SOLVE B AND D

In the distant future, Earth has sent three immense starships on a journey from Sol $($our star$)$ to Sirius, $8\mathrm{.}6$ light years distant. The three ships, named Alpha, Beta, and Gamma, are arranged in a triangle with the line of travel in the plane of that triangle. They use a standard nautical coordinate system. "Ahead" and "Astern" describe the line of travel, with "Ahead" towards Sirius and "Astern" towards Sol. In the plane of the triangle formed by the three ships, to the left of the line of travel $($when facing Ahead$)$ is "Port", and to the right of the line of travel $($when facing Ahead$)$ is "Starboard". The questions below concern a time when the three ships are very far from any massive object $($planet or star$),$ and are cruising in a straight line at constant speed.

Alpha is the largest ship, with a mass of $8\mathrm{.}50$million$$kg$$million$$kg $.$ Beta has a mass of $3\mathrm{.}90$million$$kg$$million$$kg $.$ Gamma, the smallest ship, has a mass of only $1\mathrm{.}00$million$$kg$$million$$kg $.$ Beta is positioned $720\mathrm{.}0$m$$m directly to Port of Alpha. Gamma is positioned $360\mathrm{.}0$m$$m to Port and $650\mathrm{.}0$m$$m Ahead of Alpha.

In the questions below, you are permitted to treat each ship as if it were a sphere. You should begin by making a drawing of the triangle formed by the three ships; let the Ahead direction point towards the top of your paper and let the Starboard direction point towards the right edge of your paper. Give all directions as an angle measured counterclockwise $($CCW$)$ from the Starboard direction; the angle can be between $0$ and $180$ degrees. If the angle must be measured CW from the Starboard direction, give a negative angle.

Part A

Part complete

What is the force on Gamma by Alpha? Give the magnitude of the force in N $($N is read "microNewtons" and designates $1066$ N$).$

Give your answer as an ordered pair, with the magnitude first, followed by a comma, followed by the direction. Give the direction as an angle measured counterclockwise $($CCW$)$ from the Starboard direction; the angle can be between $0$ and $180$ degrees. If the angle must be measured CW from the Starboard direction, give a negative angle.

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magnitude, direction $=$

$1030,-61\mathrm{.}0$

N$,$ degrees CCW from Starboard

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All attempts used; correct answer displayed

Part B

What is the force on Gamma by Beta? Give the magnitude of the force in N$.$

Give your answer as an ordered pair, with the magnitude first, followed by a comma, followed by the direction. Give the direction as an angle measured counterclockwise $($CCW$)$ from the Starboard direction; the angle can be between $0$ and $180$ degrees. If the angle must be measured CW from the Starboard direction, give a negative angle.

View Available Hint$($s$)$for Part B

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magnitude, direction $=$

uuN, degrees CCW from Starboard

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Incorrect; Try Again; $8$ attempts remaining

Part C

Complete previous part$($s$)$

Gravitational Forces on a Space Pod Passing the $"$L Point" Between Alpha and Beta

For the next set of questions, assume that Gamma has left the formation temporarily to do some exploring, and is thus temporarily far away from the formation. For transportation between Alpha and Beta, the star voyagers use small spherical space pods; the mass of a pod, with a solo pilot, is about $1200\mathrm{.}0$kg$$kg $.$ The pods travel on a straight line between Alpha and Beta. A talented pilot can fire a brief rocket burst to leave Alpha, coast across the intervening space, and then fire a second brief rocket burst, for braking, upon arriving at Beta. The pilots of the pods know that there is a special location $429\mathrm{.}245$m$$m from Alpha where the acceleration of a pod is exactly zero $($remember that the rocket motor is off at this location$)$; the pilots call this point the $"$L point".

Part D

When a pod is at the L point, what is the force on the pod $($and its pilot$)$ by Alpha, in N$?$ Also, what is the force on the pod $($and its pilot$)$ by Beta, in N$?$ In each case, give the P$-$S component, with Starboard positive.

Give your answers as an ordered pair, with the force on the pod by Alpha first, followed by a comma, followed by the force on the pod by Beta. Give the P$-$S component of each force, with Starboard positive.

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

force on pod by Alpha, force on pod by Beta $=$

N$,$ N