How to Use the Universal Gravitation Simulator
 

Mode

• Exploration focuses on the force between two masses, Fg = G·m1·m2 / r².

• Orbit lets you launch an object and watch the path that gravity creates.
   

Theme

• Choose Space for a starfield background, or Dark or Light for a simplified view.
   

Exploration Mode

Sub-mode

• Explore lets you change the variables freely. Lab lets you collect and graph data. Challenge tests your calculations.
   

Variables

• Use the sliders to set m1, m2, and the distance r. The values are shown in scientific notation because real astronomical masses and distances are enormous.

• The Fg readout updates live as you change any variable.
  Mastery tip: Predict before you move a slider. Doubling one mass should double the force. Doubling the distance should cut the force to one fourth. Check both.
   

Display

• Force vectors (Fg) draws the gravitational force on each object. Labels adds the names and values.

• Compare the force on each object, even when one mass is far larger than the other. By Newton's third law, the two forces are always equal in size and opposite in direction.
  Note for teachers: The third-law pair is worth pausing on. Most students expect the larger mass to pull harder on the smaller one than the other way around.
   

Lab Mode

• Choose your Independent variable: m1, m2, or r. The other two stay constant.

• Move the slider for your independent variable and click Record data point after each change. A minimum number of points is needed before the simulator will fit your data.

• Choose Linear or Log–log axes. The force vs. mass graphs are linear. The force vs. r graph is not, so use log–log axes or plot Fg vs 1/r² to linearize it.

• The fit reports the slope, intercept, and R² of your data.

• Enter a Lab label if you want it included in the filename of your exported CSV data file.
  Mastery tip: On log–log axes, the slope of Fg vs. r tells you the power in the relationship. What value should it be for an inverse-square law?
   

Challenge Mode

• Each challenge gives you two of the values and a target force. Your job is to find the third value.

• Enter your answer in scientific notation using the two boxes: the number on the left and the power of ten on the right.

• Click Check answer, and use New Challenge for another problem.
  Mastery tip: Solve the equation for the unknown variable before you plug in any numbers. It keeps the powers of ten much easier to manage.
   

Orbit Mode

Sub-mode

• Standard lets you set up and launch orbits. Kepler Lab lets you collect data to test Kepler's third law.
   

Scenario

• Circular: the object is launched at exactly the speed needed for a circular orbit (v₀/vc = 1.00).

• Elliptical: the object is launched slower than circular speed, so it falls into an elliptical orbit.

• Escape: the object is launched at about √2 times circular speed, fast enough to escape.

• Binary Star: two equal masses orbit their shared center of mass.
   

Masses & Orbit

• Set the two masses, the starting distance r, and the launch speed as a multiple of circular speed (v₀/vc).

• The note under the speed slider tells you what kind of orbit to expect.

• Use Units to switch between Proportional (simplified sim units) and Real (SI) values.

• The Initial State panel shows the starting force, distance, speed, and orbital period. Press Launch to start.
   

Display

• Choose which elements to show: Force vectors (Fg), Velocity vector (v), Orbital trail, Labels, and Center of mass.

• Turn on both vectors for an elliptical orbit. The force always points toward the central mass, but it is only perpendicular to the velocity at the closest and farthest points. That is why the object speeds up and slows down.
  Note for teachers: Binary Star with Center of mass turned on is a nice way to show that both objects orbit a shared point, not one around the other.
   

Kepler Lab

• Vary the launch radius (r₀) and launch speed (v₀/vc) to run different circular and elliptical orbits.

• Press Launch & Measure. The simulator measures the period T and calculates the semi-major axis a.

• Collect at least three orbits, then fit your data. On the T² vs. a³ log–log graph, a slope close to 1 confirms Kepler's third law.

• If a warning says the orbit will leave the canvas, decrease r₀ or increase v₀/vc before launching.