Which would cause the greatest increase in the acceleration of a satellite?

a decrease in the radius and the tangential speedan increase in the radius and the tangential speeda decrease in the radius and an increase in the tangential speedan increase in the radius and a decrease in the tangential speed

The correct answer is

a decrease in the radius and an increase in the tangential speed

In fact, the centripetal acceleration of the satellite is given by:

where v is the tangential speed and r is the radius. We see that the larger the tangential speed, the greater the acceleration, and the smaller the radius, the greater the acceleration. Therefore, we see that we can obtain the greatest increase in acceleration if we increase the tangential speed and we decrease the radius.