To determine which planet an object would weigh the most on, we can use the formula for gravitational force, which is given by:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( F \) is the gravitational force (or weight of the object)
- \( G \) is the gravitational constant
- \( m_1 \) is the mass of the planet
- \( m_2 \) is the mass of the object
- \( r \) is the radius of the planet
Since we are told to assume that the planets have similar radii, the weight of an object on each planet is directly proportional to the mass of the planet. Therefore, the planet with the greatest mass will have the greatest gravitational force acting on an object.
From the table you provided:
- Mass of Planet W = \( 6.4 \times 10^{23} \) kg
- Mass of Planet X = \( 3.3 \times 10^{23} \) kg
- Mass of Planet Y = \( 59.7 \times 10^{23} \) kg
- Mass of Planet Z = \( 48.7 \times 10^{23} \) kg
Among these, Planet Y has the largest mass of \( 59.7 \times 10^{23} \) kg.
Thus, an object would weigh the most on Planet Y.