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Estimate the mass of the sun, assuming t...

Estimate the mass of the sun, assuming the orbit of Earth around the sun to be a circle. The distance between the sun and the Earth is `1.49 xx 10^(11) m`, and `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.

Text Solution

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Here the revolving speed of earth can be given as
`v = sqrt((GM)/(r ))` [Orbital speed]
Where M is the mass of sun and r is the orbit radius of earth.
We know time period of earth around sun is `T = 365` days, thus we have
`T = (2 pi r)/(v )`
or `T =2pi r sqrt((r )/(GM))`
or `M = (4pi^(2)r^(3))/(GT^(2))`
`= (4xx(3.14)^(2)xx(1.49xx10^(11))^(3))/((365xx24x3600)^(2)xx(6.66xx10^(-11)))=1.972xx10^(22)kg`
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