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Is it possible with current technologies to propel a cubesat, which is launched from Earth, to the moon?

If current propulsion systems are able to do so, how do I continue the research in this topic and what calculations do I have to do to to continue?

Very Possible

Cubesats are small - typically the base cube is 10 cm square and under 1.5kg and larger cubesats can be made of combinations of this base size. Much larger spacecraft have been sent to the moon, and I imagine there are any number of possible launchers and propulsion systems to allow this. In fact, multiple groups are currently working on it:

• ESA Contest


• Vermont Technical College


• JPL

Cubesats have already been to Mars, as part of the InSight lander mission.

Self Propelled

It's not clear from your question if you are asking about a self propelled cubesat, possibly starting at LEO? If so, check this recent paper out. A lot of the necessary equations are explained within. The concept of cubesats with significant propulsion capabilities is newer, but presumably one could add modules containing enough fuel for a cubesat to get itself to the moon.

What Do You Need To Study?

Maybe start with the vis viva equation and the rocket equation and their respective formulations. This is a decent primer on orbital mechanics if you are starting completely from scratch.

Yes, but it has not been done yet.

NASA is currently sending three CubeSat missions I know of to the moon on EM-1 sometime in 2020 (according to current estimates of the SLS timeline). I believe they are all 6U spacecraft.
http://exploredeepspace.com/news/the-cubesats-of-slss-em-1/

The three missions are:

• LunaH: http://lunahmap.asu.edu/
  


• Lunar: IceCube https://en.wikipedia.org/wiki/Lunar_IceCube
  


• SkyFire: https://en.wikipedia.org/wiki/SkyFire_(spacecraft)
  

All three will use solar-electric propulsion to change orbits. Only LunaH and Lunar IceCube will actually establish orbits around the moon though.

Further study of orbital mechanics will help in evaluating the trade-offs between the delta-v provided by the launch vehicle, solar power systems, and low thrust trajectory optimization.

Let's look at some possible examples, building on @ben's answer and @ Knudsen's answer.

We know that the MarCo cubesats were able to navigate from Earth to Mars, with

• attitude control via reaction wheels and cold gas thrusters


• science data and image collection


• communication directly with Earth via a unique pop-up flat high gain antenna


• 70W of solar power at 1 AU via two deployable solar panels plus battery storage


• standard 6U form factor

for more see this answer and links therein.

So let's adopt the MarCo design. They didn't provide their own propulsion, so let's add a propulsion system directly to MarCo's 6U, 14kg initial configuration, and call it 10U and 22 kg. The extra 4U volume is mostly for engines and extra propellant, the extra 8 kg mass budget is for engines and additional solar panels for more electric power, especially out near Mars and a whole bunch more propellant!

Looking for at least apparently existing cubesat electric propulsion systems that you could put in a 3U cubesat today (or soon), the first one that came up in my search is the IFM Nano Thruster for CubeSats. I am sure thee are other options out there, let's just use this as an example. According to that page:

Dynamic thrust range        10 μN to 0.5 mN

Nominal thrust              350 μN

Specific impulse            2,000 to 5000 s

Propellant mass             250 g

Total impulse               more than 5,000 Ns

Power at nominal thrust     35 W incl. neutralizer

Our cubesat will have enough electric power for two engines at 1 AU, since we've expanded the form factor by 4 U and mass budget by 8 kg will allow for larger solar panels.

Our two off-the-shelf engines with 250 g propellant tanks each can provide a total impulse of as much as 10,000 Newton seconds. With an average mass of about 20 kg, that only provides a delta-v of 500 m/s. But how much do we need?

Luckily there's an existing mission that addresses this already! Answers to Going from LEO to lunar using only low-thrust ion propulsion - can it be done? say that the SMART-1 mission has done this already!

According to that article the propulsion system used to provide a trajectory from GTO to the Moon (crash landing) demonstrated a total delta-v of about 3,900 m/s.

Luckily we'd added 8kg to our mass budget, so if we'd added an extra 5 kg of propellant we'd have a total impulse of 100,000 Newton seconds and a delta-v of about 5,000 m/s.

Conclusion:

A back-of-the-envelope calculation starting with a MarCo-like cubesat with demonstrated capability of going from Earth all the way to Mars, augmented from 6U 14 kg to 10U 22 kg with two existing engine designs and another 5 kg of propellant, we can get from GTO to the Moon using solar-electric propulsion.

The extra delta-v allows for maneuvering near the Moon and doing a bit of sight-seeing and selfie-taking.

Alternatively you could use the extra delta-v to boost yourself from LEO to GTO, allowing for a more standard cubesat deployment option as long as the inclination were not too high. That would probably need another few kg of propellant, so it's marginal. Best way to proceed would be to piggy-back on one of the many existing launches to GTO in a similar way to how the MarCo's piggy-backed to the transfer orbit to Mars.

Source: MarCO: Mars Cube One

below: Source: Emily Lakdawalla's Planetary Society blogpost MarCO: CubeSats to Mars!

Found in this answer.

MARCO SPACECRAFT: Engineer Joel Steinkraus stands with both of the Mars Cube One (MarCO) spacecraft at NASA's Jet Propulsion Laboratory. The one on the left is folded up the way it will be stowed on its rocket; the one on the right has its solar panels fully deployed, along with its high-gain antenna on top.

An alternative, future propulsion system with even higher Isp and therefore needing less propellant mass:

• http://neumannspace.com/science/


• https://spacenews.com/more-startups-are-pursuing-cubesats-with-electric-thrusters/


• Will the Neumann drive start testing aboard the ISS some time in 2018?


• Which way will the Neumann drive (on the ISS) point, what will be its maximum possible thrust?

An encouraging video: