In the distant future, Earth has sent three immense starships on a journey from Sol (our star) to Sirius, 8.6 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 a straight line at constant speed. Alpha is the largest ship, with a mass of 7.30 million kg . Beta has a mass of 5.20 million kg . Gamma, the smallest ship, has a mass of only 0.90 million kg . Beta is positioned 900.0 m directly to Port of Alpha. Gamma is positioned 450.0 m to Port and 510.0 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.

In the distant future, Earth has sent three immense starships on a journey from Sol (our star) to Sirius, 8.6 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 a straight line at constant speed. Alpha is the largest ship, with a mass of 7.30 million kg . Beta has a mass of 5.20 million kg . Gamma, the smallest ship, has a mass of only 0.90 million kg . Beta is positioned 900.0 m directly to Port of Alpha. Gamma is positioned 450.0 m to Port and 510.0 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.