Solution:

Given, mass of the satellite, m
Radius of the earth, R
Altitude of the orbit, h = 2R

To find: Minimum energy required to launch the satellite into circular orbit

1. Calculation of potential energy at height h above the earth's surface
The potential energy of the satellite at height h is given by:
U = - GMm / (R + h)
where G is the universal gravitational constant and M is the mass of the earth.

Substituting the values, we get:
U = - GMm / (3R)

2. Calculation of kinetic energy required for circular motion of the satellite
The kinetic energy required for circular motion of the satellite is given by:
K = (1/2) mv^2
where v is the velocity of the satellite.

The velocity of the satellite in circular orbit is given by:
v = (GM / (R + h))^(1/2)

Substituting the value of v, we get:
K = (1/2) m (GM / (R + h))^(1/2)^2
K = (1/2) m GM / (2R)

3. Calculation of total energy required for launching the satellite
The total energy required for launching the satellite into circular orbit is given by:
E = U + K
Substituting the values of U and K, we get:
E = - GMm / (3R) + (1/2) m GM / (2R)
E = - GMm / (6R) + GMm / (4R)
E = GMm / (12R)

4. Calculation of minimum energy required for launching the satellite
The minimum energy required to launch the satellite is when the satellite is launched with zero velocity from the earth's surface. In this case, the potential energy of the satellite is given by:
U = - GMm / R

The total energy required for launching the satellite is given by:
E = U + K
Substituting the values of U and K, we get:
E = - GMm / R + (1/2) m GM / R
E = - GMm / R + GMm / (2R)
E = GMm / (2R)

Comparing the two values of E, we get:
Minimum energy required = (1/2) x Total energy required
Minimum energy required = (1/2) x (GMm / (12R))
Minimum energy required = (5/6) mgR

Hence, the correct answer is option B, 5/6 mgR.