For old/obsolete ICs like this, you can sometimes find them on eBay.
Here is one listing from China for the UM66, and another one from France.
Note that there are some unscrupulous semiconductor vendors on eBay so be careful, I would always buy from somewhere like Digikey, Mouser, Farnell, etc if you can (I had a quick look but couldn't see anything particularly suitable)
You could quite easily make a similar circuit using a small micro, a 555 timer or two, using discrete transistors, etc. It depends on your level of knowledge and whether you actually want to design a circuit or simply build an existing one. There are many doorbell circuits/kits out there that do have parts you can find - Velleman make lots of kits, here is a doorbell/tone generator kit that may be of interest.
Atmospheric pressure, or the lack thereof, does affect electronic components. Components in low to near-zero pressure tend to outgas, and while ICs are relatively simple to condition for this, parts like electrolytic capacitors will fail. Hence, components specifically designated for zero-pressure are used instead.
Radiation affects ICs in two ways:
Firstly, semiconductor behavior changes significantly under increased ionizing radiation, such as exists outside the earth's protective atmosphere, and in the highly ionized belts of the stratosphere. Hence, radiation-hardened parts are manufactured specifically for such purposes, and are used in space electronics.
Secondly, under normal operation (on the ground) the thermal output of any IC gets removed from the package by a combination of radiation and by being carried away passively by moving air... In low pressure or vacuum, only radiation of heat works, not passive air-borne cooling, thus changing thermal dissipation calculations for any component.
Thus non-traditional cooling mechanisms and considerably greater distribution of conductive cooling paths are required.
Regarding gas-related precautions for space electronics: Manned space vehicles have sometimes used oxygen enriched environments. This leads to a necessary rethinking of such circuit design elements as PCB spark gaps, which could lead to catastrophe.
Also, non-design sparking, such as due to motor / coil field collapse, metal contacts of switches, or just a loose connection, need to be eliminated entirely - much more critical than for normal earth atmosphere. Silicone-filled contact casings, like the classic oil-filled switches, are worth considering. Similarly, space-safe epoxy potting of practically all exposed metal including PCB traces, is a way to go.
Further, there is the whole thermal operation range to be considered, especially for unmanned craft: From very hot (due to solar exposure without atmospheric protection), to very cold (due to no "atmospheric" heat when facing away from the sun).
This cyclic heating and cooling causes potential metal fatigue, junction stress and fracture such as at solder joints, and loose contacts due to uneven mechanical expansion and contraction between different materials.
Finally, not all semiconductor components are specified for extremely low temperatures. While heat might be an obvious concern, cold is an equally big issue. Some parts are specifically manufactured, and tested, for extreme low temperature operation. For other parts, the component behavior changes need to be taken into design consideration. For instance, the simplest PTC resettable fuse is no longer a trivial circuit element in space electronics.
I hope this has given an insight into just some of the factors around your question. For the rest, a search engine is your best bet.
Best Answer
The RC circuit in the question is not an integrator but, it can behave like one, providing the output level is low enough (compared to the input level) and, this only happens, for continuous signals, when the frequency applied is significantly greater than the low-pass cutoff frequency. Consider the transfer function of the circuit and compare it with an integrator: -
The 3dB point is when the amplitude response is at 0.7071 and this happens when \$\omega_0 = \dfrac{1}{RC}\$.
And now the integrator: -
The difference is that the gain of the integrator at low frequencies continues to rise as frequency drops. That cannot happen with a low-pass RC network and so only the sloping part of the line mimics an integrator as it tends to become close to attenuating at 20 dB per decade.
You could make a case that this happens at twice \$\omega_0\$ or you could be more picky and say it doesn't really get accurately close until 10x \$\omega_0\$. You could be a perfectionist and say 100x or 1000x.
So, what margin of error is acceptable? Do I know? No of course I don't know - there is no theoretical point at which it can be regarded as behaving exactly like an integrator - it just gets closer and closer as frequency rises.
So what is the answer the OP should give in his homework? He should, I believe make a case for 2x, 10x and 100x the frequency and explain what the error is if a sinewave was the signal inputted. Alternatively you could make a case for a square wave being inputted and look how linear the resulting triangle wave will be. It's his call.
BTW it's the same for an RC differentiator - it's not a perfect differentiator.