39
Dr.House
·2010-08-09 22:12:07
Radius vector is a vector starting at the center of coordinates and ending at some point of ellipse.
39
Dr.House
·2010-08-09 22:12:33
and here, the center of coordinates is a focus of this ellipse
66
kaymant
·2010-08-09 23:29:18
@johny,
The center of coordinates is NOT the focus but the center of the ellipse itself.
39
Dr.House
·2010-08-09 23:32:33
its not always the case.. i had read otherwise in many articles before
39
Dr.House
·2010-08-09 23:36:43
i have taken the keppler laws as my base and you being a physics professor should be knowing what as i said
anyways i am not completely sure about my clainin maths
but AS FAR AS THE PHYSICS I HAVE READ, the center of coordinates IS THE focus of the ellipse
1
rajuabcd pqrs
·2010-08-10 07:49:34
@johny,

centre of coordinate is the centre of ellipse not the focus as far as i know
CENTRE OF ELLIPSE IS NOT D FOCUS
i think that onli kayamat sir wanted to say
1
rajuabcd pqrs
·2010-08-10 08:03:06
i got the answer
i hav taken a vector from d centre of ellipse which is the centre of coordinates in this particular case to any point of the ellipse
but what would i do if the equation is not in the standard formsuppose the origin is shifted
then,
in that case what would be the radius vector of the ellipse
should i take it from the origin of coordinate syastem or from the centre of the ellipse
PLEAZZZ REPLY IF ANYONE HA ANY SORT OF IDEA ABOUT THIS
1
rajuabcd pqrs
·2010-08-10 08:04:20
but what would i do if the equation is not in the standard formsuppose the origin is shifted
then,
in that case what would be the radius vector of the ellipse
should i take it from the origin of coordinate syastem or from the centre of the ellipse
PLEAZZZ REPLY IF ANYONE HA ANY SORT OF IDEA ABOUT THIS
66
kaymant
·2010-08-10 11:17:45
@johny
usually in polar coordinates, the conic sections are specified by giving the distance of a point from the focus. However, in the present case, the radius vector is measured relative to the center of coordinates.
As far as the problem is concerned, proceed as follows:
Any point on the ellipse is of the form (a cos t, b sin t). Here t is eccentric angle. As such the radius vector is r = √a2 cos2t + b2 sin2 t. Next, we notice that
tan θ = b sin ta cos t = ba tan t
which gives us
tan t = ab tan θ.
As such we have
cos2 t = 11+tan2 t = b2b2 + a2 tan2θ = b2 cos2θb2 cos2θ + a2 tan2θ
And
sin2t = tan2t1+tan2 t = a2 sin2θb2 cos2θ + a2 tan2θ
Hence,
r = √a2 b2b2 cos2θ + a2 tan2θ
as required.
1
rajuabcd pqrs
·2010-08-11 06:08:06
but from where should i take the radius vector
from the centre of coordinates
or
from the centre of coordinate system
or
from the focus
if it is not in the standard form