Final answer:
The orbital period of an asteroid with a 7:2 orbital resonance with Jupiter can be calculated to be approximately 41.51 years by multiplying 5.93 years, which is half of Jupiter's orbital period of 11.86 years, by 7.
Step-by-step explanation:
To find the orbital period of an asteroid with a 7:2 orbital resonance with Jupiter, we must first know Jupiter's orbital period, which is approximately 11.86 years. An orbital resonance of 7:2 means that for every 7 orbits Jupiter makes, the asteroid completes 2 orbits. Therefore, to calculate the asteroid's orbital period (T), we divide Jupiter's period by 2 and then multiply by 7:
T = (11.86 years / 2) × 7
T = 5.93 years × 7
T = 41.51 years
Thus, the asteroid's orbital period is approximately 41.51 years.