion.

EngMan

Homework Statement


consider the motion of a comet in an elliptical orbit around a star. the eccentricity of the orbit is given by e= 0.20 and the distance between the perhelion and the aphelion is 1.0 × 10^power8

a- find the distances of nearest and farthest approaches of the comet.
b- if the speed of the comet is 81 km/s at perihelion, what is its speed at aphelion?

there is a solution but i can't understand it
i hope someone help me step by step

fBqzNxJ.jpg


sJFPtNK.jpg

Homework Equations

The Attempt at a Solution

 

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Which part is unclear?
 
mfb said:
Which part is unclear?
how Rmax=1×10^8 × 1.20 ÷ 2
is the second picture
 
By definition, the eccentricity tells you how much periapsis and apoapsis deviate from the semi-major axis, here 20%=0.2. Periapsis is at (1-0.2) times the semi-major axis, and apoapsis is at (1+0.2) times the semi-major axis.

The semi-major axis is the mean of the two, and you are given the sum, so you have to divide the sum by 2 to get the the semi-major axis.
 

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