To determine the truth of the statements provided, we need to understand the difference between geometric altitude and geopotential altitude.
- Geometric altitude is the height above sea level measured with a standard barometer, while geopotential altitude takes into account the varying gravitational field of the Earth and the distribution of air density.
The relation between geometric altitude (h) and geopotential altitude (H) can be approximated by the formula:
\[ H \approx h \left(1 - \frac{h}{2R}\right) \]
where \( R \) is the radius of the Earth (approximately 6,371 kilometers).
Now let's analyze the statements:
-
Statement 1:
- Geometric altitude = 10,000 meters
- Geopotential altitude = 9,978 meters
- This suggests that the gravitational effects map to a slightly lower geopotential altitude compared to the geometric one. This is plausible given that the Earth’s gravity decreases with altitude.
-
Statement 2:
- Geopotential altitude = 12,000 meters
- Geometric altitude = 12,023 meters
- In this case, the geometric altitude is higher than the geopotential altitude; however, the difference is inconsistent with the expected behavior of how these altitudes relate to one another. Typically, at high altitudes, the geometric altitude should not exceed the geopotential altitude significantly.
Given the established principles of geometric and geopotential altitude, only Statement 1 is true, while Statement 2 is likely false due to the unusual and inconsistent relation observed.
So the correct answer is:
Only statement 1 is true.
1 answer