EXERCISE 4.4 An astronaut lands on Ganymede , a giant moon of Jupiter that is larger than the planet Mercury, Gany. mede has one-fortieth the mass of Earth and two-fifths the radius. Find the weight of the astronaut standing on Gany. mede in terms of his Earth weight u_(E) ANSWER w_(G)=(5/32)w_(E)

To find the weight of the astronaut on Ganymede in terms of his Earth weight, we need to use the relationship between weight, mass, and gravitational acceleration.1. **Weight on Earth**: 2. **Weight on Ganymede**: Where:- is the mass of the astronaut.- is the gravitational acceleration on Earth.- is the gravitational acceleration on Ganymede.Given:- Ganymede has one-fortieth the mass of Earth ( ).- Ganymede has two-fifths the radius of Earth ( ).The gravitational acceleration on a planet is given by: Therefore, the gravitational acceleration on Ganymede ( ) can be expressed as: Since the weight is the product of mass and gravitational acceleration: And since the mass is the same on both Earth and Ganymede, we can relate it to the Earth weight: Thus: Therefore, the weight of the astronaut standing on Ganymede in terms of his Earth weight is: