# Force on Earth by the radiation pressure of Sun

• SL_1719
In summary, the force on Earth due to the pressure of radiation from the Sun can be estimated by multiplying the radiation pressure by the surface area of the Earth, which is approximately πr². Taking into account the angle of sunlight and assuming that all radiation is absorbed, the estimated force is 5.823e8 N.
SL_1719

## Homework Statement

Estimate the force on Earth due to the pressure of the radiation on Earth by the Sun. (At Earth's orbit, the intensity of sunlight is 1.37 kW/m^2.)

## Homework Equations

Pressure=F/A
Using SA of earth=510,072,000 km2

## The Attempt at a Solution

So I have been working at this problem for a while now and can't seem to get the correct answer. I found the radiation pressure to be 4.5667e-6 N/m^2. I have since then tried taking this and multiplying it by the surface area of the Earth in many different forms to no avail. What am I missing? I have tried these coefficients to Prad*SA, 1 (acting on whole surface), 1/2 (half the surface since sun is on one side), 1/(2sqr2) (thought possibly rms), 1/sqr2 (similar to before, just trying anything), and 1/(4sqr2), 1/4. My force for Prad*SA=2.329e9 N.

Welcome to PF!
I agree with 4.5667e-6 N/m^2.
I'm puzzled with what area to use. The sun only shines on one side of the Earth at a time so you certainly wouldn't use the whole surface area. Half of it doesn't seem right either because the sun hits a good part of it at a very high angle, drastically reducing the intensity. I think taking the area to be πr² is the best first estimate because it counts all of the radiation hitting the Earth. Of course all this assumes that the radiation is absorbed rather than reflected.

Thank you for welcoming me and thank you for the help, using just pi*r^2 worked. 5.823e8 N is the answer.

## 1. What is radiation pressure from the Sun?

Radiation pressure from the Sun is the force exerted by sunlight on objects in space. It is caused by the transfer of momentum from photons in sunlight to the surface of an object.

## 2. How does radiation pressure affect objects on Earth?

Radiation pressure from the Sun on Earth is relatively weak and has a negligible effect on large objects such as buildings or people. However, it can have a significant impact on small particles in space, such as dust and gas, which can be pushed around by the force of sunlight.

## 3. What causes the force of radiation pressure?

The force of radiation pressure is caused by the transfer of energy from photons in sunlight to the surface of an object. When a photon hits an object, it exerts a small amount of force on that object, which can add up over time.

## 4. How is the force of radiation pressure measured?

The force of radiation pressure can be measured using a device called a radiometer. This instrument consists of a set of vanes that are suspended in a vacuum and are free to rotate. When exposed to sunlight, the vanes will rotate due to the force of radiation pressure, allowing scientists to measure the force.

## 5. Can radiation pressure be harnessed for use on Earth?

Yes, radiation pressure can be harnessed for various purposes on Earth. Solar sails, for example, use the force of radiation pressure to propel spacecraft through space. On Earth, it is also used in solar power technology, where sunlight is converted into electricity using photovoltaic cells.

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