Companion to the reading passage The Law That Can't Explain Itself: Gravity and the Biggest Myth in Science. 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.
Astronauts aboard the International Space Station (ISS) appear to float. The ISS travels in a nearly circular orbit about 420 km above Earth’s surface. Both the station and the astronauts inside it move around Earth together, so an astronaut does not press against the floor. Table 1 lists data for the ISS orbit and for one astronaut.
Table 1: ISS Orbit Data
| Quantity | Value |
|---|---|
| Radius of ISS orbit (from Earth’s center) | 6.79 × 106 m |
| Orbital speed of ISS | 7.66 × 103 m/s |
| Mass of Earth | 5.97 × 1024 kg |
| Radius of Earth | 6.37 × 106 m |
| Mass of astronaut | 80. kg |
| Universal gravitational constant, G | 6.67 × 10−11 N•m2/kg2 |
1. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
2. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the centripetal acceleration of the ISS. Then calculate the acceleration.
Newton’s law of universal gravitation (1687) describes how strongly two masses attract and how that force changes with distance, but Newton said he could not explain why masses attract. In 1915 Einstein’s general theory of relativity offered an explanation: mass curves space and time. A class used a computer simulation built only on Newton’s law. They placed a satellite at increasing distances from Earth’s center and recorded the gravitational force on it each time. The simulation’s predictions matched real satellite orbits closely.
3. Which graph best represents the relationship between the magnitude of the gravitational force on the satellite and its distance from Earth’s center?
4. Place a check mark next to the three statements that describe predictions the class’s simulation, which is based only on Newton’s law, is able to make.
Global Positioning System (GPS) satellites orbit much farther from Earth than the ISS. Engineers use Newton’s law of gravitation to predict each satellite’s position, and they use Einstein’s relativity to correct each satellite’s atomic clock. A satellite’s orbital radius affects both its motion and its clock. Table 2 compares the two orbits.
Table 2: Orbital Radii
| Spacecraft | Orbital Radius (from Earth’s center) |
|---|---|
| ISS | 6.79 × 106 m |
| GPS satellite | 2.66 × 107 m |
5. Which row correctly describes the gravitational force of Earth on a GPS satellite and the magnitude of the gravitational field strength (g) at the GPS satellite’s orbit? (Columns: Gravitational Force of Earth on the Satellite / Magnitude of g at the Satellite’s Orbit)
6. The students say their Newton-only simulation is a useful model for planning satellite orbits. State one limitation of this model for a technology like GPS, based on the information above.