bs@linus.UUCP (Robert D. Silverman) (10/22/86)
A new orbit puzzle: Assume that an object in a circular orbit suddenly has its mass cut in half. What happens to the orbit? By the way, the factor of 2 in the above question is critical. If it is greater than 2 something else happens and if it is less than 2 something else happens. Bob Silverman
johnf@apollo.uucp (John Francis) (10/24/86)
> Assume that an object in a circular orbit suddenly has its mass cut in half. > What happens to the orbit? > By the way, the factor of 2 in the above question is critical. If it is > greater than 2 something else happens and if it is less than 2 something else > happens. Both halves of the object continue in a circular orbit :-) Assuming that what the problem *really* means is that the mass is reduced to 1/2 the original mass while something else is left unchanged - what does not change ? Is it the momentum or the energy ? SPOILER FOLLOWS As under Newtonian dynamics the orbits of all objects moving in a central inverse-square field are conic sections, the original poser is obviously looking for the answer "the orbit becomes a parabola". If the factor is greater than 2 the orbit will become hyperbolic, and if less than 2 it will become elliptical. Given this fact, deduce whether the momentum or the energy should be assumed not to have changed.
aka@cbrma.UUCP (Andy Kashyap) (10/24/86)
In article <352@linus.UUCP> bs@linus.UUCP (Robert D. Silverman) writes: >A new orbit puzzle: > >Assume that an object in a circular orbit suddenly has its mass cut in half. >What happens to the orbit? > >By the way, the factor of 2 in the above question is critical. If it is >greater than 2 something else happens and if it is less than 2 something else >happens. > >Bob Silverman There is some confusion. If by "mass cut in half" you mean, half the mass suddenly vanishes then the answer is "nothing". Orbits have nothing to do with masses (excepting relativistic effects), but with velocity and altitude alone. On the other hand if you mean, the mass somehow explodes in two equal masses then the answer is more interesting: There must be conservation of angular mementum. So the center of mass of the two mass system will continue as before. Now, if the two masses are moving apart then (by conservation of linear momentum) one must be moving faster than the center of mass and the other slower. They both will end up in a elliptical orbit. The faster one in a more eccentric orbit than the slower one. However, if the explosion is strong enough, the faster one will spiral out of the system forever, and the slower one will spiral in and collapse. In this case, what happens to the center of mass? BEATS ME??? Oh well, I tried. -- +---------------------------------------------------------------------------+ : What is reality anyway but a collective hunch. : Andy Kashyap : : Reality is fine in small doses ... : AT&T Bell Labs : : ... but as a life style, it's too confining. : Columbus OH : : -- The Tonight Show : ..!cbosgd!cbrma!aka: +---------------------------------------------------------------------------+
gwyn@brl-smoke.ARPA (Doug Gwyn ) (10/27/86)
In article <352@linus.UUCP> bs@linus.UUCP (Robert D. Silverman) writes: >Assume that an object in a circular orbit suddenly has its mass cut in half. >What happens to the orbit? This can't be answered without making some additional assumptions, such as: it retains its previous momentum. If you simply split it into two halves, each half maintains the same orbit as before.
james@reality1.UUCP (james) (10/27/86)
In article <352@linus.UUCP> bs@linus.UUCP (Robert D. Silverman) writes: >Assume that an object in a circular orbit suddenly has its mass cut in half. >What happens to the orbit? >By the way, the factor of 2 in the above question is critical. If it is >greater than 2 something else happens and if it is less than 2 something else >happens. Um, intuition makes me say nothing happens. If a shuttle astronaut lets go of the vehicle, he just floats there. It doesn't matter how big the astronaut is. Since the same would be true of a rock, I would expect that if a rock were cut in half in orbit, nothing would happen. Aren't orbits about the earth a function of the velocity of the satellite and not the mass??? -- James R. Van Artsdalen ...!ut-ngp!utastro!osi3b2!james "Live Free or Die"
bs@linus.UUCP (Robert D. Silverman) (10/28/86)
> > Assume that an object in a circular orbit suddenly has its mass cut in half. > > What happens to the orbit? > > By the way, the factor of 2 in the above question is critical. If it is > > greater than 2 something else happens and if it is less than 2 something else > > happens. > > Both halves of the object continue in a circular orbit :-) > > Assuming that what the problem *really* means is that the mass is reduced to 1/2 > the original mass while something else is left unchanged - what does not change ? > Is it the momentum or the energy ? > > > SPOILER FOLLOWS > > As under Newtonian dynamics the orbits of all objects moving in a central > inverse-square field are conic sections, the original poser is obviously > looking for the answer "the orbit becomes a parabola". If the factor is > greater than 2 the orbit will become hyperbolic, and if less than 2 it will > become elliptical. > > Given this fact, deduce whether the momentum or the energy should be assumed > not to have changed. As a followup one can assume 3 separate conditions: (1) Momentum is conserved (2) Kinetic energy is conserved (3) Momentum changes from mv to mv/2 and energy from 1/2mv^2 to 1/4mv^2 What happens in each???? Bob Silverman