**The electromagnetic sail as space launcher**

If this electromagnetic sail is possible, I see it as a space launcher. The terrestrial magnetic field extends to several thousands kilometers from ground. It could thus provide a support to an electromagnetic sail until in orbit.

To obtain an effective sail, the material constituting the conducting ring must carry the electric current most intense possible. The best choice for this material is a superconductor. To ensure that this superconductor can be used for an electromagnetic sail, the minimal condition is Laplace force that is applied to it higher than its weight. Following simple calculation shows that two criteria are significant to satisfy this condition: the critical current density that can carry the superconductor and its density.

**Criteria of the superconductor for an electromagnetic sail**

Let a conducting square circuit located at the terrestrial equator. The circuit is orthogonal to the terrestrial magnetic field. The direction of the electric current is such as Laplace forces are directed towards the outside of the circuit. The forces applied to the western and eastern parts of the circuit cancel each other. The low part of the circuit is coated with the magnetic shielding described in my first message and thus does not undergo Laplace force. The high part of the circuit undergoes a Laplace force that is not compensated. What should be this Laplace force to support the weight of the whole circuit?

F = I. B. L

With F: Laplace force applied to the higher part of the circuit,

I: intensity of the electric current,

B: horizontal component of the terrestrial magnetic field,

L: length of the higher part of the circuit.

P = 4. d. v. g

With P: weight of the whole circuit,

d: density of the circuit material,

v: volume of the higher part of the circuit,

g: acceleration of terrestrial gravity.

It is necessary that: F > P

I. B. L > 4. d. v. g

With s: section of the circuit,

j: density of the electric current.

j. s. B. L > 4. d. g. s. L

j. B > 4. d. g

Finally, to obtain a Laplace force higher than the weight, it is necessary that:

j > 4. d. g/B

The current density that the superconductor must carry to be used in an electromagnetic sail depends on its density and the ratio g/B.

First criterion: density of the superconductor

Among all known superconductors, it seems to me that the magnesium diboride shows the most interesting characteristics: a low density of 2.57 g/cm3 and a critical current density of 10000 A/mm2 (3). MgB2 seems to satisfy the minimal condition to constitute an electromagnetic sail. For example, in a horizontal magnetic field of 40 µT, the density of current necessary to ensure that the Laplace force equalizes the weight of a square circuit of MgB2 is 2520 A/mm2, level much lower than the critical current density of material.

To obtain a complete electromagnetic sail, it remains to add the mass of the magnetic shielding and especially the mass of the cooling system because the magnesium diboride becomes superconductive only below 40 K.

Second criterion: the ratio g/B

The Internet site (4) calculates the parameters of the terrestrial magnetic field anywhere on the terrestrial sphere and in altitude. It shows that the horizontal component of the terrestrial magnetic field, the only usable for a space launching, is maximum at the equator.

The acceleration of terrestrial gravity g also varies according to altitude. The following mathematical formula (5) calculates g:

g(h) = g0/(1 + (2h/R) + (h2/R2))

With g0: acceleration of terrestrial gravity to altitude 0,

g(h): acceleration of terrestrial gravity to altitude h,

h: altitude,

R: terrestrial radius.

The following table shows the variation of the magnetic field and terrestrial gravity according to altitude:

[attachment=20637]

The data of this table are shown in the following graph:

[attachment=20639]

These data show that the magnetic field decreases more quickly than the acceleration of terrestrial gravity when altitude increases. The g/B ratio thus increases with altitude. This ratio determines the effectiveness of the electromagnetic sail. The propulsion force of the electromagnetic sail decreases with altitude. As the electric current in the superconductor cannot exceed the critical current, there is a limit altitude beyond that the sail ceases working.

(3) [http://iopscience.iop.org/article/10.1209/epl/i2002-00479-1/meta;jsessionid=E3DÇ22DC2891E013CCDD261AE163683.c1]

(4) [http://www.geomag.bgs.ac.uk/data_service/models_compass/igrf_form.shtml]

(5) [http://e.m.c.2.free.fr/poids-and-gravitation.htm]