Q7.4: NCERT Physics - Part 1 GRAVITATION 7.4 Solution: Io, one of the satellites of Jupiter, has an orbital period of…

Question

Verified Solution • 2025–26 Session moderate

Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is

4.22 \times 10^8

m. Show that the mass of Jupiter is about one-thousandth that of the Sun.

Accepted Answer

**Answer:** Mass of Jupiter is about one-thousandth that of the Sun. **Step-by-Step Explanation:** For Io orbiting Jupiter:

T^2 = \frac{4\pi^2 r^3}{GM_J}

M_J = \frac{4\pi^2 r^3}{GT^2}

Substituting

r = 4.22 \times 10^8

m,

T = 1.769

days

= 1.769 \times 86400

s,

G = 6.67 \times 10^{-11}

N m_/kg_:

M_J = \frac{4\pi^2 (4.22 \times 10^8)^3}{6.67 \times 10^{-11} \times (1.769 \times 86400)^2} \approx 1.9 \times 10^{27} \text{ kg}

Mass of Sun

M_S = 2 \times 10^{30}

kg.

\frac{M_J}{M_S} = \frac{1.9 \times 10^{27}}{2 \times 10^{30}} \approx 9.5 \times 10^{-4} \approx 10^{-3}

Hence, the mass of Jupiter is about one-thousandth that of the Sun.

Step-by-Step Verified Solution