What is a zero velocity surface & what is its significance?

Answer 1

After delving through Google for a while my incomplete understanding is that a zero velocity surface is a boundary in three dimensional space that traces all possible points between three masses where the smallest of the masses cannot ever move. It is a concept that pops up on google searches in connection with the "three body problem" which uses classical newtonian mechanics to analyse the gravitational interaction between three masses in space, one of which may be much smaller. An example of three masses that are easier to analyse would be the Sun, Jupiter, and a comet whose orbit did not take it too close to Jupiter's gravitational well.

The zero velocity surface is a significant parameter in describing all manner of weak gravitational interactions between orbiting bodies, e.g. comets in our solar system, Oort cloud bodies such as dwarf planets, or on a much larger scale, galaxy clusters. Astronomers can determine which nearby galaxies are true members of our own "Local Group" by determining whether they lie inside or outside the zero velocity surface formed by such galaxies' gravitational attractions to each other before such force is overcome by the Hubble expansion of the universe as a whole.

I think the zero velocity surface is an important parameter in locating Lagrange points in local space as well: Lagrange points are places in local space where we could eventually establish space stations or remote telescopes such that they remained stationary, "locked in", as it were, at places where the gravitational forces exterted by Earth, the Sun and the Moon cancel each other out to zero.

Answer 2

When you transform into a rotating frame, you must subtract the rotational energy from the total energy. When you do this you introduce cross terms between the coordinates and the moment into the energy. These terms prevents the separation of the energy into kinetic and potential. The zero velocity surface (ZVS) is introduced in this case to replace the potential energy. It is constructed by requiring that all velocities are equal to zero, where the potential energy is constructed by requiring that the momenta are equal to zero. the ZVS only arises when working within a rotation frame of reference.

Answer 3

Something with no movement has no energy thus its frozen or very cold?

I forgot what its called, maybe Absolute Zero? (no energy = no atomic, electron movement)


Is that what your talking about?

Answer 4

Hi. This site mentions it. http://farside.ph.utexas.edu/teaching/336k/lectures/node125.html
It affects the Lagrange points.

Answer 5

Sorry, I have never heard that term before and I have been studying science for forty-five years.