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i have a question-

Find approximately the 3rd cosmic velocity v3, i.e. the minimum velocity that has to be imparted to a body relative to the Earth's surface to drive it out of the solar system.The rotation of the Earth about its own axis is to be neglected.

just as we deduce escape velocity,i went for the following equation-

-(GMm)/R -(GM'm)/r +mv3^2/2 =0

or,v3={2GM/R +2GM'/r}^1/2

However,the answer is v3~{2GM/R +(2^0.5-1)^2.GM'/r}^1/2

~17 Km/s [~means approximately;can't get the real sign]

Here,M=earth's mass

M'=Sun's mass

R=earth's radius

r=radius of earth's orbit.

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this is not a homework.thanking you all in advance

Find approximately the 3rd cosmic velocity v3, i.e. the minimum velocity that has to be imparted to a body relative to the Earth's surface to drive it out of the solar system.The rotation of the Earth about its own axis is to be neglected.

just as we deduce escape velocity,i went for the following equation-

-(GMm)/R -(GM'm)/r +mv3^2/2 =0

or,v3={2GM/R +2GM'/r}^1/2

However,the answer is v3~{2GM/R +(2^0.5-1)^2.GM'/r}^1/2

~17 Km/s [~means approximately;can't get the real sign]

Here,M=earth's mass

M'=Sun's mass

R=earth's radius

r=radius of earth's orbit.

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this is not a homework.thanking you all in advance

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