hi
how can i proof :( :
$\displaystyle
v=(mu/a)^{1/2} (1+e cosE/1-e cosE)^{1/2}
$
where $\displaystyle v =(v_{Ap}^2 + v_{peri}^2)^{1/2}$
if the planet orbit on ellipse ???
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hi
how can i proof :( :
$\displaystyle
v=(mu/a)^{1/2} (1+e cosE/1-e cosE)^{1/2}
$
where $\displaystyle v =(v_{Ap}^2 + v_{peri}^2)^{1/2}$
if the planet orbit on ellipse ???
A bit more explanation of what the symbols stand for is needed, alsoQuote:
Originally Posted by sweet
we are guessing what you have been asked to prove, I assume it is:
$\displaystyle
v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}
$
but that leaves us guessing is $\displaystyle mu$ supposed to be $\displaystyle \mu$?
Is $\displaystyle e$ the eccentricity? $\displaystyle a$ the semi-major axis?
Also what is $\displaystyle E$?
We can guess but it is just making it more work for the helpers here.
RonL
ok ;)
mu = $\displaystyle
\mu
$
e= the eccentricity
a= the semi-major axis
E=the eccentric anomaly
we want to proof
$\displaystyle
v=(\mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}
$
if the planet orbit on ellipse ???
where
$\displaystyle
v =(v_{Ap}^2 + v_{peri}^2)^{1/2}
$
Thanks for helping me!
Since the eccentric anomaly is a variable depending on the point of theQuote:
Originally Posted by sweet
planet in its orbit and v as defined here is a constant, as are e mu and a
this cannot be true for almost all values of eccentricity.
Or have I misunderstood something?
RonL
E divined like in the graph
and v isn't constant it's a Velocity
What's this:Quote:
Originally Posted by sweet
$\displaystyle
v =(v_{Ap}^2 + v_{peri}^2)^{1/2}
$
$\displaystyle v_{AP}$ is Aphelion Velocity
$\displaystyle v_{peri}$ is pericentre Velocity
and v is aggregate of $\displaystyle v_{AP} ,v_{peri}$
so
$\displaystyle
v^2=v_{peri}^2+v_{AP}^2
$
which would make it a constant velocity.Quote:
Originally Posted by sweet
RonL
Quote:
Originally Posted by CaptainBlack
why u say it's constant
:confused: :confused:
I know what a "perihelion" velocity would be. What is a "pericenter" velocity?Quote:
Originally Posted by sweet
-Dan
:eek:Quote:
Originally Posted by topsquark
i'm sorry it's Perihelion velocity not pericenter velocity :rolleyes:
In that case I agree with CaptainBlack. The perihelion and aphelion speeds are constant (meaning they don't vary with how many orbits have occurred.) Thus v^2 as you have defined it will also be constant. Since the eccentric anomaly changes over the course of the orbit (if I'm reading your diagram correctly) there must be an error in your formula.Quote:
Originally Posted by sweet
-Dan
ok i agree with u that v is aconstant ...but the problem is how can i proof the formulaQuote:
Originally Posted by topsquark
$\displaystyle
v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}
$
it,s verey hard ....
v is constant but E is not. The only way that formula can work is if you are calculating v for a particular point on the orbit (that is to say for a particular value of E), which we are not given.Quote:
Originally Posted by sweet
-Dan
No No No. v is now the speed of the planet as a function of eccentric anomaly.Quote:
Originally Posted by topsquark
RonL