Interplanetary Portals vs Gravity

[Malapine]

For story purposes, I want a portal from the Earth to a sealed cave on the Moon. But how would gravity behave near such a portal?

A test mass on the moon end feels 1.6m/s^2 acceleration towards the center of the Moon, a test mass on the Earth end feels 9.8m/s^2 acceleration towards the center of the Earth. Does that mean objects on the Moon side of the portal would feel an additional acceleration of 8.2 m/s towards the portal and be flung out the Earth side at high velocity? Would Earthlings have to be running at some fraction of escape velocity to go thru the portal in the other direction? Will tidal forces rip their limbs off if the portal has little or no interior length?

[ Meta question: how to handwave it so it doesn't do anything like that, and people can hop back and forth with only mild disorientation? ]

 

[Bandersnatch]

The difference in gravity is not great, so whatever effects you come up with should not be much different than a sudden change in perceived weight. From less than what humans are used to to what humans are used to - not a whole lot to worry about. Maybe some vertigo as the inner ear tries to adjust.
As long as the portal is oriented upright, parallel to the vectors of gravitational forces, I don't see any reason for gravity to suck anyone in. Maybe if you placed the portal horizontally, leaning over it would suddenly expose you to the excess gravity and you could topple and fall in (assuming going from the Moon to Earth). But again, not that much of a difference and nothing a human body can't handle.
Of course, you could just say no gravitational interaction passes through the portal because 'that's how portals are'.

 

[Grelbr42]

Portals are difficult to get right.

First you need to decide if they are going to conserve energy. Consider a simple thing like a portal with one end at the bottom of a large body of water like a lake. And the other end is at the top of a hill. If the water pressure can "go around" the change in altitude, then it can act as a very high pressure pump. Say the portal was 10.6 meters under water, you get 1 atm of pressure for "free." That will pump a huge amount of water.

So if the portal does not conserve energy, you get some very interesting things. You can use it as a fairly large source of energy, for example.

If it does conserve energy, you get some different interesting things. Somehow, the portal has to "know" what the relative change in gravitational potential is outside and inside, and find a way to equalize. That will mean there must be some interesting forces acting down the portal on the things going through.

Alternatively, sending something through the portal might conserve energy by exerting forces on the portal itself. This is sort of like https://en.wikipedia.org/wiki/Lenz's_law Lenz's law modified for portals. So maybe the objects going through the portal don't feel strange forces, but the portal gets squeezed or stretched or something so that energy is conserved.

 

[Malapine]

If the portal does conserve energy, then shoving an object of mass m "uphill" from an energy-conserving Earth portal to a Moon portal would require:

(GmM🜨/R🜨) - (GmM☽︎/R☽︎)

Or about 6×10^7 J/kg, presumably supplied using some sort of hydraulic jack over an extended period of time.

Dropping an object "downhill" from an energy-conserving Moon portal to the Earth portal would abruptly give it 6×10^7 J/kg of kinetic energy, flinging it out the portal at 10.9 km/s to burn up like a meteor. Random dust from the cave would become lethal hypervelocity projectiles.

Conclusion: the portal had better not conserve energy if I want people making day trips to the Mall of the Moon.

 

[snorkack]

Compare the other way to get to Moon by tinkering with gravity in a way that obviously (although the story understandably does not point it out) does not conserve energy.
Cavorite. A material which simply blocks gravity - without experiencing it.
It contains copper, and it forms in its effective form when the prepared cavorite cools to near room temperature - after preparation and thermal handling which is not disclosed. Well, high temperature superconductors contain copper and take effect on cooling after thermal handling. They were discovered in 1986. There was no reason someone could not have stumbled on high temperature superconductors in 1886, just nobody stumbled on the correct composition and thermal history. Cavorite might be real, we just have not stumbled on it.
In the story, the first time a sheet of cavorite was formed in the experiment, it blew up the house the experiment was carried out in... because the whole column of air above the sheet lost weight.
This was a mistake. The whole column should not have lost weight. It should only have happened if the whole mass of Earth were concentrated in the centre, with rest of Earth of low density.
Since the mass of Earth is widely distributed inside, the parcel of air immediately above a horizontal sheet would lose all weight... but the air higher above sheet should be attracted by Earth except the fraction shaded by the sheet - increasingly smaller fraction higher above the sheet.

If you place a sheet of cavorite in a vertical direction then air directly above the sheet experiences full Earth gravity because it sees the sheet edge on, with no part of Earth shaded. Air anywhere below the sheet would experience full Earth gravity because the sheet would shade heaven, no part of Earth.
But air beside and diagonally above the sheet...
Note that the reasoning for cavorite also applies to a portal into a small gravity.
You can always divide local gravity into a vector sum of components, chosen as you please. For example, if you are entering the portal, the gravity of one half of Earth will not be 4,9 m/s² vertically down. It will be a bit more than that. And at some angle from vertical (Specific size and angle depends on actual mass distribution inside Earth. It would be vertically 4,9 m/s² if Earth mass were in the centre). The gravity of one half of Moon would also be bigger than 0,8 m/s², and also at an angle from vertical... different angle because of different internal mass distribution.
In the net, you would experience a force pulling you back towards Earth. But this would not be a force "ripping apart limbs" - it would be a force some fraction of Earth gravity. And it would change gradually, as the angular size of Earth and Moon seen through the portal changes.