Final answer:
The radius of the orbit of the International Space Station (ISS) can be calculated from its orbital velocity and period. However, after calculation, the correct orbital radius does not match any of the provided answers, suggesting a possible error in the question or the answer options. The closest answer is the Earth's radius itself, which should be less than the orbital radius.
Step-by-step explanation:
To calculate the radius of the orbit of the ISS, we can use the relationship between orbital velocity (v), orbital radius (r), and period (T). The orbital velocity is given as 7.67 km/s and the period as 92.49 minutes. First, we should convert the period to seconds: T = 92.49 minutes × 60 seconds/minute = 5549.4 seconds. The relationship we use to find the radius is given by v = 2πr/T, resulting in r = v×T/(2π). Plugging in the values, we get r = (7.67×10³ m/s) × (5549.4 s)/(2π) = approximately 6.98 × 10¶ meters. However, this value represents the distance from the center of the Earth to the ISS. To find the orbital radius above Earth's surface, we have to subtract the Earth's radius from this value. The Earth's radius is approximately 6.371 × 10¶ meters, therefore the orbital radius is approximately 6.98 × 10¶ meters - 6.371 × 10¶ meters = 0.61 × 10¶ meters (610 km). However, none of the available answer options exactly match this result, suggesting there may be a rounding or calculation error in the initial data given or answer options. The closest correct answer from the provided options is b) 6.37 × 10¶ meters, which is actually the radius of Earth itself and not the orbital radius of the ISS. Therefore, the question may contain a mistake or may be testing for understanding that the orbital radius must be larger than the Earth's radius.