# Richard Answers a question about zero gravitational acceleration, nanogravity, synthetic acceleration fields

Is there any space with zero gravity in the Universe? by Chinnaraji Annamalai, Indian Institute of Technology Kharagpur
Richard:
The gravitational potential fills all of space. The earth, sun, moon, planets all have their own potential that adds to this. The total potential from all masses in the universe adds to roughly c^2 = (2.99792458E8 meters/second)^2 = 8.98755179E16 Joules/Kilogram.

To get the gravitational acceleration for anywhere on earth, you take the spherical harmonic model for the earth’s gravitational potential and differentiate it. In words, “take the gradient of the gravitational potential”. That gives an acceleration. Check the units and dimensions. The gradient operator itself has units of (1/Meters) or Meters^-1.

[ Grad ] * [ GravitationalPotential ] = [ meter^-1] * [ meter^2/second^2 ]
which yields [meters/second^2] which is acceleration.

The potential around the earth is not constant. It is pretty stable. If you check the International Centre for Global Earth Models (ICGEM) the current temporal models are 2160×2160 and updated once each month. But every moment new updates to the potential are changing the accelerations at the earth.  [ http://icgem.gfz-potsdam.de/home ]
The sun and moon vector tidal signal is stable and easy to measure. It is the signal picked up by the network of superconducting gravimeters. There are better and low cost instruments now. There are MEMS gravimeters that are basically cell phone MEMS accelerometers that have been upgraded to be sensitive enough to track the sun and moon tidal signal.

When things happen on the sun, or as it moves relative to earth the change in the potential diffuses at the speed of light, updates the earth potential which is already here, and the acceleration signal from the sun only matches the earth based detectors, if you allow for the finite speed of the gravitational potential. For frequencies faster than about 40 samples per second, the spatial resolution is smaller than the earth. So if you want to use gravitational signals for imaging something that is 1 km, you need to use gravimeters that can operate faster than (2.99792458E8 meters/second)/(1000 meters) = 299,792.458 SamplesPerSecond about 300 Ksps. It is hard, but not impossible. I am looking at detectors that can work at 100 GigaSamplesPer Second (100 Gsps).

The gravitational field is not difficult to understand but it does require considerable effort. I recommend you decide what you want to do with it, then work hard on that. If you try to look at the whole of it, that will take you decades of very hard work. Learn Python, find the data and models, use the best that you can find, and do not waste time on freshman arguments.

To answer your question. Satellites in orbit, the centrifugal acceleration balances the gravitational acceleration so that orbit is stable, not growing or shrinking. That gives a “microgravity” environment where the average acceleration is zero, but there are still variations at about the “micro-g” level about 9.8E-6 meters/second^2. It is possible to create acceleration fields using acoustic, magnetic and electromagnetic fields to measure and balance the external gravitational potential and its gradients. This is not hard, just requires care and effort, fast sensors and computers.

I follow the micro and nanogravity groups. They want to create nanogravity fields on earth to simulate and benefit from zero accelerations. And they want to make synthetic acceleration fields for people living in orbit, taking long trips to Mars and back, and even ones living in orbit long term around Mars and Moon, even Venus and other places. For the Internet Foundation I put all of those kinds of things into a new field, “gravitational engineering” that gets things done, builds measures and tests.

I encourage you to look at what is going on and try to write it down. Not just talk, but do.
You might want to start with the mass of what you want to hold steady. If you have a kilogram mass on the earth and want to keep it levitated with fields, you have to provide the proper power, energy density, gradients and timings – so you do not damage anything. I am working out the power and field requirements to replace the whole first (“booster”) stage for the SpaceX Starship. Rather than using all the chemical fuel, carefully and powerfully lift and accelerate the second stage to height and velocity it needs to begin its mission. That takes about 36 GigaWatts of power for several minutes. Not impossible even with today’s methods. But I do it to check the planning and collaboration process when people from all countries and backgrounds work with “global open collaborative worksites” on interesting and challenging problems that require complete and precise models and verification.
Best wishes,

Richard Collins, The Internet Foundation