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Q7.13: NCERT Physics - Part 1 GRAVITATION 7.13 Solution: How will you 'weigh the sun', that is estimate its mass? The…

⚠️ Common Exam Traps & Conceptual Pitfalls

When applying Kepler’s third law, every quantity must be in SI units. The mean orbital radius is given as $1.5 imes10^8$ km, which must be converted to $1.5 imes10^{11}$ m before substituting into $T^2= rac{4pi^2 r^3}{GM}$. Using the radius in km (or any non‑SI unit) will produce a mass that is off by a factor of $10^9$.

How will you 'weigh the sun', that is estimate its mass? The mean orbital radius of the earth around the sun is 1.5×1081.5 \times 10^8 km.

Step-by-Step Verified Solution

**Answer:** Mass of Sun =2×1030= 2 \times 10^{30} kg. **Step-by-Step Explanation:** Using T2=4π2r3GMST^2 = \frac{4\pi^2 r^3}{GM_S} with T=1T = 1 year =3.15×107= 3.15 \times 10^7 s and r=1.5×1011r = 1.5 \times 10^{11} m:
MS=4π2r3GT2=4π2(1.5×1011)36.67×10−11×(3.15×107)2=2×1030 kgM_S = \frac{4\pi^2 r^3}{GT^2} = \frac{4\pi^2 (1.5 \times 10^{11})^3}{6.67 \times 10^{-11} \times (3.15 \times 10^7)^2} = 2 \times 10^{30} \text{ kg}

All Questions in this Chapter

Q7.1 Q7.2 Q7.3 Q7.4 Q7.5 Q7.6 Q7.7 Q7.8 Q7.9 Q7.10 Q7.11 Q7.12 Q7.13 Q7.14 Q7.15 Q7.16 Q7.17 Q7.18 Q7.19 Q7.20 Q7.21

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