Central forces in elliptic and parabolic orbits

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Homework Help Overview

The discussion revolves around two problems from a textbook on spherical astronomy concerning central forces in parabolic and elliptic orbits, specifically Euler's theorem and Lambert's theorem. The original poster seeks assistance with these problems, indicating they have been struggling with them for over a week.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants question the original poster's attempts to solve the problems, suggesting that sharing their working might facilitate better assistance. There is also a discussion about the clarity of the provided image and the relevance of the Earth's orbit in the context of the problems.

Discussion Status

The conversation reflects a lack of explicit consensus, with some participants expressing frustration over the original poster not sharing their attempts. Others have offered general guidance on the nature of the problems, but no specific solutions have been proposed.

Contextual Notes

There is mention of the original poster's reluctance to share their workings, which may hinder the collaborative problem-solving process. Additionally, the clarity of the provided image is noted as a potential barrier to understanding the problems.

armin.hodaie
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hi,can anyone solve this two problems??
these are from the "textbook on spherical astronomy" written by W.smart
chapter five,problem number 18 and 19,Euler's theorem and Lambert's theorem
thank you ;-)
 

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Is this homework? You should try to do the problem yourself first. We are only meant to help on homework. P.S. the .bmp image is a bit difficult to read.
 
yes,this is homework.i have been trying to solve this two question for more than a week,but i can't solve it ;-(
 
nobody?really?
 
You haven't tried the questions yourself yet, so it is hard to give help. Also, I can't read the bmp image. And I'm guessing that's why there haven't been other replies yet.
 
dear BruceW,
i have been trying for more than a week,but i can't solve them,so don't tell me that i haven't tried !
these are not simple problems :D
bmp files are readible,but i will write down questions right now !

1.if r and r1 are the radii vectors of two points C and C1 in a parabolic orbit and if k is the distance C-C1.prove that the time in the orbit between C and C1 is:

(T0/12pi)[((r+r1+k)/a)^(3/2)-((r+r1-k)/a)^(3/2)]
where T0 is the length of the sidereal year and 'a' is the semi-major axis of the Earth's orbit

2.if r and r1 are the radii vectors of two points C and C1 in a elliptic orbit and if k is the distance C-C1.'t' the time required by the planet to move from C to C1 and T the orbital period,prove that:

(2pi*t/T)=H-sin(H)-(H1-sin(H1))

where sin(H/2)=(1/2)((r+r1+k)/a)^(1/2)
sin(H1/2)=(1/2)((r+r1-k)/a)^(1/2)
 
the bmp is not completely readable, but thanks for writing it out, I know what it means now.

Maybe you have tried, but you haven't written anything on this thread. You've just asked for someone to solve them for you. The idea of this forum is that you post your working and/or say where you are stuck, then people try to help.

I know it is a pain to write all your working here, but otherwise, I don't know how to help.
 
The general idea is to use your knowledge of parabola and ellipses to show why the theorems must be true.

The first question is weird because it talks about a parabolic orbit and mentions the Earth's orbit, which is definitely not parabolic.
 
i won't write my workings here,and i think there is no one to help me.this forum is really weak,bye4ever
 
  • #10
byebye
 

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