Final answer:
The mass m can be found from the gravitational field strength formula by rearranging it to m = gr²/G, where g is the gravitational field strength, r is the radius, and G is the gravitational constant.
Step-by-step explanation:
To find the mass m using the gravitational field strength formula g = Gm/r², you need to rearrange the formula to solve for m. The rearranged formula to find m is m = gr²/G.
Here, g is the gravitational field strength, r is the distance to the center of Earth, and G is the gravitational constant, which is 6.674 × 10⁻¹¹ N·m²/kg².
When you cancel the mass m in Newton's equation for weight, F = GmM/r², you get the familiar value of g near Earth's surface.