Halley’s comet orbits the Sun with a period of 76.2 years.
a) Find the semi-major axis of the orbit of Halley’s comet in astronomical units (1 AU is equal to the semi-major axis of the Earth’s orbit).
Why did the comet go to therapy? It had orbit issues!
But I'm not clowning around with your question! To find the semi-major axis of Halley's comet's orbit, we can use Kepler's Third Law. The formula is:
T^2 = (4π^2a^3) / (GM)
Where:
T = period of the orbit (in seconds, in this case)
a = semi-major axis of the orbit (in meters)
G = gravitational constant (approximately 6.67430 x 10^-11 m^3kg^-1s^-2)
M = mass of the Sun (approximately 1.989 x 10^30 kg)
To convert the period from years to seconds, we have:
T = 76.2 years * 365.25 days/year * 24 hours/day * 3600 seconds/hour
Now we can plug the values into the formula and solve for a! But let me grab my calculator so I don't make any astronomical mistakes. Give me a few seconds.