image
Physics Forums Logo
image
image
* Register * Upgrade Blogs Library Staff Rules Mark Forums Read
image
image   image
image

image Gravitation problem Share It Thread Tools Search this Thread image
Old Oct3-05, 10:56 PM                  #1
jakeowens

jakeowens is Offline:
Posts: 34
Gravitation problem

Here's the problem i've been working on.

Gold has density of 19.3x103 kg/m3. How big would a solid gold sphere have to be if the acceleration due to gravity at its surface is to be 9.87 m/s2? (Check your answer against the radius of the Earth, which has a mean density of 5.5x103 kg/m3.)

Now I'm probably making this way to hard, and I am completely lost, and was wondering if anyone could help me out. The only way i could think to do this problem, was to calculate out the mass, then the radius, and volume of the earth. Then use the density of gold to find out how large a gold ball would have to be to be the same weight as earth.

But then when i get the radius of the gold ball and plug it into the equation g=G*(Me/Re^2) which should equal 9.87, but it equals like 15. so i know i screwed up somewhere.

I just cant think of how to do this problem.

any help is much appreciated
  Reply With Quote
Old Oct3-05, 11:07 PM                  #2
jakeowens

jakeowens is Offline:
Posts: 34
Either my problems are incredibly hard, and expect way to much from you, or i am being stupid and trying to do things the hard way.

Each of the Apollo Lunar Modules was in a very low orbit around the Moon. Given a typical mass of 14.7 E 3 kg, assume an altitude of 64.0 km and determine the orbital period.

this problem has me stumped to. I find myself having to look up things on the internet, such as the mass of the moon and radius of the moon and crap like that. This can't possibly be that involved can it. So that's why i think i'm doing this all wrong, and was just wondering if anyone could point me in the right direction.
  Reply With Quote
Old Oct3-05, 11:34 PM                  #3
SpaceTiger

SpaceTiger is Offline:
Posts: 2,931
Recognitions:
PF Contributor PF Contributor
Science Advisor Science Advisor
Retired Staff Retired Staff
Originally Posted by jakeowens
Gold has density of 19.3x103 kg/m3. How big would a solid gold sphere have to be if the acceleration due to gravity at its surface is to be 9.87 m/s2? (Check your answer against the radius of the Earth, which has a mean density of 5.5x103 kg/m3.)
Consider the equation for acceleration due to gravity:

LaTeX Code: g=\\frac{GM}{r^2}

Consider also the equation relating mass, density, and size:

LaTeX Code: M=\\frac{4}{3}\\pi r^3 \\rho

Can you see a way to combine those equations to get a size, given acceleration and density?

Forget about the earth, it's a red herring, all you need to know is its acceleration due to gravity (9.8 m/s^2).
  Reply With Quote
Old Oct3-05, 11:37 PM                  #4
SpaceTiger

SpaceTiger is Offline:
Posts: 2,931
Recognitions:
PF Contributor PF Contributor
Science Advisor Science Advisor
Retired Staff Retired Staff
Originally Posted by jakeowens
Each of the Apollo Lunar Modules was in a very low orbit around the Moon. Given a typical mass of 14.7 E 3 kg, assume an altitude of 64.0 km and determine the orbital period.
Consider Kepler's Third Law:

LaTeX Code: P^2=\\frac{4\\pi^2a^3}{GM}

Hint: You don't need the mass of the module.
  Reply With Quote
Old Oct4-05, 12:10 AM                  #5
jakeowens

jakeowens is Offline:
Posts: 34
what does that p looking sign mean in your first post, is that density?
  Reply With Quote
Old Oct4-05, 12:16 AM                  #6
jakeowens

jakeowens is Offline:
Posts: 34
Alright i got the first problem now, thanks. Hadnt considered combining those 2 problems, going to work on the 2nd now :D
  Reply With Quote
Old Oct4-05, 12:21 AM                  #7
jakeowens

jakeowens is Offline:
Posts: 34
what do you mean i dont need the weight of the module? I'm having a hard time with this one. What values am i supposed to use for a? or M?
  Reply With Quote
Old Oct4-05, 01:03 AM                  #8
SpaceTiger

SpaceTiger is Offline:
Posts: 2,931
Recognitions:
PF Contributor PF Contributor
Science Advisor Science Advisor
Retired Staff Retired Staff
Originally Posted by jakeowens
what do you mean i dont need the weight of the module? I'm having a hard time with this one. What values am i supposed to use for a? or M?
Kepler's Third Law relates the period of an orbiting body to the semimajor axis of its orbit and the mass of the body around which it orbits. In a circular orbit, the semimajor axis is just the radius of the orbit.
  Reply With Quote
image image
Reply
Thread Tools


Similar Threads for: Gravitation problem
Thread Thread Starter Forum Replies Last Post
Gravitation Problem :( kim3648 Introductory Physics 3 Dec12-07 04:27 AM
Gravitation problem Collegestudent5 Introductory Physics 1 Nov7-07 12:54 AM
Gravitation problem Gauss177 Introductory Physics 2 Dec19-06 11:25 PM
help please with gravitation problem nick727kcin Introductory Physics 5 Mar21-06 07:10 PM
gravitation problem melodrameric Introductory Physics 4 Nov22-05 12:38 AM

Powered by vBulletin Copyright ©2000 - 2009, Jelsoft Enterprises Ltd. © 2009 Physics Forums
Sciam | physorgPhysorg.com Science News Partner
image
image   image