The intensity of sunlight reaching the earth is 1360 W/m^2
Part A:
Assuming all the sunlight is absorbed, what is the radiation-pressure force on the earth?
Give your answer in newtons.
Part B:
Give your answer as a percentage of the sun's gravitational force on the earth.
I tried for part A to do I=P/A. So I used the radius of the sun (6.955*10^8) and did (4 pi (6.955*10^8)^2 1360) to get the power then divide by the speed of light c to get my answer of 2.76*10^13 but my program said it was wrong. Part B I have no idea how to figure out.
So I used the radius of the sun....
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Only the radiation hitting the earth is intended by the statement about all the radiation REACHIN EARTH is absorbed. Use the radius of earth, not sun.
The force is then that pressure times 4 pi Rearth^2 again
You know the gravitational force on earth
F = G mass sun * mass earth / distance between squared
divide the force from part A by the gravitational force and multiply by 100 to get percent.
To calculate the radiation-pressure force on the earth (Part A), you can use the formula:
Force = Power / Speed of Light
Given that the intensity of sunlight is 1360 W/m^2 (power per unit area), we can use this value directly as the power since intensity is already power per unit area.
Therefore, the radiation-pressure force on the earth is:
Force = 1360 W/m^2 / Speed of Light
Before proceeding further, we need to convert the units of the speed of light to match the unit of power we have.
The speed of light is approximately 3 x 10^8 m/s.
Substituting the values and calculating:
Force = (1360 W/m^2) / (3 x 10^8 m/s)
Force ≈ 4.53 x 10^-6 N
So, the radiation-pressure force on the earth is approximately 4.53 x 10^-6 N.
Moving on to Part B:
The percentage of the sun's gravitational force on the earth can be calculated by comparing the radiation-pressure force to gravitational force.
The sun's gravitational force on the earth is given by Newton's law of universal gravitation:
Force_gravity = (Gravitational Constant * Mass of the sun * Mass of the earth) / (Distance between the sun and the earth)^2
For simplicity, we can use approximate values:
- Mass of the sun ≈ 1.989 x 10^30 kg
- Mass of the earth ≈ 5.972 x 10^24 kg
- Distance between the sun and the earth ≈ 1.496 x 10^11 m
Let's calculate the gravitational force:
Force_gravity = (6.67430 x 10^-11 N m^2/kg^2 * 1.989 x 10^30 kg * 5.972 x 10^24 kg) / (1.496 x 10^11 m)^2
Force_gravity ≈ 3.52 x 10^22 N
Now, we can find the percentage of the radiation-pressure force compared to the sun's gravitational force:
Percentage = (Radiation-pressure force / Sun's gravitational force) * 100
Percentage = (4.53 x 10^-6 N / 3.52 x 10^22 N) * 100
Percentage ≈ 1.29 x 10^-17 %
Therefore, the radiation-pressure force is approximately 1.29 x 10^-17 % of the sun's gravitational force on the earth.
To calculate the radiation-pressure force on the Earth, you need to use the formula:
Force = Power / Speed of Light
In this case, the power is the intensity of sunlight reaching the Earth, which is given as 1360 W/m^2. The speed of light is approximately 3 × 10^8 m/s.
Part A:
To find the radiation-pressure force on the Earth, you need to multiply the power by the surface area of the Earth. The surface area of a sphere is given by:
Surface Area = 4πr^2
where "r" is the radius of the Earth.
You have mentioned using the radius of the Sun in your calculation, but you should be using the radius of the Earth. The radius of the Earth is approximately 6.371 × 10^6 m.
So, the calculation for the radiation-pressure force on the Earth is as follows:
Force = Power * Surface Area / Speed of Light
= 1360 * (4π(6.371 × 10^6)^2) / (3 × 10^8)
Please note that the intensity of sunlight is given in W/m^2, so you don't need to multiply it by the area again.
Now, let's calculate the value:
Force = 1360 * (4π(6.371 × 10^6)^2) / (3 × 10^8)
≈ 3.439 × 10^9 N
Therefore, the radiation-pressure force on the Earth is approximately 3.439 × 10^9 Newtons.
Part B:
To find the percentage of the sun's gravitational force on the Earth, you need to calculate the ratio of the radiation-pressure force to the gravitational force.
The gravitational force between the Sun and the Earth is given by Newton's law of gravitation:
Force_gravity = (GM_solar * M_earth) / R^2
where:
- G is the gravitational constant, approximated as 6.67 × 10^-11 Nm^2/kg^2
- M_solar is the mass of the Sun, approximately 1.989 × 10^30 kg
- M_earth is the mass of the Earth, approximately 5.972 × 10^24 kg
- R is the distance between the Sun and the Earth, which is approximately 1.496 × 10^11 m (average distance)
Now, let's calculate the gravitational force:
Force_gravity = (6.67 × 10^-11 * 1.989 × 10^30 * 5.972 × 10^24) / (1.496 × 10^11)^2
≈ 3.52 × 10^22 N
To find the percentage, simply divide the radiation-pressure force by the gravitational force and multiply by 100:
Percentage = (Force / Force_gravity) * 100
= (3.439 × 10^9 / 3.52 × 10^22) * 100
Calculating the value:
Percentage ≈ 9.78 × 10^-12 %
Hence, the radiation-pressure force on the Earth as a percentage of the sun's gravitational force is approximately 9.78 × 10^-12 %.