Central forces in elliptic and parabolic orbits

[armin.hodaie]

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 ;-)

 

[BruceW]

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.

 

[armin.hodaie]

yes,this is homework.i have been trying to solve this two question for more than a week,but i can't solve it ;-(

 

[armin.hodaie]

nobody?really?

 

[BruceW]

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.

 

[armin.hodaie]

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)

 

[BruceW]

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.

 

[BruceW]

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.

 

[armin.hodaie]

i won't write my workings here,and i think there is no one to help me.this forum is really weak,bye4ever

 

[BruceW]

byebye