Example in chapter: Gravitation

AI Thread Summary
The discussion focuses on calculating the distances of a comet's nearest and farthest approaches in its elliptical orbit, given an eccentricity of 0.20 and a distance between perihelion and aphelion of 1.0 × 10^8. The semi-major axis is determined by averaging the distances of periapsis and apoapsis, which are derived from the eccentricity. The formula for the maximum distance (Rmax) is clarified as Rmax = 1 × 10^8 × 1.20 ÷ 2. Additionally, the speed of the comet at aphelion can be calculated using conservation of energy principles. Understanding these steps is essential for solving the problem correctly.
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

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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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