Companion to the reading passage Newton's Cannonball: The Thought Experiment That Explained Orbits. Answer each question, then click Check. Multiple-choice and number questions grade themselves; for written answers, compare yours with the model answer and checklist, then score yourself honestly.
Isaac Newton imagined a cannon on top of a mountain so tall that its peak is above the atmosphere. In Model 1, Earth is drawn as a large circle with the mountain at the top. Five cannonballs, A through E, are fired horizontally from the peak, each with a greater launch speed than the one before. Paths A and B curve down and strike Earth, B landing farther away than A. Path C is a circle around Earth that returns to the peak. Path D is a larger ellipse. Path E curves away and never returns. Air resistance is ignored.
Model 1: Newton’s Mountain
Sketch of Model 1 (not to scale). C is a circle through the peak; D is a larger ellipse through the peak; E never returns.
1. Which statement best describes the force acting on cannonball C as it travels along its circular path?
2. Identify one way that Model 1 differs from the way a real rocket places a satellite into orbit, and state why the model is still useful.
Today, rockets do the job of Newton’s cannon. Table 1 lists data for two objects orbiting Earth in the same circular orbit at an altitude of 4.0 × 105 m. The orbital radius, measured from Earth’s center, is 6.77 × 106 m. The mass of Earth is 5.97 × 1024 kg.
Table 1: Two Objects in the Same Orbit
| Object | Mass (kg) | Orbital radius (m) |
|---|---|---|
| International Space Station (ISS) | 4.20 × 105 | 6.77 × 106 |
| Small CubeSat | 1.3 | 6.77 × 106 |
3. Which row correctly compares the ISS with the CubeSat? (Columns: orbital speed / magnitude of gravitational force from Earth.)
4. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the gravitational force of Earth on the ISS. Then calculate the force.
Astronauts on the ISS float inside the station, and many people believe there is no gravity in orbit. At Earth’s surface, Earth’s gravitational field strength is 9.81 N/kg, and Earth’s radius is 6.37 × 106 m.
5. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
Students modeled cannonball A from Model 1 near Earth’s surface. Air resistance is ignored, and the ground is the zero level for gravitational potential energy. At the instant cannonball A leaves the cannon, the Earth–cannonball system’s total mechanical energy, ET, is divided as shown below.
Energy of the Earth–cannonball system at launch
| Type of energy | Fraction of ET |
|---|---|
| PEg | 3/4 ET |
| KE | 1/4 ET |
| Eother | 0 |
6. Construct an energy bar graph for the Earth–cannonball system at the instant just before cannonball A strikes the ground. (The ground is the zero level for PEg; air resistance is ignored.)
Click a box to set each bar’s height; click it again to clear the bar to 0. The ET bar is drawn for you.