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I recently studied projectile motion which consists of only downward parabolas. But I was wondering whether is it possible for a particle to go in a upward parabola provided that the particle doesn't have any propellers or things like those which can artificially make it happen and assuming that air resistance is absent?

Upward Parabola Image

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  • $\begingroup$ Any projectile, briefly upwardly projected will follow an upward parabolic trajectory. en.wikipedia.org/wiki/… $\endgroup$
    – Gert
    Apr 17 at 13:26
  • $\begingroup$ Since you are a student, if you continue studying you will see Kepler's laws of gravitation, en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion that describe mathematically how two gravitational bodies interact. For earth and an asteroid the trajectory can be a parabola, with the earth in its focus. For smaller projectiles and directed on earth the parabola faces down, as explained by the answers. see en.wikipedia.org/wiki/Parabolic_trajectory $\endgroup$
    – anna v
    Apr 17 at 19:47

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You get an upward parabola, only if you have a constant acceleration upward. This could be an electric field and a charged particle. It ist part of the way an electron moves in an oscillograph between the plates of a condensator

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The reason the equation of motion of a particle in a gravitational field is a downward parabola is that gravitational fields always exert attractive forces on particles. If you have a force which can be repulsive in nature(electromagnetic)then the equation of motion of a particle can be a upward parabola.

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Does a Parabolic orbital trajectory count?

As per Kepler's first law, objects in orbit follow conic sections; Ellipses if they are moving below escape velocity, Parabolas if they are moving exactly at escape velocity, and hyperbolas if moving above escape velocity.

Assuming your initial graph is $y=2x^2$, expressed in arbitrary Distance Units $D$ and Time units $T$...

If there was a self-gravitating object at the focus of the parabola $(0,\frac{1}{8})$ with gravitational parameter $\frac{1}{16}\,D^3/T^2$, a negligible-mass particle placed on the parabola at $(0,0)$ with an initial velocity of $1\,D/T$ parallel to the x-axis would follow the trajectory provided, if no other forces besides besides the aforementioned gravitational attraction acted upon it.

If we shift the origin to put it on the focus of the parabolic trajectory, it will look like this:

Parabolic trajectory

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  • $\begingroup$ Could you please explain it in a little easy language as I am just a 10th grade student. $\endgroup$ Apr 17 at 18:10
  • $\begingroup$ @TanmayGupta Basically, if you release an object in space near the Earth, moving at exactly the minimum Earth-relative speed to have it fly away from Earth forever (the escape velocity ), the orbital path it traces out will be a parabola. if it never comes under the gravitational influence of any other body. $\endgroup$
    – notovny
    Apr 17 at 19:37

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