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Any object under the influence of a central force will have two components of velocities: Radial and rotational I understand that the rotational velocity is there due to the centripetal force. But where does the radial velocity come from? Is it because the object had some velocity along the radial direction before?

For example: If we consider a planet, Is it that before it got 'captured' by some star, it was travelling at some velocity along the radial direction (with respect to the star)?

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    $\begingroup$ "Any object under the influence of a central force will have two components of velocities: Radial and rotational I understand that the rotational velocity is there due to the centripetal force." No. Who on Earth told you that? $\endgroup$ – Gert Oct 30 '19 at 10:06
  • $\begingroup$ Planets get formed from the primordial protoplanetary disc. They are not "captured" objects from interstellar space.. $\endgroup$ – Pieter Oct 30 '19 at 10:20
  • $\begingroup$ An elliptical orbit will have a radial component of velocity.. $\endgroup$ – Farcher Oct 30 '19 at 10:59
  • $\begingroup$ Yes. Thank you @gret, I thought it was so. Actually I was also not sure about how the planets came into existence/started moving along the elliptical path. Need to study about primordial protoplanetary disks $\endgroup$ – Swaroop Joshi Oct 30 '19 at 13:06
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An object rotating in a circle around a centre has a relative velocity to the centre in a direction perpendicular to the radius only. The total velocity would be the vector addition of the mentioned rotational velocity and the translational velocity of the centre itself.

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  • $\begingroup$ No, a circular orbit has no radial component, but an elliptical orbit does. $\endgroup$ – Lewis Miller Oct 30 '19 at 11:51
  • $\begingroup$ I didn't mention a radial component, I said perpendicular to the radius. If you mean the translational velocity of the centre, then yes it wouldn't be a circle from the prespective of an observer outside a centre but rather a spiral. $\endgroup$ – Peter Oct 30 '19 at 13:40
  • $\begingroup$ You are right, I misread your answer. $\endgroup$ – Lewis Miller Oct 30 '19 at 13:58

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