the period of the orbit of halley's comet is about 75 years. what is the comet's average distance from the sun?
if it comes within 0.35 AU of the sun, what is its maximum distance from the sun in miles?
To find the average distance of Halley's comet from the Sun, we can use Kepler's Third Law, which states that the square of the period of an orbit (in years) is proportional to the cube of the average distance (in AU) between the object and the Sun.
We know that the period of Halley's comet is about 75 years. Let's represent the average distance as "d" AU. So, we have:
Period^2 = Average Distance^3
Plugging in the values, we get:
75^2 = d^3
5625 = d^3
Taking the cube root of both sides, we find:
d ≈ 17.4 AU
Therefore, the average distance of Halley's comet from the Sun is approximately 17.4 astronomical units (AU).
Now, to determine the comet's maximum distance from the Sun in miles when it comes within 0.35 AU, we need to calculate the maximum distance between the Sun and the comet.
To convert AU to miles, we can use the fact that 1 AU is approximately 93 million miles.
Let's calculate the maximum distance:
Max Distance = (Average Distance + 0.35 AU) * Conversion Factor
Max Distance = (17.4 + 0.35) AU * 93 million miles
Max Distance ≈ 1,651 million miles
Therefore, when Halley's comet comes within 0.35 AU of the Sun, its maximum distance from the Sun is approximately 1,651 million miles.