Final answer:
The astronaut's weight on Earth is adjusted for the new planet's mass and diameter, resulting in a calculated apparent weight, which needs to be reconciled with the actual gravitational conditions on the new planet.
Step-by-step explanation:
An astronaut weighs 788 N on Earth and wants to find their weight on a newly discovered planet with 1/7 of Earth's mass and 1/6 of Earth's diameter. The astronaut's weight on this planet can be calculated using Newton's law of universal gravitation, which states that weight is proportional to the mass of the object (in this case, the planet) and inversely proportional to the square of the distance from the center of the mass (the planet's radius).
To calculate the astronaut's weight on the new planet, we need to adjust the weight according to the changes in mass and distance (radius). Since the mass is 1/7th of Earth's, and the weight is proportional to the mass, we start by multiplying the weight by 1/7. However, as the planet's diameter is 1/6th of Earth's, the radius is also 1/6th, and the weight is inversely proportional to the square of the radius, we need to then multiply by (6/1)2 or 36 to account for the change in radius.
Weight on new planet = 788 N * (1/7) * (62) = 788 N * (1/7) * 36 = 112.8 N * 36 = 4056.8 N (This would be the apparent weight if the gravity on the planet was similar to Earth's, but since the question states that gravity would vary according the planet's mass and diameter, the calculation for the actual weight must take into account the new gravitational field strength.)