How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5 × 108 km

Asked by Pragya Singh | 1 year ago |  102

##### Solution :-

Given:

Earth’s orbit, r = 1.5 × 1011 m

Time taken by the Earth for one complete revolution,

T = 1 year = 365.25 days

i.e. T = (365.25 × 24 × 60 × 60) seconds

Since, Universal gravitational constant, G = 6.67 × 10–11 Nm2 kg–2

Therefore, mass of the Sun, M = $$\dfrac{4\;\pi ^{2}r^{3}}{G\;T^{2}}$$

$$\\\Rightarrow M =\dfrac{4\times (3.14)^{2}\times (1.5\times 10^{11})^{3}}{(6.67\times 10^{-11})\times (365.25\times 24\times 60\times 60)^{2}}$$

$$⇒ M=\dfrac{1.331\times 10^{35}}{66.425\times 10^{3}}$$

$$=2.004\times 10^{30}\;kgM$$

Therefore, the estimated mass of the Sun is 2.004 × 1030 Kg

Answered by Sudhanshu | 1 year ago

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