How will you weight the sun, i.e. estimate its mass ? You will need to know the period of one of its planets and the radius of the planetary orbit. The mean orbit radius of the earth around the sun is `1.5 xx 10^(8)km`, then the mass of the sun would be calculated as

Options

A. `2 xx 10^(15)kg`
B. `2 xx 10^(20)kg`
C. `2 xx 10^(27)kg`
D. `2xx 10^(30)kg`

Answer

D

Explanation

Mean orbital radius of the earth around the sun,
`r = 1.5 xx 10^(8) km = 1.5 xx 10^(11)m`
The period of the earth around the sun
`= 1yr = 365` days
`=365 xx 24 xx 60 xx 60s`
As, required centripetal force is obtained from the gravitational force, therefore
Centripetal force = Gravitational force
`(mv^(2))/(r) = (GM_(s)m)/(r^(2)), v^(2) = (GM_(s))/(r)`
`(r omega)^(2) = (GM_(s))/(r)` or `omega^(2) = (GM_(s))/(r^(3)) [ :' v = r omega]`
But, `omega = (2pi)/(T)`
`:. ((2pi)/(T))^(2) =(GM_(s))/(r^(3))` or `M_(s) = (4pi^(2)r^(3))/(GT^(2))`
`= (4xx (3.14)^(2)xx (1.5xx 10^(11))^(3))/(6.67 xx 10^(-11)(365 xx 24xx 60 xx 60)^(2))`
`~~ 2xx 10^(30)kg`