Estimating the radius of planets

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The discussion revolves around estimating the radius of a planet based on the escape velocity needed for a person to leap vertically upward. The initial calculations involve using the formula for escape velocity, but the participant struggles with determining the escape velocity, denoted as 'k', and its relation to the planet's gravitational acceleration. A key point raised is that the jumping speed of a person is independent of the planet's gravitational acceleration, which complicates the calculations. The participant seeks clarification on how to proceed without sufficient information, particularly regarding the gravitational conditions of the planet. The conversation highlights the need for a deeper understanding of the relationship between jumping speed and gravitational forces in this context.
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there' s a problem that tells " estimate the radius of a planet that a man can escape it's gravitation only by leaping vertically upward..that density of the planet is assumed to be same as earth..."

it seems to me that there's not enough information provided here to solve the problem..
i tried it this way,

escape velocity V= root over(2GM/R)
so R=2GM/V^2
and i fianally ended up with
R^2=3k^2/8pi PG ( here k=escape velocity of the planet, p= density of planet, G= gravitational constant)
now my question is i still don know the escape velocity of the planet, then should i guess here the velocity or i should apply other formula or other way to solve it...please help me solve it out....
 
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trina1990 said:
there' s a problem that tells " estimate the radius of a planet that a man can escape it's gravitation only by leaping vertically upward..that density of the planet is assumed to be same as earth..."

it seems to me that there's not enough information provided here to solve the problem..
i tried it this way,

escape velocity V= root over(2GM/R)
so R=2GM/V^2
and i fianally ended up with
R^2=3k^2/8pi PG ( here k=escape velocity of the planet, p= density of planet, G= gravitational constant)
now my question is i still don know the escape velocity of the planet, then should i guess here the velocity or i should apply other formula or other way to solve it...please help me solve it out....

What you are looking for are the conditions for which k= the vertical jumping speed of a man. So what does that suggest to you as to what you should use for k in your equation?
 
but unfortunately i could not get the point of estimating the vertical jumping speed of a man =k
may i try this way?
k=gt...?


then again i have to know the gravitational acceleration of the planet...another variable.
please provide me the specificity of theses problem...where the mystery of solution lies?
 
Last edited:
trina1990 said:
but unfortunately i could not get the point of estimating the vertical jumping speed of a man =k
may i try this way?
k=gt...?


then again i have to know the gravitational acceleration of the planet...another variable.
please provide me the specificity of theses problem...where the mystery of solution lies?

Hint: His jumping speed is independent the g of the planet.
 
hmm..i didn't get it
 

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