Final answer:
The free fall equations for Mars and Jupiter follow Newton's Universal Law of Gravitation. The acceleration due to gravity (g) on each planet's surface can be calculated using the formula g = G*M / R², where G is the gravitational constant, M is the planet's mass, and R is its radius.
Step-by-step explanation:
The equations for free fall near the surface of Mars and Jupiter involve the application of Newton's Universal Law of Gravitation which states the gravitational force (Fgravity) between two masses is given by the product of the universal gravitational constant (G), the mass of the first object (m), and the mass of the second object (M), divided by the square of the distance (r) between their centers.
For an object at the surface of Mars, we assume r to be the radius of Mars (R(Mars)), giving us the equation:
F (gravity) = G*M(Mars)*m / [R(Mars)]²
For an object on the surface of Jupiter, r would similarly be the radius of Jupiter (R(Jupiter)):
F (gravity) = G*M(Jupiter)*m / [R(Jupiter)]²
To find the acceleration due to gravity, we can set Fgravity equal to mg (where g is the acceleration due to gravity) and solve for g. It's important to note that this equation assumes the object is at or near the surface of the planet, so we use the planet's radius for r and not an additional distance above the surface.
This yields the acceleration due to gravity at the surface of Mars as g(Mars) = G*M(Mars) / [R(Mars)]² and at the surface of Jupiter as g(Jupiter) = G*M(Jupiter) / [R(Jupiter)]². Using the values for G, M(Mars), M(Jupiter), R(Mars), and R(Jupiter), these equations can be solved to find the specific values of g on each planet.