Orbit around a square planet.

A thousand years from now, we have interstellar spacecraft, a team finds an artifact the size of a planet but cube-shaped, 15,000 Km across one face and it masses the same as the earth, 6 E24 Kg.
There is no atmosphere. What is the lowest orbit you can safely acheive around such an object? It is homogenous density wise. What is the shape of the orbit?

It's the BORG! Run away!

The 15k Km face? Is that just its lengths or from corner to corner diagonally?

Originally posted by jatrius
The 15k Km face? Is that just its lengths or from corner to corner diagonally?

Each square side is 15,000 Km, about the size of the earth in diameter. So the diagonal would be 15K * Square root of 3 = 25,980 Km and change.

Nobody has tackled this (and I will not either) but I suspect there is no stable orbit.

At enough distance a standard elliptical orbit would do the job (the bigger the orbit the longer it would be OK)

The diameter of the earth in kilometers is actually 12,756😛

Originally posted by sonhouse
A thousand years from now, we have interstellar spacecraft, a team finds an artifact the size of a planet but cube-shaped, 15,000 Km across one face and it masses the same as the earth, 6 E24 Kg.
There is no atmosphere. What is the lowest orbit you can safely acheive around such an object? It is homogenous density wise. What is the shape of the orbit?

This is unsolvable analytically. It can only be solved numerically by using a computer program using some numerical methods. Hence it is a boring puzzle. Not worth even attempting..

Originally posted by howzzat
This is unsolvable analytically. It can only be solved numerically by using a computer program using some numerical methods. Hence it is a boring puzzle. Not worth even attempting..

Shyaddup... 😠

Originally posted by sonhouse
A thousand years from now, we have interstellar spacecraft, a team finds an artifact the size of a planet but cube-shaped, 15,000 Km across one face and it masses the same as the earth, 6 E24 Kg.
There is no atmosphere. What is the lowest orbit you can safely acheive around such an object? It is homogenous density wise. What is the shape of the orbit?

the lowest orbit is just above zero 🙂 , or h_lowest = sqrt( 7500^2 + 7500^2 ) = 10 607km from the center of the cube, and the shape of the orbit is a superellipse I believe.

If you put your pencil down and traced the outside of this shape it would look like this....


\ /
.|
/ \

except the corners would be rounded (sorry best I could do for a drawing on here

Originally posted by sonhouse
Each square side is 15,000 Km, about the size of the earth in diameter. So the diagonal would be 15K * Square root of 3 = 25,980 Km and change.

If I'm following along, this would make this 'artifact' less dense than the earth, no?

Originally posted by nakazanie
It's the BORG! Run away!

And to think, I thought I was clever for being about to make that post until I read yours. Talk about your all time backfires.

Originally posted by Suzianne
If I'm following along, this would make this 'artifact' less dense than the earth, no?

There's no way to determine that from the information given.

Originally posted by AThousandYoung
There's no way to determine that from the information given.

We know the mass of the cube and can work out the volume and therefore the density. And can compare that to the Earth.

Thats if you can be bothered .. I can't!

Originally posted by wolfgang59
We know the mass of the cube and can work out the volume and therefore the density. And can compare that to the Earth.

Thats if you can be bothered .. I can't!

Oh, sorry, didn't notice that the mass was given.