Question

A spherical particle with the density of 1. 0 g/cm3 is located at the same distance from the Sun as the Jupiter, 7. 8×1011 m. Assume that the particle absorbs 100 percent of the solar intensity of 52 W/m2. Find the largest size of a particle when the force exerted by the solar radiation is larger than the gravity exerted on the particle by the Sun. Use the gravitational constant of 6. 7×10−11Nm2/kg2 and the solar mass of 2. 0×1030 kg

Answer 1

Step-by-step explanation:

2. Calculating Solar Radiation Force:

The force exerted by solar radiation on the particle is given by:

Force (F_solar) = (Intensity × Area) / speed of light (c)

The area of the particle is given by:

Area = 4π × radius^2

Given Intensity = 52 W/m² and speed of light (c) = 3.0 × 10^8 m/s, we can calculate the force (F_solar).

3. Calculating Gravitational Force:

The gravitational force exerted by the Sun on the particle is given by:

Force (F_gravity) = (G × Sun's mass × Particle's mass) / distance^2

4. Setting Up the Inequality:

We want to find the largest size of the particle for which the solar radiation force is greater than the gravitational force. Mathematically, this can be written as:

F_solar > F_gravity

Solving for the Radius (Size) of the Particle:

Substitute the expressions for F_solar and F_gravity. Solve the inequality to find the radius (size) of the particle.

This will give us the largest size of the particle for which the force exerted by solar radiation is greater than the gravitational force exerted on the particle by the Sun.