We can work out what it would take to get a 40 minute free-fall orbit by applying Kepler's third law to the ISS:

The ISS orbits in 90 minutes, at a radius of around 6700km from the center of the Earth

According to Kepler, the square of the orbital period (P2) of an object is directly proportional to the cube of the semi-major axis of its orbit (a3).

For a circular orbit, a is equal to the orbital radius.

To get a free-fall orbit of 40 minutes, the ratio of the periods is 40/90=44%

And the ratio of the orbital radii is 58%, or 3800km, which is well inside the Earth's 6400km radius.

Don't worry about air resistance - Puck would need to be a very fast mole!

However, Kepler's laws assume that planetary bodies are geometrical points, and his laws are invalid if you go subterranean.

You would need to compress the entire Earth a lot denser than its current 5.5g/cm2 to achieve a 40 minute free-fall orbit - and that will take a lot of kW!

I stand totally corrected. Please ignore this fossil's poor excuse for very rusty back of envelope math.

I put pen to paper to solve for a 40 minute orbit and I wasn't even close as your calculation showed. Using Orbit r = The "3rd root of GMP²/4π²", Where G is the gravitational constant, M is the Mass of Earth, and P is the orbital period in seconds, I too got a radius of 3,873.441 Km.

With the Earth radius at 6,371 Km, I think you were being extra kind to me to suggest a very fast mole Puck could do it.

My math is obviously in need of some practice.

Thank you for pointing out my totally misleading first answer.

Now how much energy would it take to compress the Earth to inside that radius? I wouldn't even know where to start for that calculation.

Now your brute force suggestion, 4.2g for 40 minutes I believe is quite achievable for Puck.

Bugger the energy requirements. That's for the engineers to figure out.