need help!!

**sweet** · May 23rd 2006, 12:43 AM

hi
how can i proof

:
$ v=(mu/a)^{1/2} (1+e cosE/1-e cosE)^{1/2} $
where $v =(v_{Ap}^2 + v_{peri}^2)^{1/2}$

if the planet orbit on ellipse ???

**CaptainBlack** · May 23rd 2006, 02:57 AM

Originally Posted by sweet

hi
how can i proof

:
$ v=(mu/a)^{1/2} (1+e cosE/1-e cosE)^{1/2} $
where $v =(v_{Ap}^2 + v_{peri}^2)^{1/2}$

if the planet orbit on ellipse ???

A bit more explanation of what the symbols stand for is needed, also
we are guessing what you have been asked to prove, I assume it is:

$ v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2} $

but that leaves us guessing is $mu$ supposed to be $\mu$ ?

Is $e$ the eccentricity? $a$ the semi-major axis?

Also what is $E$ ?

We can guess but it is just making it more work for the helpers here.

RonL

**sweet** · May 23rd 2006, 04:23 AM

ok

mu = $ \mu $

e= the eccentricity
a= the semi-major axis
E=the eccentric anomaly

we want to proof
$ 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
$ v =(v_{Ap}^2 + v_{peri}^2)^{1/2} $

Thanks for helping me!

**CaptainBlack** · May 23rd 2006, 06:21 AM

Originally Posted by sweet

ok

mu = $ \mu $

e= the eccentricity
a= the semi-major axis
E=the eccentric anomaly

we want to proof
$ 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
$ 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 the
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

**sweet** · May 23rd 2006, 07:53 AM

E divined like in the graph

and v isn't constant it's a Velocity

**CaptainBlack** · May 23rd 2006, 08:41 AM

Originally Posted by sweet

E divined like in the graph

and v isn't constant it's a Velocity

What's this:

$ v =(v_{Ap}^2 + v_{peri}^2)^{1/2} $

**sweet** · May 23rd 2006, 09:08 AM

$v_{AP}$ is Aphelion Velocity
$v_{peri}$ is pericentre Velocity

and v is aggregate of $v_{AP} ,v_{peri}$

so
$ v^2=v_{peri}^2+v_{AP}^2 $

**CaptainBlack** · May 23rd 2006, 09:11 AM

Originally Posted by sweet

$v_{AP}$ is Aphelion Velocity
$v_{peri}$ is pericentre Velocity

and v is aggregate of $v_{AP} ,v_{peri}$

so
$ v^2=v_{peri}^2+v_{AP}^2 $

which would make it a constant velocity.

RonL

**sweet** · May 23rd 2006, 09:15 AM

Originally Posted by CaptainBlack

which would make it a constant velocity.

RonL

why u say it's constant

**topsquark** · May 23rd 2006, 12:44 PM

Originally Posted by sweet

$v_{AP}$ is Aphelion Velocity
$v_{peri}$ is pericentre Velocity

and v is aggregate of $v_{AP} ,v_{peri}$

so
$ v^2=v_{peri}^2+v_{AP}^2 $

I know what a "perihelion" velocity would be. What is a "pericenter" velocity?

-Dan

**sweet** · May 23rd 2006, 12:52 PM

Originally Posted by topsquark

I know what a "perihelion" velocity would be. What is a "pericenter" velocity?

-Dan

i'm sorry it's Perihelion velocity not pericenter velocity

**topsquark** · May 24th 2006, 12:45 PM

Originally Posted by sweet

i'm sorry it's Perihelion velocity not pericenter velocity

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.

-Dan

**sweet** · May 24th 2006, 03:21 PM

Originally Posted by topsquark

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.

-Dan

ok i agree with u that v is aconstant ...but the problem is how can i proof the formula
$ v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2} $

it,s verey hard ....

**topsquark** · May 25th 2006, 03:37 AM

Originally Posted by sweet

ok i agree with u that v is aconstant ...but the problem is how can i proof the formula
$ 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.

-Dan

**CaptainBlack** · May 25th 2006, 09:29 AM

Originally Posted by topsquark

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.

-Dan

No No No. v is now the speed of the planet as a function of eccentric anomaly.

RonL

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