Universal formulation-Kepler's problem(math help)

[AE031]

Hi,
I am deriving the universal formulation for time of flight which is in the book 'Fundamentals of Astrodynamics' by Bate, Mueller, & White.

dx=dr/sqrt(-p+2r-(r^2/a)) ----- 1

For e not equal to 1, the indefinite integral calling the constant of integration c_0 is

x+ c_o= sqrt(a) sin^-1 [(r/a)-1]/sqrt(1-(p/a)) ------2

I would like to know the intermediate steps that lead to equation 2 from equation 1.

 

[jsky]

Hi,
I am deriving the universal formulation for time of flight which is in the book 'Fundamentals of Astrodynamics' by Bate, Mueller, & White.

dx=dr/sqrt(-p+2r-(r^2/a)) ----- 1

For e not equal to 1, the indefinite integral calling the constant of integration c_0 is

x+ c_o= sqrt(a) sin^-1 [(r/a)-1]/sqrt(1-(p/a)) ------2

I would like to know the intermediate steps that lead to equation 2 from equation 1.

This looks like someone's calculus or physics homework assignment. As opposed to giving you step-by-step answers, let me assign you a reading on Integration Techniques with Trigonometric substitution which, upon completion will teach you how to complete your homework accordingly.

Good luck. Best learn it before the final :thumbup: