#### Answer

The gravitational force on the 1.0-kg sphere is 8.94 N

#### Work Step by Step

If the 1.0-kg sphere is 300 km above the earth's surface, then the distance from the earth's center is 6380 km + 300 km which is 6680 km.
We can find the gravitational force on the 1.0-kg sphere. Let $M_e$ be the mass of the earth. Let $M_s$ be the mass of the sphere.
$F = \frac{G~M_e~M_s}{R^2}$
$F = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(5.98\times 10^{24}~kg)(1.0~kg)}{(6.68\times 10^6~m)^2}$
$F = 8.94~N$
The gravitational force on the 1.0-kg sphere is 8.94 N.