What are the military pros and cons of a low gravity world vs a high gravity one?

Question

I've seen this question raised in several different bits of sci fi media. In games its often that low gravity = lower construction cost or some such. But I've begun to wonder, is it really that cut and dried? Obviously, high gravity has some applications. Defensively, it could make it annoying for enemies to attack you with armored vehicles, due to the additional wear and tear, as well as the enormous cost to retreat an entire army plus gear from the atmosphere.

The base assumption of these games and this question being that if the gravity is not enough to kill you outright, such as a neutron star, or black hole, then long term health effects from switching between planets of different gravities is ignored.

(Realistically, bombardment is one of the most potent ways to open an invasion, however, sci tropes are being adhered to an extent here, meaning that landings are generally necessary.)

Answer 1

Living on a high-gravity world comes with plenty of annoyances:

• Literally everything you build will need to be sturdier to not break down under its own weight.
• Any transportation will require more energy. This especially applies to air travel. But land-based vehicles will also be affected because they will be more affected by friction and the aforementioned problem of requiring a sturdier build to load the same mass.
• You require far more energy to get things into orbit or land them safely.

Regarding defending against a planetary invasion:

A higher gravity world will be more vulnerable to an orbital bombardment with simple kinetic projectiles, because those will reach a far higher impact speed. Also, when a building collapses from bombardment, anyone inside will have a far lower chance to survive.

But if the enemy wants to land, they are facing the same problems you do:

• Landing troops requires more energy. Their landing crafts might even have insufficient thrust-to-weight ratio to land safely.
• Their vehicles and equipment might not be built for operating in a high-gravity environment. They might lose functionality or even get damaged by their own weight.
• They might underestimate how much their mobility suffers from the high gravity, so they run into strategic and logistic problems.
• They might underestimate the additional fatigue suffered by their biological soldiers. The defenders, however, will be used to the high gravity and not tire as easily.
• Any ballistic weapons will have a lower range.
• Because all the buildings on the planet are built much sturdier to withstand gravity, they also offer better protection from weapon fire. Any civilian building might be built like a military-grade bunker, making them easier to defend.

But these are all problems which will only affect attackers who didn't do their homework before invading. They can all be overcome with proper preparation.

Answer 2

Defensively, it could make it annoying for enemies to attack you with armored vehicles.

No. It woud be even more comical easier to fight your enemies in high gravity. In low gravity your enemies may survive a landslide by hiding in a tent. In jovian gravity a paintball falling from a few kilometers up could maybe rip a person right in two.

If you wish to fight someone in high gravity, warfare may become a game of dropping stuff up on your opponents.

That said, the pains of high-gravity are:

• More expensive life support: we know humans handle low gravity, and even microgravity quite well. People are able to live for months in the ISS without any major, long lasting health issues. But we feel sick and can get knocked out by high gravity, as evidenced from simple things like some ******* rollercoasters to more complicated stuff such as jet fighters and rockets (in some cases you need special suits just not to pass out).

• The energy bill: the real issue is that the formula for the potential energy of a gravity field goes like this:

$$ E = Mgh $$

Where M is the mass of a body and h is how high it is from a reference height. The problem is the g, which is the gravity involved.

Let's compare three hypothetical planets, with distinct masses. Let's call them planets A, B anc C. Let A have the mass of Enceladus, B have the mass of Earth and C have the mass of Jupiter.

If you are in a building and wish to take some load to another level that is 10 meters upwards, the energy cost will be different in each. Assuming that the load weights one metric ton, the energy cost for each planet would be:

• Planet A: $ 10^3kg \times 10m \times 0.0113m/s^2 = 113 \space joules $

• Planet B: $ 10^3kg \times 10m \times 9.8m/s^2 = 98,000 \space joules $

• Planet C: $ 10^3kg \times 10m \times 24.79m/s^2 = 247,900 \space joules $

If you have a power supply unit that can only power one elevator in a jovian gravity, the same PSU will be able to power two elevators simultaneously on Earth, or up to 2,193 elevators on Enceladus at the same time.

Conversely, a 10 meters drop in each planet would mean an impact with just as much kinect energy. In planet A you could jump from a hill and land like a feather. In planet B you could jump just like on Earth. On Planet C you risk serious injury and even death if you just trip on the sidewalk.