Question about gravity at the rotational poles...

[SRH]

Have there ever been any experiments measuring gravity in space above the rotational poles of any celestial body (Earth, Moon, Sun, etc.)?

I don't mean an orbit that passes near the rotational pole, but rather an orbital path that passes through the exact rotational axis?
And not on the surface of the celestial body, but in space - perhaps at the distance where satellites orbit the Earth or greater, however many miles above the surface that is.

The reason I ask is because from what I understand, satellites never orbit in a path that would cross through the axis. The reasons that I have heard are:
1. the data gathered from such an orbital path is relatively less helpful for GPS applications, and
2. there may be "relativistic effects" which make that path more difficult to transverse (whatever that means - it's over my head), and
3. in order to achieve such an orbital path, i would require more energy/fuel, making the satellite launch process much more expensive.

I assume that Newton's gravitational laws still holds in space along the rotational axis (b/c gravity is a function of mass and distance, not orientation with respect to rotation), but I was wondering if there have ever been any experiments to confirm it.

Also, what is meant by relativistic effects?

Thank you.

[ngc3314]

Polar orbits do take more energy to reach from any non-polar launch sites than lower inclinations (since launching with an eastward component starts with that fraction of the Earth's rotational velocity as a head start). Polar orbits are used for:

- remote-sensing and reconnaissance applications where one wants to see every point on the surface at some time. These orbits should then pass close enough to the pole to get a view at whatever desired slant range there is.

- missions which require either having constant sunlight or seeing the surface at the same sun angle on each pass. The Earth's oblateness makes an orbit precess at a rate depending on altitude and inclination - a slightly retrograde orbit (inclination 98 degrees, typically) is this kind of sun-synchronous orbit. These are used for both Earth-sensing and astronomical missions. IRAS and WISE, for example, could survey the entire sky just by pointing outward, and without having to move their solar arrays.

- applications where every point on the surface must have a view of a satellite (or a member of a constellation of them). This applies to the Iridium phone satellites and the GPS systems and its analogs Galileo and GLONASS. Orbital inclinations for them are 86.4 degrees for Iridium, 55 for Iridium since they are fairly high, 64.8 for GLONASS, 56 for Galileo.

So there are orbits that are close to polar (within 3-4 degrees both ways), but I know of none that are exact (and perturbations by the Sun and Moon wouldn't leave such an orbit exactly polar for a long time anyway).

[Van Rijn]

I assume that Newton's gravitational laws still holds in space along the rotational axis (b/c gravity is a function of mass and distance, not orientation with respect to rotation), but I was wondering if there have ever been any experiments to confirm it.

You do have to remember though that the Earth isn't exactly spherical. It's a bit thicker at the equator than the poles, and there are areas of higher density. So the gravity isn't quite what it would be for a uniform sphere, and these variations are sources of perturbations for orbiting satellites. Also the Moon and Sun are significant sources of perturbations as well.

[Jeff Root]

Relativistic effects are the effects which are described by
either special relativity or general relativity. Except in
situations involving extremely high speeds, extremely
strong gravity, or extremely high precision, relativistic
effects are small enough to ignore. GPS measurements
require sufficiently high precision in order to work that
relativistic effects must be taken into account.

Relativistic effects would not make going exactly over the
rotational poles more difficult. But as noted by ngc3314
and Van Rijn, any satellite will very quickly be moved off of
an "exact" polar orbit by perturbations from the Moon, Sun,
and variations in Earth's gravity, plus uneven atmospheric
drag. These are all much larger than the relativistic effects.

There is, of course, no reason to think that gravity would
be any different over the poles from what it is elsewhere.
Rotation of a planet does not figure in the Newtonian
measurement of gravity at all. It is irrelevant unless you
are on the planet and need to take the centrifugal effect
into account when you measure your weight. Centrifugal
effect and greater distance from Earth's center combined
make a person who weighs 200 pounds at either pole
weigh 199 pounds at the equator.

-- Jeff, in Minneapolis

[utesfan100]

Gravity Probe B was not only placed in an orbit traversing the poles of Earth, its intended mission was to test general relativity by measuring the twisting of space-time due to the rotation of the Earth.

http://en.wikipedia.org/wiki/Gravity_Probe_B