If the Sun were halved in mass while maintaining its current radius, the gravitational force exerted by the Sun would decrease significantly, affecting the orbits of planets and other celestial bodies in the solar system.
Class 11 Physics
Gravitation
CBSE EXAM 2024-25
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By the principle of conservation of angular momentum, the orbital period ratio of two orbits is proportional to the ratio of their radii raised to the power of three-halves. For a new orbit with a radius reduced to half of the original, the ratio becomes (R₂/R₁)³/²= 1/2√2. Therefore, the new orbital period is 1/2√2 x T₁, where T₁ is the original period. If the initial period is 1 year, the new period becomes \1/2√2 years. This reduction indicates that the duration of the year will decrease significantly.
By conservation of angular momentum,
T₂/T₁ = (R₂/R₁)³/² = ((R₁/2)/R₁)³/² = 1/2√2
T₂ = 1/2√2 T₁ = 1/2√2 x 1 year = 1/2√2 year
Hence the duration of the year will become less.