why the orbits of the planets is in elliptical shape and not in any other shape?

Answer 1

Any object that travels will do so in the shortest possible path. in case of celestial objects, The shortest possible path is made up of curves (in the sense that they have no corners). That is why no object moves around another in straight lines.

As for eliipses, we first consider conic sections (circles, ellipses, parabolae, and hyperbolae). These curves are the paths followed by objects traveling in space. Objects can then either orbit something or just pass by it.

For orbiting objects, we need to have a closed path. In comes the ellipse. (the circle is a special kind of ellipse, with the foci coinciding at one point)

For one-time passing objects (some comets, asteroids, etc) the path is open. Meaning hyperbolae and parabolae.

Answer 2

Okay. Lets assume that a planet is moving at any velocity V and the Sun is somewhere nearby. The planet's angular momentum relatively to the Sun is L = [r V], where r is the radius vector from the Sun to the planet. L is perpendicular to the force F||r of interaction between the Sun and the planet. Therefore, dL/dt = M = [r F] = 0. So V is always in the same plane, and |L| = const.

This leads to r^2*da/dt = L/m = const , where (r, a) are polar coordinates of the planet. Also, the law of mechanical energy conservation stipulates

K + P = W = const,

where K is the kinetic energy of the planet, P is the potential energy of the planet, and W is the full energy. Since

K = mV^2/2 = m/2((dr/dt)^2) + (r*da/dt)^2) = m/2((dr/dt)^2 + (L/mr)^2)

and

P = -ymM/r,

we have (dr/dt)^2 + (L/mr)^2 - 2yM/r = 2W/m.

So the movement equation of the planet in polar coordinates is

r=p/(1+ecosa),

where p = L^2/ym^2M and e = (2WL^2/y^2m^3M^2 + 1)^1/2. Since W < 0, we have e < 1, and the trajectory is an ellipse

Answer 3

Isaac Newton proved that with an inverse square gravity law, only an elliptical orbit would conserve the total (kinetic plus potential) energy of the planet. The energy has nowhere else to go, so it must be conserved, so the orbit must be elliptical. As the planet's distance from the sun varies, either its potential energy is increasing and its kinetic energy decreasing, or vice versa.

Answer 4

That is just the way gravity, momentum and energy work. If a planet is moving at EXACTLY the right speed and direction, then it would orbit in a circle. At any other speed, it is going either too fast or too slow to stay at the same distance. If too slow, it starts to fall toward the Sun, but as it falls it gains speed, as falling things always do, and ends up closer to the Sun but now going too fast. That causes it to fly away from the Sun, but as it flies away it slows down, as objects thrown up always do, so it ends up farther away from the Sun but going too slow again. This repeats endlessly in the frictionless vacuum of outer space and the result is an elliptical orbit.

Answer 5

sun exerts gravitational force on planets
this acts as the centripetal force and planets revolve around it
centripetal force always gives rise to circular motion
but as planets also have fairly large mass they dont readily fall into circular orbit so,the orbit is elliptical

Answer 6

Because a circle is simply a special case of an ellipse with ellipticity of 0.


Doug

Answer 7

dat comes frm d law f gravitation, principle f conservation f angular momentum f sys of planets n sun n also energy conservation. check sum bk fr d details.
d properties f d orbits f planets r satisfied by ellipse..

Answer 8

the planets r not allowed to touch each other and also the orbits r another set of imaginary line

Answer 9

Its a very good question actually...

This is because the sun, which is the centre of revolution is not fixed, it rotates by itself and revolves around the centre of milky way...
So if seen over a very short duration of time, the orbit of any planet is circle but when seen over longer durations, it is an ellipse since the sun is not stationary with respect to our milky way galaxy

Answer 10

it is because of centrifugal force which is acted by sun along the planets