Gravity Well Lab Handout
Demonstration Lab • Page 1
Gravity Well & Orbital Motion
Name
Date
Period
1. Mass Warps Spacetime: Mass tells space how to curve. A heavier central mass creates a deeper, steeper gravitational well.
2. The Orbital Balance: An orbit occurs when forward velocity (inertia) balances the inward pull of gravity, producing a continuous curve!
A
Part 1 • Mass & Depth of the Well (Curvature)
Observe how the stretchy fabric deforms as different masses are placed in the center. Record observations for each test:
| Central Object |
Well Depth & Slope |
Path of Rolling Test Marble |
| Flat Fabric (No mass) |
Depth: 0 mm |
|
| Small Mass (e.g. Golf ball) |
|
|
| Large Mass (e.g. Steel ball) |
|
|
Side-View: Small Mass Well
Sketch dip curve
Side-View: Heavy Mass Well
Sketch dip curve
B
Part 2 • Launch Speed & Orbital Trajectory
With a heavy central mass in place, test rolling the test marble sideways (tangentially) at different speeds:
| Launch Condition |
Path Shape (Sketch or Describe) |
Observed Outcome |
| 1. Zero Sideways Speed |
|
|
| Dropped straight from rest |
|
|
| 2. Low Sideways Speed |
|
|
| Gentle horizontal push |
|
|
| 3. Moderate Speed (“Orbital”) |
|
|
| Balanced tangential roll |
|
|
| 4. High Speed (“Escape”) |
|
|
| Fast, forceful flick |
|
|
C
Part 3 • Critical Analysis & The Space Connection
1. The Friction Factor: On the fabric well, every marble eventually spirals into the center and crashes. Why has Earth been able to orbit the Sun for 4.5 billion years without spiraling into it?
2. Orbital Speed vs. Distance: What happened to the marble’s speed as it moved closer to the central mass? How does this demonstrate Kepler’s law (why Mercury orbits faster than Neptune)?
Physics Demonstration Lab: Spacetime Curvature & Orbital Motion Page 1 of 2 • Turn over for Gravitation Graphing
Conceptual Physics • Page 2
Understanding the Gravitational Curve
Student: _______________________
The Geometry of Gravity: Why Does It Follow an Inverse-Square Law? \(F_g = G \frac{m_1 m_2}{r^2}\)
1 At Distance \(1r\)
Gravitational pull passes through a single unit of area: Strength = \(100\%\) (\(1.00\))
2 At Double Distance \(2r\)
Gravity spreads across \(2 \times 2 = 4\) times the surface area: Strength = \(\frac{1}{4} = 25\%\)
3 At Triple Distance \(3r\)
Gravity spreads across \(3 \times 3 = 9\) times the surface area: Strength = \(\frac{1}{9} \approx 11\%\)
Conceptual Proportions: How Gravity “Dilutes” Notice how rapidly force drops off early on!
| Orbital Distance (\(r\)) |
Spreading Factor (\(r^2\)) |
Fraction Remaining (\(1/r^2\)) |
Relative Force (\(F_g\)) |
Conceptual Region |
| \(1r\) (Close In) |
\(1^2 = 1\) |
\(1/1 = 1\) |
100% (or 100 N) |
Extreme Gravity Well |
| \(2r\) (Doubled) |
\(2^2 = 4\) |
\(1/4\) |
25% (or 25 N) |
Steep Cliff Transition |
| \(3r\) (Tripled) |
\(3^2 = 9\) |
\(1/9\) |
11.1% (or 11 N) |
Gentle Slope |
| \(4r\) (Quadrupled) |
\(4^2 = 16\) |
\(1/16\) |
6.25% (or 6 N) |
Outer Shallows |
| \(5r\) (Distant) |
\(5^2 = 25\) |
\(1/25\) |
4.0% (or 4 N) |
Flat Cosmic Plateau |
Graphing Task: Plot the Curve & Label the 2 Key Zones • Connect points with a curve • Circle & label Zone A & Zone B
Gravitational Force (\(F_g\)) (% of Surface)
Zone A: Steep Cliff (Drops 75%) Zone B: Flat Cosmic Shallows (Slow Change) 100% 80% 60% 40% 20% 0% 0 1r 2r 3r 4r 5r
Distance Multiplier (\(r\)) from Center of Body
Conceptual Mastery: Decoding the Curve
1. The Linear Fallacy: A classmate says: “If I double my distance from Earth, gravity should drop by half (\(50\%\)).” Looking at your plotted graph, explain why your classmate is wrong and state what actually happens.
