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. Question 8.13 Gravitation
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Mean orbital radius of earth around the sun = 1.5×10¹¹ m
Time period (T) = 1 Yr
= 365 × 24 × 3600 s
Let mass of the sun = Ms
Mass of the planet = m
We know,
Centripetal force = Gravitational force
mv²/r = GMsm/r²
v² = GMs/r
(2πr/T)² = GMs/r
Ms = 4π²r³/GT²
Put the values of r , G , and T
Ms = 4×(3.14)² × (1.5×10¹¹)³/6.67×10^-11×(365×24×3600)
≈ 2 × 10^30 Kg
Time period (T) = 1 Yr
= 365 × 24 × 3600 s
Let mass of the sun = Ms
Mass of the planet = m
We know,
Centripetal force = Gravitational force
mv²/r = GMsm/r²
v² = GMs/r
(2πr/T)² = GMs/r
Ms = 4π²r³/GT²
Put the values of r , G , and T
Ms = 4×(3.14)² × (1.5×10¹¹)³/6.67×10^-11×(365×24×3600)
≈ 2 × 10^30 Kg
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