Space is full of dust, but not of all sizes. The sun pushes some of the...

Transcribed Image Text:

Space is full of dust, but not of all sizes. The sun pushes some of the finer grains out of the solar system. Let's work out how large the dust needs to be to stay around. (See Ch. 32 for more on radiation pressure). Aron Visuals (Unsplash) Pretend the dust is spherical and has a radius a and mass density p = 3 × 10³ [kg/m³]. a) Write the gravitational force F,(r) felt by a grain at some distance r. Take the mass of the Sun to be M 2 x 103⁰ [kg]. b) The luminosity of the Sun (aka power) is 4 x 1026 [W]. Find the intensity I that reaches this grain (at some distance r). c) The radiation intensity impinging on a material can be related to a radiation force (for a totally absorbing material, which we will assume for this problem) by Frad = I A/c, where A Ta² is the cross-section area of the grain (this is different from the total surface area). Find the dust radius a such that the radiation and gravitational forces balance. Grains smaller than this are "blown" away. = Space is full of dust, but not of all sizes. The sun pushes some of the finer grains out of the solar system. Let's work out how large the dust needs to be to stay around. (See Ch. 32 for more on radiation pressure). Aron Visuals (Unsplash) Pretend the dust is spherical and has a radius a and mass density p = 3 × 10³ [kg/m³]. a) Write the gravitational force F,(r) felt by a grain at some distance r. Take the mass of the Sun to be M 2 x 103⁰ [kg]. b) The luminosity of the Sun (aka power) is 4 x 1026 [W]. Find the intensity I that reaches this grain (at some distance r). c) The radiation intensity impinging on a material can be related to a radiation force (for a totally absorbing material, which we will assume for this problem) by Frad = I A/c, where A Ta² is the cross-section area of the grain (this is different from the total surface area). Find the dust radius a such that the radiation and gravitational forces balance. Grains smaller than this are "blown" away. =

Answer rating: 100% (QA)

a The gravitational force felt by a grain at some distance r from the Sun can be calculated using Ne... View the full answer