The weight w of an object on or above the surface of a plane

The weight w of an object on or above the surface of a planet varies inversely as the square of the distance d between the object and the center of the planet. If you weigh 120 pounds on the surface of Venus(radius 3800 miles), how much will you weigh 400 miles above the surface of Venus.

Solution

Let w = a/d²  where w is the weight of the object, d is its distance from the center of Venus and a is an arbitrary constant. The radius of Venus is 3800 miles. Thus, when d = 3800 miles, w = 120 lbs so that 120 = a/( 3800)² or, a = 120 * (3800)² . When the object is 400 miles above the surface of Venus, d = 3800 + 400 = 4200 miles. Then, w = a/ (4200)² = 120*(3800)²/ (4200)² = 120 * (19)²/(21)² = 120*361/ 441 = 98.232129252 lbs = 98.23 lbs ( on rounding off to 2 decimal places).