1. ## need help!!

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 ???

2. Originally Posted by sweet
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, also
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

3. 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!

4. Originally Posted by sweet
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 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

5. E divined like in the graph

and v isn't constant it's a Velocity

6. Originally Posted by sweet
E divined like in the graph

and v isn't constant it's a Velocity
What's this:

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

7. $\displaystyle v_{AP}$ is Aphelion Velocity
$\displaystyle v_{peri}$ is pericentre Velocity

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

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

8. Originally Posted by sweet
$\displaystyle v_{AP}$ 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.

RonL

9. Originally Posted by CaptainBlack
which would make it a constant velocity.

RonL

why u say it's constant

10. Originally Posted by sweet
$\displaystyle v_{AP}$ is Aphelion Velocity
$\displaystyle v_{peri}$ is pericentre Velocity

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

so
$\displaystyle v^2=v_{peri}^2+v_{AP}^2$
I know what a "perihelion" velocity would be. What is a "pericenter" velocity?

-Dan

11. 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

12. 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

13. 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
$\displaystyle v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}$

it,s verey hard ....

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

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.

-Dan

15. 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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