Final answer:
On a planet with twice Earth's mass and radius, a person's weight would be half what it is on Earth due to the squared relationship between radius and gravitational force.
Step-by-step explanation:
If human beings travel to a planet whose mass and radius are both twice that of the Earth, we need to consider how gravitational force is affected. According to the law of universal gravitation, the force of gravity is directly proportional to the mass of the objects and inversely proportional to the square of the distance between their centers. In this case, if the planet has twice the mass (2M) of Earth and a radius twice as large (2R), the gravitational force (Fgravity) at the surface would be calculated as Fgravity = G*(2M)/(2R)^2. Simplifying, we see that Fgravity = (G*M/R^2)*(1/2), indicating that the gravitational force at the planet’s surface would be half that of Earth’s gravity. Since weight is the product of mass and the gravitational force (weight = mass * gravity), a person’s weight on this new planet would also be half their weight on Earth.