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Focal points

Focal points ( F 1 and F 2 ) lie on semi major axis at a distance from the origin given by

Focal points

Focal distances from the center of ellipse

f = a e

The focus of an ellipse is at a distance “ae” from the center on the semi-major axis. Area of the ellipse is "πab".

Semi latus rectum

Semi latus rectum is equal to distance between one of the foci and ellipse as measured along a line perpendicular to the major axis. This is shown in the figure.

Semi latus rectum

Semi latus rectum is perpendicular distance as shown in the figure.

For an ellipse, Semi latus rectum has the expression in terms of “a” and “b” as :

= b 2 a

We can also express the same involving eccentricity as :

= a 1 e 2

Solar system

The solar system consists of Sun and its planets. The reason they are together is gravitation. The mass of the planet is relatively small with respect to Sun. For example, Earth compares about 10 5 times smaller in mass with respect to Sun :

Mass of Earth : 5.98 X 10 24 k g

Mass of Sun : 1.99 X 10 30 k g

The planetary motion, therefore, fits nicely with elliptical solution obtained from consideration of mechanics. Sun, being many times heavier, appears to be at the “center of mass” of the system i.e. at one of the foci, while planets revolve around it in elliptical orbits of different eccentricities.

Equation in polar coordinates

Polar coordinates generally suite geometry of ellipse. The figure shows the polar coordinates of a point on the ellipse. It is important to note that one of foci serves as the origin of polar coordinates, whereas the other focus lies on the negative x-axis. For this reason orientation of x-axis is reversed in the figure. The angle is measured anti-clockwise and the equation of ellipse in polar coordinates is :

Equation in polar coordinate

Second focus lies on negative x-axis.

r = 1 + e cos θ

Substituting expression for semi latus rectum

r = a 1 e 2 1 + e cos θ

Perihelion distance

Perihelion position corresponds to minimum distance between Sun and planet. If we consider Sun to be at one focus (say F 1 ), then perihelion distance is " F 1 A " as shown in the figure. We can see that angle θ = 0° for this position.

r min = a 1 e 2 1 + e = a 1 e

Minimum and maximum distance

Positions correspond to perihelion and aphelion positions.

From the figure also, it is clear that minimum distance is equal to “a - ae= a(1-e)”.

Aphelion distance

Aphelion position corresponds to maximum distance between Sun and planet. If we consider Sun to be at one focus (say F 1 ), then perihelion distance is " F 1 A ' " as shown in the figure. We can see that angle θ = 180° for this position.

r max = a 1 e 2 1 e = a 1 + e

From the figure also, it is clear that maximum distance is equal to “a + ae= a(1+e)”.

We can also prove that the semi-major axis, “a” is arithmetic mean, whereas semi-minor axis, “b”, is geometric mean of “ r min ” and “ r max ”.

Description of planetary motion

We can understand planetary motion by recognizing important aspects of motion like force, velocity, angular momentum, energy etc. The first important difference to motion along circular path is that linear distance between Sun and planet is not constant. The immediate implication is that gravitation force is not constant. It is maximum at perihelion position and minimum at aphelion position.

Questions & Answers

what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply
A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is
Lucky Reply
work done by frictional force formula
Sudeer Reply
Misthu Reply
Why are we takingspherical surface area in case of solid sphere
Saswat Reply
In all situatuons, what can I generalize?
Cart Reply
the body travels the distance of d=( 14+- 0.2)m in t=( 4.0 +- 0.3) s calculate it's velocity with error limit find Percentage error
Clinton Reply
Explain it ?Fy=?sN?mg=0?N=mg?s
Admire Reply

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