Question

As a follow-up to the two previous questions

What is the scientific reason for the inclination of earth's rotation axis?

and

How much effort would be required to fix the Earth's rotation?

What would be the energy needed to change Earth current inclination of an amount of 1 degree toward the vertical?

I recall a classic novel by Jules Verne where a group try to make the axis completely perpendicular to the ecliptic plane with a huge canon but discover they are off by many order of magnitudes.

Edit:

I looked at a summaries of Verne novels and found the one I was referring too. In fact there are the same characters than in the "From the Earth to the Moon".

Answer 1

To move the axis of rotation of the earth, you need to change its angular momentum; this in turn means you need to transfer the angular momentum to an object that is not (no longer) attached to the earth.

The "energy" needed for that can literally be anything, since the relationship between angular momentum and energy depends on the moment of inertia (or if you like, the velocity of the cannon ball).

But let's assume we do this by shooting a cannon ball at the surface of the earth, and let's give the cannon an evacuated barrel that reaches to the outer atmosphere, so there is no atmospheric drag (which would cost a lot of energy but it would keep the angular momentum on earth).

Using round numbers:

The mass of the earth is

The radius of earth is:

Moment of inertia of sphere =

Rate of rotation:

, so angular momentum is

We need a 1