2. Connecting Graph to the Fabric Well: Look at Zone A (the cliff from \(1r\) to \(2r\)). How does this steep vertical drop on your graph physically explain why marbles roll so violently fast and spiral tightly near the center of the stretchy fabric?
3. The Asymptote Mystery (Infinite Reach): Does this curve ever reach an absolute zero line (\(F_g = 0\)), even at \(100r\) or \(1{,}000r\)? What does this reveal about whether an object can ever truly escape the gravity of a star or planet?
Physics Lab: Universal Gravitation • Inverse Square Law Conceptual Analysis Page 2 of 2 • Complete
Gravity Well Slides
Physics Investigation • Gravity & Motion
Gravity Wells & Orbital Motion
How mass curves space, and how forward speed keeps planets in orbit.
Key Science Vocabulary
Mass How much matter is inside an object.
Inertia Moving forward in a straight line.
Orbit A repeating curved path in space.
Part 1 • Fabric Demonstration
Mass Bends the Fabric of Space
Curvature = A Bend or Dip
1
Flat Fabric (No Mass)
A rolled marble moves in a straight line at a steady speed.
Physics Reason: Forward inertia keeps it straight.
2
Curved Fabric (Heavy Mass)
A heavy mass creates a deep dip. Straight paths bend toward the center!
Physics Reason: Mass bends space; space curves motion.
Discussion Stem: “When we add a heavier central mass, the fabric dip becomes deeper, which makes the marble curve more sharply.”
Part 2 • Launch Speed
What is an Orbit? A Balance of Two Forces
Forward Speed vs. Inward Pull
An orbit is not floating without gravity. An orbit is falling toward the star while moving sideways fast enough to keep missing it!
1. No Sideways Speed
Direct Fall
Gravity pulls straight inward. The marble drops and crashes into the center.
2. Balanced Speed
Stable Orbit
Forward motion balances inward pull. The marble circles in a repeating curve.
3. Very High Speed
Escape
Forward motion is too strong for the dip. The marble flies out of the well.
Sentence Stem: “To stay in orbit, a planet needs enough sideways speed so it doesn’t fall into the star.”
Part 3 • Reading the Graph
How Gravity Drops With Distance (\(F_g \propto 1/r^2\))
Inverse = Opposite Rule
Rule: As distance grows, gravity drops rapidly!
\(1r = 100\%\) \(2r = 25\%\) (\(\frac{1}{4}\)) \(3r = 11\%\) (\(\frac{1}{9}\))
Zone A • The Steep Cliff (\(1r\) to \(2r\))
Gravity drops by 75% when you double distance!
Example: Mercury orbits very fast because gravity is intense near the Sun.
Zone B • The Cosmic Shallows (\(3r\) to \(5r\))
Gravity becomes weak and flattens out (drops below 5%).
Example: Neptune feels weak gravity and orbits slowly for 165 years.
Graph Sentence Stem: “When distance doubles from \(1r\) to \(2r\), the gravitational force drops from \(100\%\) down to \(25\%\).”
Part 4 • Big Question
Why Doesn’t Earth Crash into the Sun?
Model vs. Space
Fabric Gravity Well
- • Has friction (rubbing against fabric).
- • Loses speed \(\rightarrow\) spirals into center and stops.
Real Outer Space
- • Space is a vacuum (empty space, no air).
- • No friction \(\rightarrow\) planets orbit for billions of years!
Summary Stem: “Marbles crash on the fabric because of friction, but Earth keeps orbiting because space has no air resistance.”
