Moon -> Earth (Gravitational Pull help any comment welcome

[fishinbro321]

Moon --> Earth (Gravitational Pull... help please any comment welcome!

Homework Statement

At what distance (AU) does a spacecraft leaving the gravity of the Earth traveling toward the moon balance the gravity of the moon? I.E. What distance in (AU) will the object begin being affected by the Moon's gravity and not that of the Earth's strong gravity?

Earth Mass 5.9 x 10 24/pwr kg
Earth Gravitational Parameter, Gm earth: 3.986004418 x 10 12/pwr km/squared
Earths Eccentricity: .081819301

Moon Mass 7.3 x 10 22/pwr kg
Moon Gravitational field Parameter: J2= +0.02027 x 10/-3pwr
Distance between the Earth and the moon: 7.84 x 10 8/pwr meters

Homework Equations

Earth gravitational pull = 0? (At what point?)
Moon gravition pull = 0 (At what point?)

Example: Apollo 13, system failure. Astronaut had to do one last safe burn to enter a safe Earth orbit in order to avoid spinning out into infinity.

The Attempt at a Solution

I am struggling writing (pwr) in this blog if someone can tip me off on how to write them I can give my progress on this problem! Thanks for those interested parties that provide feedback, positive, negative or troll!

-James
Space Coast, FL

 

[LowlyPion]

Welcome to PF.

As to your problem draw a picture and recognize that D_e and D_m sum to the distance between Earth and Moon.

Your equations simplify then to

M_e/D_e² = M_m/D_m²

and

D_e + D_m = D_em

If you click the Quote button you can see the codes in all the posts.

 

[JoAuSc]

The question is at what radius r will the gravitational forces of the Earth and the Moon be equal. Do you know the formula for the gravitational force between two objects?

I.E. What distance in (AU) will the object begin being affected by the Moon's gravity and not that of the Earth's strong gravity?

[/QUOTE]

The object will always be affected by both the Earth and the Moon's gravity. The question is which force is larger.

 

[fishinbro321]

Welcome to PF.

As to your problem draw a picture and recognize that D_e and D_m sum to the distance between Earth and Moon.

Your equations simplify then to

M_e/D_e² = M_m/D_m²

and

D_e + D_m = D_em

If you click the Quote button you can see the codes in all the posts.

Wow mate~! Awesome response time and data points. I am curious if you could direct me to a web site, online source, etc. where that formula is from? I don't understand the variables of that formula. Both of the posters thus far are helping me see outside the box. I can't belv this website its so awesome. I called my mom with a headache from class today and she went onto google.com and found this site. Then tonight I joined it... Wow... Gotta keep pencilin I guess But i don't understand the variables of the formula yet...

-Happy James

 

[LowlyPion]

http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

Since the 2 forces must be equal at the tipping point,

GM_em/D_e² = G*M_mm/D_m²

That simplifies to the equation provided. (The m of the object simply cancels along with G)

The D's are distances to the centers of the Earth or moon.

 

[fishinbro321]

http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

Since the 2 forces must be equal at the tipping point,

GM_em/D_e² = G*M_mm/D_m²

That simplifies to the equation provided. (The m of the object simply cancels along with G)

The D's are distances to the centers of the Earth or moon.

SPECIFICALLY WRITTEN: At what distance from the Earth to the moon is the Earth's gravitational force equal to the Earth's gravitational force of the moon? This would be the accurate question I think my Aerospace Systems II Prof. is reaching for..

 

[fishinbro321]

I promise I am not mentally challenged. I am struggling with my book to find the attributes for the formula you gave me. I am not asking for the answer. I am asking if you can point me in the right direction by way of an outside web site. Where I can locate the data? I feel bad writing another help question really, but I see how this can be a valuable resource for assistance. I want to do the problem and find the answer but I can't seem to locate the data to plug into the formula.

-Last cry for help.
James
Space Coast, FL

 

[LowlyPion]

http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation
http://en.wikipedia.org/wiki/Earth
http://en.wikipedia.org/wiki/Moon

Honestly you can look it up as easily as anyone else.