Density of Asteroids, Escape Velcoity and Jumping

In summary, the maximum radius an asteroid can escape from by simply jumping is 470km. However, this isn't giving me the right answer. I've checked that it's 3.7km using a 10^-3 conversion factor.
  • #1
TFM
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[SOLVED] Density of Asteroids, Escape Velcoity and Jumping

Homework Statement



The question wants to know the maximum radius of an asteroid that you can escape from by simply jumpibng off.

The Variables given:
densities = 2500 kg/m cubed
radii = 470km downwards
height of jump = 1m

Homework Equations



v(Escape) = sqrt(GM/r)
m = d/r cubed
V squared = U squared + 2as (for initial jump speed)

The Attempt at a Solution


using a = 9.8 and s = 1, I calculated the initial jump speed is 4.43
rearranging the equation for EScape Velocity:
v(escape) = sqrt[(G(d/r cubed))/r]
v sqyared = (G(d/r cubed))/r
v squared = GD/r squared
r squared = Gd/v sqyared
r = sqrt [GD/v squared]

but this isn't giving me the right answer?
 
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  • #2
TFM said:
[
m = d/r cubed

This isn't right. mass is density * volume. and the volume of a sphere is?
 
Last edited:
  • #3
HI TFM,

It's given that you can jump 1 m on earth. Using that, find the speed you can generate at the start of the jump. Then apply that speed for v_escape to find r. All other data are given.
 
  • #4
The question assumes the asteroids are speherically symmetrical - which is why I should use the volume of a sphere, 4/3 Pi r cubed.

i.e:

(escape) = sqrt[(G(d/(4/3) pi r cubed))/r]

TFM
 
  • #5
TFM said:
The question assumes the asteroids are speherically symmetrical - which is why I should use the volume of a sphere, 4/3 Pi r cubed.

i.e:

(escape) = sqrt[(G(d/(4/3) pi r cubed))/r]

TFM

Yes, spherically symmetrical and of uniform density. However, the following formula you've written is not correct.

>
2. Homework Equations

v(Escape) = sqrt(GM/r)

>
 
  • #6
I've just checked -its sqrt[(2GM)/r]

this all gives:

R squared = (3*V escape squared)/(8*G*density*pi)

TFM
 
Last edited:
  • #7
I have now got the (right) answer of 3.7km (using a 10^-3 conversion factor):smile:

Thanks all,

TFM
 

Related to Density of Asteroids, Escape Velcoity and Jumping

1. What is the density of asteroids?

The density of asteroids can vary greatly depending on their composition and size. On average, the density of asteroids is around 2 grams per cubic centimeter, which is less dense than Earth's crust but more dense than water.

2. How is the density of an asteroid measured?

The density of an asteroid is typically measured by taking its mass and dividing it by its volume. This can be done using spacecraft observations, telescopic measurements, or by analyzing meteorites that have fallen to Earth.

3. What is escape velocity?

Escape velocity is the minimum speed that an object needs to reach in order to break free from the gravitational pull of another object. For example, the escape velocity of Earth is about 11.2 kilometers per second.

4. How does the density of an asteroid affect its escape velocity?

The density of an asteroid does not directly affect its escape velocity. However, a more massive and dense asteroid would require a higher escape velocity to break free from its own gravitational pull.

5. Can you jump on an asteroid?

Yes, you could technically jump on an asteroid. However, because most asteroids have a very weak gravitational force, your jump would likely result in you floating off the surface rather than coming back down.

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