Question

1. so if the mass of an orbiting object or center object increases, what could be changed to balance the orbit? (select the 2 that would balance it)

increase distance
decrease distance
increase orbital velocity
decrease orbital velocity

Explanation:

Step1: Recall gravitational - orbital force formula

The centripetal force for an orbiting object is provided by the gravitational force, $F = \frac{GMm}{r^{2}}=m\frac{v^{2}}{r}$, where $G$ is the gravitational constant, $M$ is the mass of the center - object, $m$ is the mass of the orbiting object, $r$ is the distance between them, and $v$ is the orbital velocity.

Step2: Analyze the effect of mass increase on distance

If $M$ or $m$ increases, from $F=\frac{GMm}{r^{2}}$, to keep the force balanced (maintain the orbit), according to the inverse - square law, we can increase the distance $r$. As $r$ increases, the gravitational force $\frac{GMm}{r^{2}}$ decreases.

Step3: Analyze the effect of mass increase on orbital velocity

From $F = m\frac{v^{2}}{r}=\frac{GMm}{r^{2}}$, we can get $v=\sqrt{\frac{GM}{r}}$. If $M$ increases, to balance the orbit, we can increase the orbital velocity $v$.

Answer:

Increase distance, Increase orbital velocity