Final answer:
An astronaut landing on Jupiter would fall faster and feel heavier due to Jupiter's stronger gravitational force. Calculations of weight can be done using Newton's Law of Universal Gravitation, showing a significant increase compared to Earth.
Step-by-step explanation:
If an astronaut were to land on Jupiter, which has much more mass than Earth, the effects of gravity would be significantly different. The gravitational force exerted by a planet is a function of its mass and the distance from its center. Since Jupiter's mass is approximately 318 times that of Earth, and assuming we could find a 'solid' surface analogous to Earth's to land on, the astronaut would experience a much stronger gravitational pull, causing her to fall faster and feel much heavier than on Earth. However, it is important to note that Jupiter does not have a true surface; it is a gas giant with a thick atmosphere and increasing density that transitions into liquid and metallic phases.
The force that our astronomer would feel can be calculated using Newton's Law of Universal Gravitation, which states that the force (F) between two masses (m₁ and m₂) is proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers, expressed as F = G(m₁*m₂)/r², where G is the gravitational constant. Due to Jupiter's immense mass, the force exerted on her would be much larger compared to Earth. If she were inside a capsule with a scale, the scale would show her weight as significantly more than her weight on Earth, assuming the scale is designed to withstand and accurately measure such extreme forces.