why is the orbit of the earth elliptical in shape even if the centripetal force is equal at every distance????

Question

and also why does the distance vary b/w earth and the sun ...
less in the left..(summers)
more in the right...(winters)

Answer 1

Gravity is a central force. The angular momentum of a particle is defined a L=pxr,
where p= m*v and r= radial dist are both vectors and 'x'=vector cross product (axb)=abcos (theta) in magnitude. Now dL/dt= Fxr (NewtonII) but F and r are orthogonal so theta =pi/2 and cos theta =0
So dL/dt=0, ie L= angular momentum =constant.
If you now equate NII to the grav force, the orbit of the particle is a conic section, ie ellipse, parabola or hyperbola with the centre of of mass at one focus.
Incidentally the Kepler equal areas law is just the conservation of angular momentum under a central force and does not require the precise inverse square formulation, only that the force acts cocentrically.
The seasons are in fact due to the tilt of of the Earth's axis wrt the plane of its orbit. The minimum intensity (W/m^2) incident on the Earth's surface is in our winter (when the earth is actually closest to the sun) when our hemisphere intercepts approx const energy/sec but spread over a larger area. The change in distance (and inv squ law of radiation) has negligible effect, although in the future as the eccentricity of the orbit tends to a max again,(110kY M-cycle) this will no longer hold.

Answer 2

Madhukar is correct. The centripetal force in this case (it's not really a force per se, but we will not go into relativity) is provided by the gravitational field of the sun, which lies at one vertex of the ellipse. Newton showed that the gravitational "force" is proportional to the inverse square of the distance between the two objects (earth and sun, in this case). So the centripetal force is much lower at greater distances and much higher at smaller distances. Kepler showed that what is equal is the area that is swept out in a fixed elapsed time by a line radiating outward from the sun to the earth. So as the earth swings around the sun, it travels a little faster on the close side and a little slower when it is farther away. All planetary orbits form ellipses - some more acute than others - probably due to the way that the early solar system formed and the fact that perfection (e.g. circular orbits) rarely occurs in nature

Answer 3

BTW

Because the Earths orbit is elliptical - which you already know from your question - is the reason why the distance between the Earth and the Sun varies!!!!!

The Earth is at its closest pont around 3 January i think (trying to work from memory here! - maybe someone else knows the exact date if i am wrong?)

Answer 4

Centripetal force is not constant at every distance. It is the angular momentum which is constant.

Answer 5

very good you have figured out a constant in the universe

Answer 6

Because the earth is not a perfect sphere!!! the earth is eleptical!!!