Moon -> Earth (Gravitational Pull help any comment welcome

The thing is, you need to have some understanding of the concepts. You don't understand what the formula means or how to use it. You don't understand the concept of center of mass. This is why you are having trouble. It's not about the data, it's about understanding the concepts.
  • #1
fishinbro321
4
0
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
 
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  • #2


Welcome to PF.

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

Your equations simplify then to

Me/De2 = Mm/Dm2

and

De + Dm = Dem

If you click the Quote button you can see the codes in all the posts.
 
  • #3


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?

fishinbro321 said:
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.
 
  • #4


LowlyPion said:
Welcome to PF.

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

Your equations simplify then to

Me/De2 = Mm/Dm2

and

De + Dm = Dem

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
 
  • #6


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

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

GMem/De2 = G*Mmm/Dm2

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..
 
  • #7


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
 

Related to Moon -> Earth (Gravitational Pull help any comment welcome

1. What is the gravitational pull between the Moon and Earth?

The gravitational pull between the Moon and Earth is approximately 1.98 x 10^20 Newtons (N) or 1.98 x 10^17 kilograms (kg).

2. How does the Moon's gravitational pull affect Earth?

The Moon's gravitational pull affects Earth in several ways. It creates tides in the oceans, which are caused by the Moon's gravitational pull on the Earth's water. It also causes the Earth to slightly bulge towards the Moon, resulting in small changes in the Earth's shape. Additionally, the Moon's gravitational pull helps stabilize the Earth's tilt, which affects our climate and seasons.

3. Does the Moon's gravitational pull affect the Earth's orbit?

Yes, the Moon's gravitational pull affects the Earth's orbit. The Moon's gravity pulls on the Earth, causing it to slightly wobble and change its orbit. This effect is known as "orbital precession" and causes the Earth's orbit to change slightly over time.

4. Can the Moon's gravitational pull ever cause the Earth to crash into it?

No, the Moon's gravitational pull is not strong enough to pull the Earth into a collision. In fact, the Moon is slowly moving away from the Earth due to tidal forces, so the distance between the two objects is actually increasing.

5. How does the Moon's gravitational pull compare to Earth's?

The Moon's gravitational pull is about 1/6th of Earth's gravitational pull. This means that if you weighed 100 pounds on Earth, you would only weigh about 16.6 pounds on the Moon. This is because the Moon has less mass than Earth and therefore has less gravitational force.

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