Radiation from the Sun reaching the Earth (just outside the atmosphere) has an intensity of 1.4

Radiation from the Sun reaching the Earth (just outside the...

Key Concepts

Radiation Pressure

Radiation pressure is the pressure exerted by electromagnetic radiation upon any surface due to the momentum carried by the light. When light is absorbed or reflected by a surface, the transfer of momentum results in a force that can be calculated by relating the intensity of the radiation to the speed of light. This concept is crucial in understanding how even negligible forces can act over large surfaces or in space, influencing objects such as satellites or dust particles.

Momentum Transfer in Electromagnetic Radiation

Electromagnetic waves, including visible light, carry momentum even though they are massless. When these waves interact with a material object, they transfer momentum to it. The amount of momentum transferred per unit time is directly related to the energy flux (intensity) of the radiation. This phenomenon is the underlying principle behind radiation pressure and is applied in various fields including astrophysics and optical manipulation techniques.

Electromagnetic Energy Intensity

The intensity of electromagnetic energy is defined as the amount of energy passing through a unit area per unit time. It is a key parameter in quantifying radiation pressure because it directly influences the force exerted by radiation. In many applications, the intensity is used along with the speed of light to determine the pressure on a surface, thereby linking energy considerations with momentum transfer.

Newtonian Gravitational Force

Newtonian gravitational force describes the attractive force between two masses according to Newton's law of universal gravitation, where the force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. This fundamental concept explains planetary motions and the gravitational interactions in many astrophysical scenarios. Comparing gravitational forces with other small forces, such as radiation pressure, highlights the dominant interactions that govern the dynamics of celestial bodies.

Geometric Considerations in Force Calculations

Geometric considerations are critical when calculating forces such as radiation pressure. The effective area which interacts with the incoming radiation must be properly accounted for, as it determines how much energy and momentum are intercepted by the object. In many problems, approximating an object as a particular geometric shape (for example, a disk or sphere) simplifies the calculation and leads to insights about the relative strength of different forces acting on the body.

Transcript

00:01 So in this question we're asked to estimate the force exerted on the earth due to radiation pressure from the sun, given that the sun emits an intensity of 1 .4 kilowatts per meter squared, and it's absorbed by the earth, and we can treat the earth as a flat disk with the radius of the earth.

00:21 And then partly we're asked to compare the magnitude of this force to the force of gravitational attraction, and see which is bigger and which is.

00:32 And by how much.

00:34 So this question, we can begin then with part a.

00:39 So in part a, we're asked to determine the force due to radiation pressure.

00:44 So we're told that the light is absorbed.

00:47 So the radiation pressure formula that we can use is pr is equal to just the intensity of the sun, i, s, over the speed of light, since it's absorbed and not reflected.

01:00 So if we work to say this equal to 1 .4 by 10 to the speed 3 watts per meter squared over the speed of light which is 3 by 10 to the 8 meters per second and if we work this out this is equal to 4 .667 by 10 to the minus 6 pascal's but we know the relationship between force and pressure for pressure is equal the force per unit area so we have that the force then is equal to the pressure p r times the area of the surface area of the disk that we're taking to be the earth.

01:40 So this is equal to then, so the radiation pressure is 4 .667 by 10 to the minus 6.

01:49 And the area of the earth is taken to be disk.

01:52 And it's going to be pi or squared.

01:55 And the radius the earth is 6 .37 by 10 to the 6 all squared.

02:02 So if we work to say out, we get that the force is equal to 5 .949 times 10 to the 20 or 10 to the 8 newtons.

02:17 So that's our answer for a.

02:18 This is the force due to radiation pressure...