If a light beam is sent tangent across earth would it curve at 9.8 $\rm m/s^2$? Just to see if my understanding of the curvature of light is correct.
 A: Yes it will curve, but not at 9.8 m/s$^2$ as predicted by Newton's theory. Its curvature will be twice that value as predicted by General Relativity.
A: For an observer at the surface of earth, close to the point where the beam is tangent to the surface, the equivalent principle is valid. The measured deflection is the same as it would happen in a rocket in space with an acceleration $g$.
But for an observer very far from earth, the total deflection is $2 \times$ the calculated considering an acceleration of $g$ on the beam.
A: The beam of light would curve under the influence of gravity, because light goes as straight as it can through curved space.  Calculating the exact amount of curvature is relatively complex, given the Einstein equations.
A: Yes the light beam would curve at 9.8 m/s2, as per Newton's theory:
To see why a deflection of light would be expected, consider Figure 2-17, which shows a beam of light entering an accelerating compartment. Successive positions of the compartment are shown at equal time intervals. Because the compartment is accelerating, the distance it moves in each time interval increases with time. The path of the beam of light, as observed from inside the compartment, is therefore a parabola. But according to the equivalence principle, there is no way to distinguish between an accelerating compartment and one with uniform velocity in a uniform gravitational field. We conclude, therefore, that a beam of light will accelerate in a gravitational field as do objects with rest mass. For example, near the surface of Earth light will fall with acceleration 9.8 m/s2.
http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf
