Question

The average density of the Sun is on the order 103 kg/ m3 . (a) Estimate the diameter of the Sun. (b) Given that the Sun subtends at an angle of about half

Answer 1

The diameter is
`\approx`
`10^(11)m` and
`r_(sun) = 10^(9)`m

Step-by-step explanation:

Given:

`m_(sun) = 10^(30) kg`

`\\p_(sun)= 10^(3)(kg)/(m^(3))`

Required:

`r_(sun)`=?

d= ?

We know,

`{v_(sun) = (m_(sun))/(p_(sun))`

=
`(10^(30))/(10^(3))`

=
`10^(27)m^(3)`

`v_(sun) = (4)/(3)*\pi r^{3_(sun)}`

`\approx`
`r^(3)_(sun)`

`r_(sun) = 10^(9)`m

From the figure attached,

`sin\theta=(r_(sun))/(d)}`

`d=(r_(sun))/(sin\theta)}`

=
`(10^(9))/(sin5)}`

`\approx`
`10^(11)m`

The diameter is
`\approx`
`10^(11)m` and
`r_(sun) = 10^(9)`m