Question

hint: if it will escape orbit, what can you do to increase the gravitational force? if it will crash, what can you do to decrease the gravitational force? then remember, if gravity increases, velocity has to increase. an orbiting spacecraft accidentally engages its engines and moves farther from earth. the orbiting object will crash into the center object. escape the orbit. what could be changed to fix the scenario? (select the 3 that would balance it)

Explanation:

Step1: Recall gravitational - force formula

The gravitational force $F = G\frac{Mm}{r^{2}}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the spacecraft, and $r$ is the distance between the spacecraft and the center of the Earth. As $r$ increases (spacecraft moves farther from Earth), the gravitational force $F$ decreases.

Step2: Analyze orbital - motion conditions

For an object in orbit, the centripetal force is provided by the gravitational force. $F_{c}=F_{g}$. When the gravitational force decreases due to an increase in $r$, the spacecraft will escape the orbit if the centripetal force is no longer sufficient to keep it in orbit.

Step3: Consider ways to fix the scenario

1. Increase mass: Increasing the mass of the spacecraft or the Earth would increase the gravitational force according to $F = G\frac{Mm}{r^{2}}$.
2. Decrease distance: Decreasing $r$ (bringing the spacecraft closer to Earth) would increase the gravitational force.
3. Increase velocity: According to the relationship between gravitational force and orbital velocity $v=\sqrt{\frac{GM}{r}}$, increasing the velocity can help maintain the orbital motion when the gravitational force changes.

Answer:

The orbiting object will escape the orbit.
To fix the scenario: Increase mass, Decrease distance from Earth, Increase velocity.