Estimating the radius of planets

In summary, the problem states that we need to estimate the radius of a planet that a man can escape its gravitation by jumping vertically upward. However, there is not enough information provided to solve the problem. One approach is to use the equation for escape velocity, but this requires knowing the escape velocity of the planet. Another approach is to use the equation R^2=3k^2/8pi PG, where k is the vertical jumping speed of a man, p is the density of the planet, and G is the gravitational constant. However, the value of k and the gravitational acceleration of the planet are still unknown. Therefore, further specificity is needed to solve the problem.
  • #1
trina1990
24
0
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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  • #2
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?
 
  • #3
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:
  • #4
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.
 
  • #5
hmm..i didn't get it
 

FAQ: Estimating the radius of planets

1. How is the radius of a planet calculated?

The radius of a planet is calculated by measuring its diameter at the equator and then dividing it by 2. This measurement can be taken using telescopes, spacecraft, or radar imaging techniques.

2. What is the unit of measurement used for the radius of a planet?

The radius of a planet is typically measured in kilometers (km) or miles (mi). In scientific calculations, the radius may also be represented in meters (m) or astronomical units (AU).

3. Why is estimating the radius of planets important?

Estimating the radius of planets is important for understanding the size and structure of the planet, as well as its potential for supporting life. It also helps in determining the planet's mass and density, which can give insights into its composition and formation.

4. How accurate are estimates of planet radii?

Estimates of planet radii can vary depending on the method used and the precision of the measurements. In general, estimates of planet radii have become more accurate with advancements in technology and techniques.

5. Can the radius of a planet change over time?

Yes, the radius of a planet can change over time due to various factors such as volcanic activity, tectonic movements, or impacts from other objects in space. However, these changes are usually very small and can take millions of years to occur.

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