Mars has a diameter that is only a little more than half that of Earth. Surface gravity on Mars should therefore be a little more than half that of Earth, assuming that Mars and Earth have similar geologies. Calculating relative surface gravity based on diameters, we get:
6779 km / 12742 km = 53% expected surface gravity on Mars relative to Earth
However, gravity on Mars is much less than this. Calculating relative surface gravity based on actual measurements, we get:
3.7 / 9.8 = 38% measured surface gravity on Mars relative to Earth
The official explanation for this discrepancy is that Earth must be made of material that is significantly more dense than Mars. There must be a super-dense core at the center of Earth.
However, this explanation seems contrived, not least because Earth has a surface that is less dense than Mars. Earth has water and hydrocarbons. Earth’s rocky mantel is relatively deficient in iron, while Mars has plenty of iron.
Mars is a dry and barren place
By NASA / USGS (see PIA04304 catalog page) – http://nssdc.gsfc.nasa.gov/photo_gallery/photogallery-mars.html http://nssdc.gsfc.nasa.gov/image/planetary/mars/marsglobe1.jpg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=19400
If planets can develop super-dense cores, it seems that Mars should be at least as likely to develop one as Earth.
Furthermore, there is no evidence for a super-dense core at the center of our planet. Jan Lamprect has long since showed that seismic evidence points towards a hollow Earth, rather than a solid one.
On the other hand, we do have evidence to suggest that Earth is substantially more charged than Mars. There are sparks in the form of lightning bolts going off all over our planet all the time.
We live on a giant capacitor that appears to be fully charged. If the enormous charge carried by our planet is only remotely important in the formation of gravity, we will have an explanation for the discrepancy between Earth and Mars.
There is no need for a super-dense core. What is required is some kind of proof that highly charged matter communicates more gravity than neutral matter.