which would cause the greatest increase in the acceleration of a satellite?\n a decrease in the radius and…

Explanation:

Step1: Recall centripetal - acceleration formula

The centripetal acceleration formula for a satellite in circular motion is $a = \frac{v^{2}}{r}$, where $a$ is the centripetal acceleration, $v$ is the tangential speed, and $r$ is the radius of the circular path.

Step2: Analyze the effect of changes

• If we decrease $r$ and increase $v$, the numerator $v^{2}$ increases and the denominator $r$ decreases. According to the formula $a=\frac{v^{2}}{r}$, this will cause the greatest increase in the value of $a$.
• If we decrease both $r$ and $v$, the effect on $a$ is not as clear - cut as the numerator decreases and the denominator also decreases.
• If we increase both $r$ and $v$, the numerator increases but the denominator also increases, so the increase in $a$ is not as significant as the case of decreasing $r$ and increasing $v$.
• If we increase $r$ and decrease $v$, the numerator decreases and the denominator increases, resulting in a decrease in $a$.

Answer:

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