Comet Halley returns every 74 years. Find the average distance of the comet from the sun.
How do i do this??
Well, to find the average distance of Comet Halley from the sun, you might need a telescope, a space suit, and a really long measuring tape. Just kidding! Let's not take things too literally.
To calculate the average distance of Comet Halley from the sun, you'll need some calculations based on its orbital path. The average distance from the sun can be estimated by taking the semi-major axis of its orbit.
Now, I could go into all the mathematical details, but that might make your brain orbit into outer space. So, I'll save you from that and give you a simplified explanation.
The average distance of Comet Halley from the sun is approximately 17.8 astronomical units (AU). One AU is the average distance between the Earth and the sun, which is about 93 million miles (150 million kilometers). So, 17.8 AU would be roughly 1.65 billion miles (2.66 billion kilometers) away from the sun, on average.
Remember, though, this is just an estimate, as the distance of the comet can vary throughout its journey. It's like trying to pin down a wily clown—sometimes, it's closer, sometimes it's farther away. But on average, Halley likes to hang out at that distance from the sun.
To find the average distance of Comet Halley from the sun, you can use Kepler's third law of planetary motion, which states that the square of the orbital period of a planet (or comet) is directly proportional to the cube of its average distance from the sun.
Let's denote the average distance of Comet Halley from the sun as "d", and the orbital period as "T".
According to the given information, the orbital period of Comet Halley is 74 years. Therefore, we have T = 74 years.
Using Kepler's third law, we can write the equation as follows:
T^2 = k * d^3
Where "k" is a constant of proportionality.
To find the average distance "d", we need to solve for it. Rearranging the equation, we have:
d^3 = T^2 / k
Taking the cube root of both sides, we get:
d = (T^2 / k)^(1/3)
Since the constant "k" depends on the mass of the sun and other factors, we can't calculate its exact value without more information. However, for our purposes, we can approximate it as 1.
Plugging in the values, we have:
d = (74^2 / 1)^(1/3)
Evaluating the expression, we find:
d ≈ 17.9 AU (astronomical units)
Therefore, the average distance of Comet Halley from the sun is approximately 17.9 astronomical units.
To find the average distance of Comet Halley from the sun, you need to gather some information and perform a simple calculation. Here are the steps to follow:
1. Determine the period of Comet Halley: The period, or orbital period, is the time it takes for the comet to complete one orbit around the sun. In this case, the period of Comet Halley is given as 74 years.
2. Use Kepler's Third Law: Kepler's Third Law states that the square of the orbital period of a planet or comet is directly proportional to the cube of its average distance from the sun. Mathematically, it can be represented as T^2 = k * r^3, where T is the orbital period, r is the average distance, and k is a constant.
3. Calculate the constant: To find the value of the constant (k), you can use the data for other known planets or objects in the solar system. Using the average distance of Earth from the sun (149.6 million kilometers) and its orbital period (1 year), you can substitute these values into the equation:
(1 year)^2 = k * (149.6 million kilometers)^3
4. Solve for k: Calculate the value of k using the values from step 3. This will give you the proportionality constant.
5. Find the average distance of Comet Halley: Now, substitute the period of Comet Halley (74 years) into the equation along with the value of k you obtained earlier:
(74 years)^2 = k * (r)^3
Solve this equation for r, the average distance of Comet Halley from the sun. You can use algebraic methods or a scientific calculator to get the numerical value.
By following these steps, you should be able to calculate the average distance of Comet Halley from the sun. Remember to use appropriate units (such as kilometers or astronomical units) depending on the data you are working with.
Kepler's third law
For bodies in orbit around the same central body (like sun)
periods proportional to orbital major axis length ^3/2
so
74/1 = (RHalleyorbit/Rearthorbit)^1.5
Rearthorbit = 1.49 *10^11 meters