The power radiated by the sun is 3.90 1026 W. The earth orbits the sun in a nearly circular orbit of radius 1.50 1011 m. The earth's axis of rotation is tilted by 27° relative to the plane of the orbit (see the drawing), so sunlight does not strike the equator perpendicularly. What power strikes a 0.575-m2 patch of flat land at the equator at point Q?

Answer in W

To find the power that strikes the patch of land at the equator at point Q, we need to consider the angle at which the sunlight strikes the patch. Since the earth's axis of rotation is tilted by 27° relative to the plane of the orbit, the angle of incidence of the sunlight at point Q will be 90° - 27° = 63°.

To calculate the power, we can use the formula:

Power = Power radiated by the sun * (Area of the patch * cos(angle of incidence))

Given:
Power radiated by the sun = 3.90 * 10^26 W
Area of the patch = 0.575 m^2
Angle of incidence = 63°

Plugging in these values into the formula, we get:

Power = 3.90 * 10^26 W * (0.575 m^2 * cos(63°))

Calculating the cosine of 63°, we find:

cos(63°) ≈ 0.448

Substituting this value back into the formula, we can find the power:

Power ≈ 3.90 * 10^26 W * (0.575 m^2 * 0.448)

Power ≈ 1.078 * 10^26 W

Therefore, the power that strikes the 0.575 m^2 patch of flat land at the equator at point Q is approximately 1.078 * 10^26 W.

To find the power that strikes the patch of flat land at the equator, we need to consider the amount of sunlight that falls on this area. Here's how you can calculate it:

Step 1: Calculate the area of the circular region at the Earth's orbit:
The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the radius is 1.50 * 10^11 m.

A = π * (1.50 * 10^11 m)²

Step 2: Calculate the area of the patch of land at the equator:
Given that the patch of land has an area of 0.575 m².

Step 3: Find the fraction of sunlight that hits the patch of land:
The fraction of sunlight that hits the land is equal to the ratio of the area of the patch of land to the area of the circular region at the Earth's orbit.

fraction of sunlight = (Area of land) / (Area of circular region)

Step 4: Calculate the power that strikes the patch of land:
Multiply the fraction of sunlight by the total power radiated by the sun.

power striking the land = fraction of sunlight * power radiated by the sun

Let's calculate the values:

Step 1:
A = π * (1.50 * 10^11 m)² = 7.07 * 10^22 m²

Step 2:
Area of the land = 0.575 m²

Step 3:
fraction of sunlight = (0.575 m²) / (7.07 * 10^22 m²)

Step 4:
power striking the land = fraction of sunlight * power radiated by the sun

Now, you can substitute the values into the equation and calculate the power striking the land in watts.

Find the intensity at the Earth surface.

Power= .575/(4PI*(1.50E11)^2 ) * 3.9E26 watts.

Now, the area is not perpendicular, so the perpendicular area is power above multiplied by cos27