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## Main Question or Discussion Point

Hello

The following thought is confusing me a little. Let say we have sphererical planet with a certain mass and radius fixed in space. Now we have a point particle that at time t0 has a velocity vo that is perpendicular to the vector from the center of the plant to the particle and has a magnitude so that v^2/r=Fgravitational. In this case it seems to me that the only possible behaviour of the particle is to continue in a perfectly circular orbit for eternity(in a mathematical sense).

Now heres the question. Lets say we have a uniform, rod that has one end just above the surface of the planet and whose direction is so that the other end has the maximum distance from the surface of the planet. At time t0 let each part of the rod have velocity perpendicular to the vector from the center of the planet to the rod of magnitude v0r where v0r where r is the distance from the center of the planet to the part of the rod. Let the length of the rod be just so that the total gravitational force on the rod F is equal to the sum of centripetal forces needed for each part of the rod to maintain a circular orbit at its velocity.

Im am now trying to think about the behaviour of this rod, in particular if it will maintain a circular orbit continuing to point radially outward(like in the beginning). My mathematical toolbox is not very sophisticated but here is my attempt. After time dt the center of mass will be where it should for this circular orbit to take place since it behaves as if all the mass and force was concentrated there. The rod will however still point in the same direction after time dt since there is no angular momentum in regards to the center of mass. This means that it no longer points radially outwards and the circular orbit fails to take place. Is this correct? My second thought is if it is possible to give the rod some initial spin so that the described circular orbit can take place?

I am not sure how much sense this question makes....

Kind regards James

The following thought is confusing me a little. Let say we have sphererical planet with a certain mass and radius fixed in space. Now we have a point particle that at time t0 has a velocity vo that is perpendicular to the vector from the center of the plant to the particle and has a magnitude so that v^2/r=Fgravitational. In this case it seems to me that the only possible behaviour of the particle is to continue in a perfectly circular orbit for eternity(in a mathematical sense).

Now heres the question. Lets say we have a uniform, rod that has one end just above the surface of the planet and whose direction is so that the other end has the maximum distance from the surface of the planet. At time t0 let each part of the rod have velocity perpendicular to the vector from the center of the planet to the rod of magnitude v0r where v0r where r is the distance from the center of the planet to the part of the rod. Let the length of the rod be just so that the total gravitational force on the rod F is equal to the sum of centripetal forces needed for each part of the rod to maintain a circular orbit at its velocity.

Im am now trying to think about the behaviour of this rod, in particular if it will maintain a circular orbit continuing to point radially outward(like in the beginning). My mathematical toolbox is not very sophisticated but here is my attempt. After time dt the center of mass will be where it should for this circular orbit to take place since it behaves as if all the mass and force was concentrated there. The rod will however still point in the same direction after time dt since there is no angular momentum in regards to the center of mass. This means that it no longer points radially outwards and the circular orbit fails to take place. Is this correct? My second thought is if it is possible to give the rod some initial spin so that the described circular orbit can take place?

I am not sure how much sense this question makes....

Kind regards James