Companion to the reading passage Physics of Geosynchronous Satellites. 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.
A satellite-TV dish can be bolted to a roof because the satellite it points at appears to stay fixed in the sky. Such a geostationary satellite moves in a circular orbit above the equator. Its orbital period equals the time for Earth to rotate once relative to the stars, about 8.62 × 104 s. The data for a typical geostationary satellite are shown in Table 1.
Table 1: A Typical Geostationary Satellite
| Quantity | Value |
|---|---|
| Altitude above Earth’s surface | 3.58 × 107 m |
| Orbital radius (from Earth’s center) | 4.22 × 107 m |
| Orbital speed | 3.07 × 103 m/s |
| Mass of satellite | 2.0 × 103 kg |
Data are representative values for practice.
1. Substitute numerical values into a mathematical representation that can be used to determine the magnitude of the centripetal acceleration of the satellite in Table 1. Then calculate the acceleration.
2. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
Any satellite whose period equals Earth’s rotation period is geosynchronous. If its orbit is tilted relative to the equator, the satellite drifts north and south during each day and traces a figure-eight path across the sky, so a fixed dish would lose its signal. Only a satellite meeting a specific set of conditions appears motionless.
3. Place a check mark next to the three conditions that a satellite must meet to be geostationary.
A shipping company is choosing a satellite internet system for its cargo ships. Table 2 compares two proposals. Radio signals travel at 3.00 × 108 m/s. Because of Earth’s curvature, a geostationary satellite cannot be seen from latitudes closer to the poles than about 81°. Motorized tracking dishes on a rolling ship deck need more maintenance than fixed dishes.
Table 2: Two Satellite Internet Proposals
| Proposal | Number of satellites | Altitude (m) | Orbital period | Ship antenna |
|---|---|---|---|---|
| A: Low Earth orbit (LEO) | 1,200 | 5.0 × 105 | 95 minutes | motorized, tracks satellites |
| B: Geostationary orbit (GEO) | 3 | 3.58 × 107 | 24 hours | fixed dish |
Data are representative values for practice.
4. Which mathematical representation can be used to determine the minimum time for a signal to travel from a ship up to a Proposal B satellite directly overhead and back down to the ship?
5. Which row correctly compares a Proposal A satellite with a Proposal B satellite of equal mass? (Columns: orbital speed / gravitational force of Earth on the satellite.)
6. Some of the company’s ships sail to Arctic ports at 82° N latitude. Explain why this route is a constraint that favors Proposal A over Proposal B.