which would cause the greatest increase in the acceleration of a satellite?\no a decrease in the radius and…

Answer:

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

Explanation:

Step1: Recall centripetal - acceleration formula

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

Step2: Analyze the effect of changing $r$ and $v$

• If we decrease $r$ and increase $v$, from the formula $a=\frac{v^{2}}{r}$, the numerator $v^{2}$ gets larger and the denominator $r$ gets smaller. This will cause a significant increase in the value of $a$.
• If we decrease both $r$ and $v$, the decrease in $v^{2}$ in the numerator and the decrease in $r$ in the denominator will have a less - clear combined effect on $a$.
• If we increase both $r$ and $v$, the increase in $v^{2}$ in the numerator and the increase in $r$ in the denominator will also have a less - clear combined effect on $a$.
• If we increase $r$ and decrease $v$, the denominator gets larger and the numerator gets smaller, which will decrease $a$.