@WilliamOliver Exactly. Potential energy is (simply said) a form of energy which is defined as the position in a force-field. So it is clear that the force which acts on the particle must be equal to its potential energy.
@WilliamOliver so according to this example: the quicker I would lift the object upwards, the stronger the gravitational field (F) would react downwards?
Essentially Force and potential energy are related by definition, you could say that what you feel when you hold a heavy object in one place is force, and the "pain" that you feel when you hold the weight is the potential energy. Its the thing in your arm that says "please drop this thing now".
@Slereah not yet. If guys like werner von Braun were more active nowadays we d have better technologies. That dude spoke about conquering Mars in the eighties...
@yuggib Let $F:\Omega\times [0,\tau]\to\Bbb R$ be smooth, where $\Omega\subset\Bbb R^n$ is open. Suppose $\partial_t F\le\Delta F+C\tau^{-2}$ on $(0,\tau]$, where $C>0$ is a constant. Why does the maximum principle imply $\sup_\Omega F(\cdot, t)\le C\tau^{-2}t$?
@0celo7 didn t know they weren t working well. Source? @Slereah we have berely sent ppl beyond mars. Let s first make sure this works well before going interstellar and so on. Most of the satellites use solar panels in combination with batteries
well we r making babysteps, ppl now use solar panels and batteries. We re now waiting on either Elon Musk to find an incredible alternative or some random dude at a university writing a paper about some hypotetical solution that can eventually work.
@0celo7 not sure about that. Depends on what you use. If you use reaction wheels or magnetorquers (which are inside the spacecraft) I think chances that those break are much smaller
