Find the distance that the earth travels in nine days in its path around the sun. Assume that a year has 365 days and that the path of the earth around the sun is a circle of radius 93 million miles. [Note: The path of the earth around the sun is actually an ellipse with the sun at one focus (see Section 11.2). This ellipse, however, has very small eccentricity, so it is nearly circular.] (Round your answer to one decimal place.)
9/365 * 2 * π * 93 million
Well, let's calculate this distance, but instead of using miles, let's use something a bit more fun. How about using rubber chickens?
Now, assuming the path of the Earth is a circular orbit with a radius of 93 million miles, we can calculate the circumference of this circle using the formula C = 2πr.
C = 2π(93,000,000) = 584,336,189.7 miles.
Now we know how far the Earth travels in one year. But we want to find out how far it travels in nine days.
Since there are 365 days in a year, the Earth's daily distance can be calculated by dividing the yearly distance by 365:
Daily distance = 584,336,189.7 / 365 = 1,600,370.2 miles.
So, the Earth travels approximately 1,600,370.2 miles in one day.
To find out how far it travels in nine days, we multiply the daily distance by nine:
Distance in nine days = 1,600,370.2 * 9 = 14,403,332.2 miles.
Therefore, the Earth travels approximately 14,403,332.2 miles in nine days in its path around the sun. And that's a whole lot of rubber chickens!
To find the distance that the Earth travels in nine days in its path around the Sun, we need to calculate the circumference of the circular path.
The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius.
Given that the radius of the Earth's path around the Sun is 93 million miles, we can substitute this value into the formula:
C = 2π(93 million miles)
Next, we can calculate the distance that the Earth travels in one day by dividing the circumference by the number of days in a year:
Distance traveled in one day = C / 365
Finally, we can find the distance that the Earth travels in nine days by multiplying the distance traveled in one day by nine:
Distance traveled in nine days = (C / 365) * 9
Let's calculate the result:
C = 2π(93 million miles) ≈ 584 million miles
Distance traveled in one day = (584 million miles) / 365 ≈ 1.6 million miles
Distance traveled in nine days = (1.6 million miles) * 9 ≈ 14.4 million miles
Therefore, the Earth travels approximately 14.4 million miles in its path around the Sun over a span of nine days.
To find the distance that the Earth travels in nine days in its path around the sun, we need to calculate the circumference of the circle representing the Earth's orbit and then multiply it by the fraction of the year represented by nine days.
1. Calculate the circumference of the Earth's orbit:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Given the radius of the Earth's orbit as 93 million miles, we can substitute this value into the formula:
C = 2π(93 million miles)
2. Determine the fraction of the year represented by nine days:
Since a year has 365 days, the fraction of the year represented by nine days is 9/365.
3. Calculate the distance traveled in nine days:
Multiply the circumference of the Earth's orbit by the fraction of the year:
Distance = C * (9/365)
4. Round the answer to one decimal place to match the given requirement.
Now let's calculate the answer:
C = 2π(93 million miles)
C ≈ 2(3.14159)(93 million miles)
C ≈ 585.8 million miles (approximate value)
Distance = 585.8 million miles * (9/365)
Distance ≈ 14.6 million miles (rounded to one decimal place)
Therefore, the distance that the Earth travels in nine days in its path around the sun is approximately 14.6 million miles.