Ahypothetical spherical planet consists entirely of iron. what is the period of a satellite that orbits this planet just above its surface?

Newton states: F=G*M*m/ r^2, where M= ρ* (4/3)*pi*r^3 is mass of iron planet, r is radius of the planet; 
 the same gravity force F=m*w^2*r is the centripetal force for the orbiting satellite, where angular speed w=2pi/T, T is period; 
 thus F=F; G*M*m/ r^2 = m*w^2*r; or; 
G*(ρ* (4/3)*pi*r^3)/ r^2 = (2pi/T)^2*r; or; 
G*ρ/3 = pi/T^2, hence T= √(3pi/(G*ρ)) = 
= √(3pi/(6.6742E-11 *7860)) =4238.62s = 70h 38’;

an orange fringe at 0°, yellow fringes at ±50° and red fringes farther out.

Explanation:

In the visible spectrum- red to violet, red has the highest wavelength.

The maximum internsity  for diffraction grating is given by,

Sinθ = mλ/d

It is concluded that the angle of diffraction increases with increase in wavelength'λ' .  So, red fringe will be farthest from the center, orange light will be at the center and yellow fringe will be at 50°.

Therefore, The new pattern consists of : an orange fringe at 0°, yellow fringes at ±50° and red fringes farther out.