Gravity in space problem just asteroids instead help

[darthxepher]

Homework Statement

Between the orbits of Mars and Jupiter, several thousand small objects called asteroids move in nearly circular orbits around the Sun. Consider an asteroid that is spherically shaped with radius r and density 2400 kg/m^3.


Part A:


You find yourself on the surface of this asteroid and throw a baseball at a speed of 30 m/s. If the baseball is to travel around the asteroid in a circular orbit, what is the largest radius asteroid on which you are capable of accomplishing this feat?

Part B:

After you throw the baseball, you turn around and face the opposite direction and catch the baseball. How much time T elapses between your throw and your catch?

Homework Equations

D = mass/(4/3*pi*r^2)

A = v^2/r

The Attempt at a Solution

No attempts... Don't even know where to start...

Please help me with this...

 

[rl.bhat]

What is the relevant equation for the orbital velocity in terms of density, gravitational constant and radius?

 

[spacester]

Assuming D is for density, the first equation is incorrect. The denominator is supposed to be the volume of a sphere but the units are wrong.

IOW it should be r^3 not r^2

 

[darthxepher]

What's IOW? and I don't know the equation that relates density in terms of gravitational constants and such... I know density is mass/volume but other than that...

 

[spacester]

IOW = In Other Words

To characterize the orbit of anything around anything else, you need to know the mass.

It seems strange that you would be given this homework problem without being provided the equation you need.

 

[darthxepher]

YA it is odd... but my teacher... makes mistakes sometimes... Any clues as to what the equation is?

 

[Nabeshin]

Think about your equation for centripetal acceleration (a=v^2/r). What must this a be equal to? What is providing this force to produce this acceleration? What is the equation for this force? Then it's simply a matter of putting everything in terms of what you know: density, and velocity.

 

[spacester]

OK, but I'm kinda new here as far as answering questions and I don't want to get in trouble by making it too easy.

The missing equation is called "Newton's Law of Universal Gravitation" so you should see that this is not just some random equation, all it did was change *everything* and usher in the age of science. :-)

The equation A = v^2 / R does not seem to be relevant, but I'm prolly missing something basic.

http://ceres.hsc.edu/homepages/classes/astronomy/spring99/Mathematics/sec10.html

 

[spacester]

Think about your equation for centripetal acceleration (a=v^2/r). What must this a be equal to? What is providing this force to produce this acceleration? What is the equation for this force? Then it's simply a matter of putting everything in terms of what you know: density, and velocity.

D'oh! Good answer! That's likely what the problem's intent was, and I did make it too easy.

 

[rl.bhat]

YA it is odd... but my teacher... makes mistakes sometimes... Any clues as to what the equation is?

Have got any textbook? If you don't have, go to the library. Open the gravitation chapter. And try to find the relevant equations. At least that much effort you have to put to solve the problem. Don't blame the teacher.

 

[darthxepher]

Ok. so what I ended up getting was this

...

I set (G *m*M)/r^2=(m*v^2)/r

Then got:

v^2 = (G*M)/r

and then applied

2400= M/((4/3)*pi*r^3)

M = 1800*pi*r^3

then by substituting M in I got

r = ((v^2)/(G*1800*pi))^1/2

I plug in my numbers and get 490,000 and that is two sig figs... but i still don't get it!

 

[rl.bhat]

r = ((v^2)/(G*1800*pi))^1/2
Check this calculation.