Question

Rank in order from largest to smallest, the free-fall accelerations on the surfaces of the following planets

Answer 1

Ranking the free-fall accelerations on the surfaces of the planets from largest to smallest: Jupiter > Earth > Mars > Mercury.

Step-by-step explanation:

The acceleration due to gravity (g) on a planet's surface is determined by its mass and radius. Newton's law of gravitation provides the formula
`\(g = (GM)/(R^2)\)`, where (G) is the gravitational constant, (M) is the mass of the planet, and (R) is its radius.

Starting with Jupiter, it has the largest mass among the listed planets, resulting in the highest gravitational acceleration. Earth follows with a smaller mass than Jupiter but larger than Mars and Mercury, placing it second. Mars has a smaller mass than Earth, and Mercury, being the smallest planet, has the least mass and, consequently, the smallest gravitational acceleration.

Calculating exact values involves specific constants and measurements for each planet. However, for a conceptual understanding, this qualitative ranking is based on the relationship between mass and gravitational acceleration.

In summary, the order of free-fall accelerations from largest to smallest is determined by the mass and size of each planet, as described by Newton's law of gravitation.