Companion to the reading passage Eyes You'll Never See: The Many Uses of Artificial 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.
Engineers place satellites at different altitudes depending on the job. Table 1 lists typical values for one satellite from each of three orbit families. The orbital radius is measured from Earth’s center (Earth’s radius is 6.37 × 106 m). In every case, Earth’s gravity is the only significant force acting on the satellite once its engines are off.
Diagram 1 shows Earth at the center with a satellite’s circular orbit drawn around it. The satellite is at the far right of its orbit (the “3 o’clock” position) and is moving counterclockwise.
Table 1: Typical Orbits of Three Satellite Families
| Orbit family (example) | Altitude (m) | Orbital radius (m) | Orbital speed (m/s) | Orbital period |
|---|---|---|---|---|
| Low Earth orbit (Earth-imaging satellite) | 4.0 × 105 | 6.77 × 106 | 7.67 × 103 | 92 minutes |
| Medium Earth orbit (GPS satellite) | 2.02 × 107 | 2.66 × 107 | 3.87 × 103 | 12 hours |
| Geostationary orbit (TV/weather satellite) | 3.58 × 107 | 4.22 × 107 | 3.07 × 103 | 24 hours |
Data are representative values for practice.
Diagram 1: Satellite in Circular Orbit
1. Which graph best represents the relationship between orbital speed and orbital radius for the satellites in Table 1?
2. In Diagram 1 (top of the page is up, right is right), choose the direction of the gravitational force (Fg) on the satellite at the 3 o’clock position. Gravity is the only force, so it also sets the direction of the satellite’s acceleration. If this is the low-Earth-orbit satellite in Table 1, determine the magnitude of its centripetal acceleration.
3. Now choose the direction of the satellite’s velocity (v) at the 3 o’clock position in Diagram 1 (it moves counterclockwise). If this is the low-Earth-orbit satellite in Table 1, enter the magnitude of its velocity.
A GPS receiver in a phone finds its position by timing radio signals from four or more GPS satellites. Each satellite broadcasts the exact time the signal left it. Radio waves travel at the speed of light, 3.00 × 108 m/s. Because the signals are so fast, the receiver’s clock must be extremely accurate: an error in the measured travel time becomes an error in the calculated distance to the satellite.
4. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
5. A receiver’s clock is off by 3.0 × 10−9 s. Substitute numerical values into a mathematical representation that can be used to determine the resulting error in the calculated distance to one GPS satellite. Then calculate the error.
Meteorologists track hurricanes with two kinds of satellites. A geostationary weather satellite completes one orbit in the same time Earth takes to rotate once, so it stays above one point on the equator and can watch the same storm continuously. A polar-orbiting satellite in low Earth orbit passes near both poles on every orbit. It takes much sharper images because it is closer to the surface, but it is above any one region for only about 10 minutes per pass. Because of Earth’s curvature, a geostationary satellite cannot be seen from locations closer to the poles than about 81° latitude.
6. Which row correctly compares a low-Earth-orbit imaging satellite with a geostationary weather satellite?
(Orbital period / Finer image detail)
7. A research station at the South Pole (90° S latitude) needs a satellite link with no daily gaps. Which design best meets this constraint?