Galaxy Mission

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B) Luma Rotational Rate: A spinning Luma makes exactly 180 complete rotations per minute. How many times will it rotate in 4.5 minutes? (Show your multi-digit multiplication below)

Answer: _________ rotations

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Puzzle 4: Grand Star Slicing Geometry

Calculate spatial coordinates and intersection angles in Mario's orbit maps.

The Scenario: Launch Star beams form geometrical shapes and intersecting vectors. Calculate the missing navigational angles for Rosalina below.

A) Supplementary Star-Beams Two orbital trajectory beams meet on a straight trajectory plane (representing 180 degrees). If Sector Beam A measures 115 degrees, what is Sector Beam B?

Beam B = ______ °

B) Complementary Launch Coordinates Rosalina's compass makes a perfect right-angle (90 degrees) to calibrate a Grand Star launch. If the local angle is 62 degrees, what is the remaining angle?

Remaining Angle = ______ °

Comet Observatory STEM Challenge Booklet Post-Viewing Math Practice Page 2 of 2

Viewing Guide & Math Solutions

Reference SOLUTIONS ONLY

Galaxy Viewing Guide Sample Answers

Q1 (Gravity Mechanics): Gravity is an attractive force pulling towards the planetoid's center of mass. Because the mass is located at the center, the pull is uniform in all directions, allowing Mario to walk upside down relative to space, but right-side up relative to the ground.

Q2 (Powering the Hub): Grand Stars represent concentrated central energy grids. This mirrors real-world reactors or solar arrays on space stations (like the ISS) that capture, convert, and distribute energy to oxygen, thermal, and navigational systems.

Q3 (Launch Stars): Launch Stars act like particle accelerators or mechanical catapults. They apply a massive forward force over a split second, giving Mario the high velocity and momentum needed to break a planetoid's gravitational escape velocity.

Q4 (Black Holes): A black hole has an incredibly dense concentration of mass, creating a gravity well so intense that nothing can escape it. Objects falling past the event horizon are compressed and pulled to the singularity.

Q5 (Energy Conservation): The Lumas' sacrifice demonstrates energy transformation. When the reactor imploded into a universe-threatening black hole, the Lumas offset the gravitational singularity by combining their thermal and physical star energy, initiating a supernova cycle that rebirthed the galaxy.

Galaxy Math Challenge Solutions

Puzzle 1: Star Bits (Scaling/Multiplication)

• A) Total Star Bits needed:
  \( 1,800\text{g} \times 3.5 = 6,300\text{ Star Bits} \).
• B) Inventory Leftover:
  Mario starts with 6,500.
  \( 6,500 - 6,300 = 200\text{ Star Bits left} \).

Puzzle 2: Navigation Codes (PEMDAS)

• Alpha: \( (20) \times 4 - 22 = 80 - 22 = 58 \)
• Beta: \( 60 - 9 \times 3 = 60 - 27 = 33 \)
• Gamma: \( (4) \times (7) + 4 = 28 + 4 = 32 \)
• Delta: \( 12 + 24 - 15 = 36 - 15 = 21 \)

Puzzle 3: Trajectory Speed & Rotation

• A) Trajectory Distance:
  \( 16.5\text; m/s} \times 50\text{ seconds} = 825\text{ meters} \).
• B) Luma Rotations:
  \( 180\text{ rotations/min} \times 4.5\text{ mins} = 810\text{ rotations} \).

Puzzle 4: Star Geometries (Angles)

• A) Supplementary Angle:
  Straight line is \( 180^\circ \).
  \( 180^\circ - 115^\circ = 65^\circ \). Beam B is \( 65^\circ \).
• B) Complementary Angle:
  Right angle is \( 90^\circ \).
  \( 90^\circ - 62^\circ = 28^\circ \). Remaining angle is \( 28^\circ \).

Galaxy Mission • Space Science Movie Unit Official Answer Keys & Solutions Page 2 of 2