In both situations, the scale would read very close to Bob’s weight on Earth as 784 N.
The weight of an object is determined by the force of gravity acting on it. The force of gravity on Earth is approximately 9.8 m/s². Therefore, if Bob weighs 80 kg, his weight on Earth would be:
80 kg * 9.8 m/s² = 784 N
However, in the given scenarios, we also need to consider the gravitational forces of the Sun and the Moon. The gravitational pull of the Sun on Earth is only 0.0006 of the strength of the Earth’s gravity. The gravitational acceleration on the Moon’s surface is approximately 1.625 m/s², about 16.6% that on Earth’s surface.
In Situation A, where the Sun, Earth, and Moon are aligned, the gravitational forces of the Sun and the Moon would add up, slightly increasing the weight reading on the scale.
In Situation B, where the Sun, Earth, and Moon form a triangle, the gravitational forces of the Sun and the Moon would partially cancel each other out, slightly decreasing the weight reading on the scale.
However, these changes would be extremely small and likely not noticeable on a standard scale due to the vast distances between the Earth, Sun, and Moon. The dominant force acting on Bob would still be the Earth’s gravity.
Therefore, in both situations, the scale would read very close to Bob’s weight on Earth, which is approximately 784 N.