Estimating the radius of planets

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Discussion Overview

The discussion revolves around estimating the radius of a planet based on the conditions under which a person can escape its gravitational pull by leaping vertically. The problem involves assumptions about the planet's density being the same as Earth's and the relationship between escape velocity and gravitational acceleration.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant expresses uncertainty about the sufficiency of the information provided to solve the problem, particularly regarding the escape velocity.
  • Another participant suggests that the escape velocity can be expressed in terms of gravitational parameters, leading to a formula involving density and gravitational constant.
  • There is a question about whether to estimate the escape velocity or use another formula, indicating a lack of clarity on how to proceed.
  • One participant proposes that the vertical jumping speed of a man could be represented as k, but struggles to connect this with the gravitational acceleration of the planet.
  • A hint is provided that the jumping speed is independent of the gravitational acceleration of the planet, but this does not resolve the confusion for some participants.

Areas of Agreement / Disagreement

Participants generally express confusion and uncertainty about the problem, with no consensus on how to approach the estimation of the radius or the necessary variables involved.

Contextual Notes

Participants highlight the dependence on various variables, such as escape velocity and gravitational acceleration, which remain unspecified in the problem. There is also mention of the need for clarity on the relationship between jumping speed and gravitational parameters.

trina1990
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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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