# What is the shape of a gravitation field for a square or cubed mass (say, size of a planet)?

most gravitation models assume a round object as most large masses in space (planets) are more or less round. It is simple to envision that it gravitation pull is also [nicely spherical and diminishes according the law of gravitation force calculations.

However, if a planet were square or a cube or flat bar shaped, what would its gravitational effect be? you would assume a stronger gravitational pull at it corners or points would be greater but does the overall gravitation 'pull' eventually become equal in all directions to the extend of effective range (i.e before the gravitational pull goes to 0) or does the gravitational field remain in a shape similar to that of the source mass?

• Without access to large quantities of unobtanium, it is approximately the field of a sphere which is after all the shape that the mass will assume after all the re-arrangement and flow finishes. – dmckee --- ex-moderator kitten Jan 29 '15 at 23:42
• – Cosmas Zachos Apr 12 '17 at 19:22

Far enough away from the source you will see the same field as would be seen if the source were perfectly spherical with mass equal to the actual mass of the source.

This may be derived from the multipole expansion for gravitation, which is straightforward enough in the Newtonian case (see wikipedia: http://en.wikipedia.org/wiki/Gravitational_potential#Multipole_expansion). I think there also exists a multipole expansion in the general relativistic treatment as well although, needless to say, things are not quite so straightforward there!

If you think about it, a cubic planet is made of millions, billions, or trillions of smaller cubes. Each of these applies a unit gravitational force on an object that is in orbit around it. That object would have a bumpy orbit if it orbited very close to a cubic planet, but if it was far away, it would have a fairly smooth orbit, as the average summation of forces would be fairly uniform.

Planets greater in diameter than about 500 km tend to have "material flows" that make them spherical. That is their summation of downward gravitational forces is greater than the individual particles resistance to lateral or angular movement.

The particles move from locations of Higher potential energy to places of lower potential energy. That is " downhill ".

This does not mean process is smooth or complete. That is why NASA made GRACE, the two satellites that chased each other around the earth, constantly measuring the distance between them as each accelerated and decelerated a tiny amount in sequence.

In reality they were really measuring the tiny variations in the surface gravity of the Earth at various locations.

If GRACE was orbiting a cubic planet, there would be a lot of variation in the surface gravity.