Final answer:
The strength of Earth's gravitational field where an 80 kg astronaut experiences an 80% reduction in weight is calculated to be 1.96 m/s². This is found by determining the astronaut's reduced weight using the weight equation W = mg and solving for g.
Step-by-step explanation:
To determine the strength of Earth's gravitational field at a point where an 80.0 kg astronaut would experience an 80% reduction in weight, we first need to understand the concept of gravitational force and the equation for weight. The weight of an object is the gravitational force exerted on it and is calculated by the equation W = mg, where m is the mass and g is the acceleration due to gravity.
If the astronaut has an 80% reduction in weight, they would feel as if they weigh 20% of their Earth weight in this new location. The astronaut's weight on Earth would be 80.0 kg × 9.80 m/s² = 784 N. At the point of interest, the weight would be 20% of this, or 156.8 N. Using the weight equation again, W = mg, we can solve for g as follows:
W = mg
156.8 N = 80.0 kg × g
g = 156.8 N / 80.0 kg
g = 1.96 m/s²
Thus, the strength of Earth's gravitational field at this point would be 1.96 m/s², which is the acceleration due to gravity that would result in the astronaut experiencing a weight that is 80% less than their weight on Earth.