the gravitational force between sun and jupiter is approximately 4×10²³N.if mass of sun =1.99×10³⁰kg, the mean distance of the Jupiter from the sun is 7.8×10¹¹m, find the mass of jupiter....
plz solve step by step
it's answer will be 1.8×10²⁷kg.
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• Given :-
The gravitational force between sun and Jupiter is approximately ( F ) = 4x10^23N.
The mass of the sun ( m₁ ) = 1.99x10^30 kg.
The mean distance of the Jupiter from the sun is ( r ) = 7.8x10^11 m.
• To find :-
The mass of Jupiter.
• Salutation :-
Let the mass of Jupiter be m₂
[ • Note :- So we need the value of m₂ ]
As the Newton's law of Gravitation
F = G × m₁ × m₂ / r²
[ • Where , G is the universal gravitational constant ]
[ G = 6.67 × 10^-11 N . m² ]
m₂ = r² × F / G × m₁
m₂ = { ( 7.8 x 10^11 )² × ( 4 × 10^23 ) } / { ( 6.67 × 10^-11 ) × ( 1.99 x 10^30 ) }
m₂ = ( 60.84 × 10^22 × 4 × 10^23 ) / ( 13.27 × 10^19 )
m₂ = ( 243.36 × 10^45 ) / ( 13.27 × 10^19 )
m₂ = 18.33 × 10^45 × 10^-19
m₂ = 18.33 × 10^26
•°• m₂ = 18.33 × 10^26 kg.
Therefore , the mass of Jupiter is 18.33 × 10^26 kg.
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