Gravitation Field between the Earth and Moon

Homework Statement

There is a point on the line between the centres of the earth and the moon where their gravitational fields have equal magnitude but are in opposite directions, effectively creating a point of zero gravity. Calculate the distance of this point from the centre of the earth.

gearth = 9.81 ms$^{}-2$
mearth = 6.02 x10$^{}24$ kg

Homework Equations

F = GMm/d$^{}2$

g = -GM/d$^{}2$

The Attempt at a Solution

Using ratio of the inverse square laws Rm$^{}2$/Re$^{}2$ = Mm/Me
Using F = 0 and gearth = gmoon

tiny-tim
Homework Helper
hi rocketgirl93!

(try using the X2 and X2 buttons just above the Reply box )
gearth = 9.81 ms−2
mearth = 6.02 x1024 kg
you'll need a lot more data than that

Thanks for the hint!

Ok, I'll try find some more, its from this horrific textbook where they dont give you all the constants/data you need at the start of the questions and its scattered throughout the chapter.

HallsofIvy
Homework Helper
Thanks for the hint!

Ok, I'll try find some more, its from this horrific textbook where they dont give you all the constants/data you need at the start of the questions and its scattered throughout the chapter.
You mean they expect you to work? How awful!

I like Serena
Homework Helper
Hey rocketgirl93!

Suppose you sky rocketed to this mysterious point...
Shall we give it a name?
Let's call it... L1!
(Yes it's actually called L1. )

Here's a neat picture!

Oh, and just to get this started, how strongly would the moon pull at you?

I take Physics, I'm not afraid to work! It makes it difficult because you dont know what you have to find first and how they want you to approach the questions.

I've found these;

Orbital radius for the Moon: 3.84 x108m
Mass of the Moon: 7.35 x1022kg
Actual Radius of the Earth: 6400km

Hey rocketgirl93!

Suppose you sky rocketed to this mysterious point...
Shall we give it a name?
Let's call it... L1!
(Yes it's actually called L1. )

Here's a neat picture!

Oh, and just to get this started, how strongly would the moon pull at you?
Hi! Would it pull at you at about 1.64 m/s2? Or at 1.64 x mass?

I like Serena
Homework Helper
Good!

Looks like you have all the ingredients you need!

So what do you think you should do next?

Edit: how did you arrive at 1.64 m/s2?

D H
Staff Emeritus
Suppose you sky rocketed to this mysterious point...
Shall we give it a name?
Let's call it... L1!
(Yes it's actually called L1. )
No, it's not.

I like Serena
Homework Helper
No, it's not.
Oops. You're right.
I forgot for a moment about the centripetal force.

Ah well, it's still a nice picture!

D H
Staff Emeritus
I take Physics, I'm not afraid to work! It makes it difficult because you dont know what you have to find first and how they want you to approach the questions.

I've found these;

Orbital radius for the Moon: 3.84 x108m
Mass of the Moon: 7.35 x1022kg
Actual Radius of the Earth: 6400km
You don't need the radius of the Earth to solve this problem. You do need the mass of the Earth. You also need one very important item which you have left out. Hint: Newton's universal law of <what>?

I like Serena
Homework Helper
You don't need the radius of the Earth to solve this problem. You do need the mass of the Earth. You also need one very important item which you have left out. Hint: Newton's universal law of <what>?
Wouldn't the ratio of the inverse square laws do the trick?

tiny-tim
Homework Helper
You don't need the radius of the Earth to solve this problem.
since she has g, she needs re if she doesn't have G

D H
Staff Emeritus
Wouldn't the ratio of the inverse square laws do the trick?
What is this inverse square law to which you are referring? The original poster hasn't said anything about an inverse square law yet.

I like Serena
Homework Helper
What is this inverse square law to which you are referring? The original poster hasn't said anything about an inverse square law yet.
It's in the attempt at a solution in the OP.

D H
Staff Emeritus
Ah. I see that now.

So, another hint: If the point is at some distance d from the center of the Earth, how far is it from the center of the Moon?

Good!

Looks like you have all the ingredients you need!

So what do you think you should do next?

Edit: how did you arrive at 1.64 m/s2?
I didnt know what g for the moon was but I remembered reading somewhere that it is about one sixth of the earths g (9.81) so i calculated this figure and guessed

You don't need the radius of the Earth to solve this problem. You do need the mass of the Earth. You also need one very important item which you have left out. Hint: Newton's universal law of <what>?
Of Gravitation, I posted that in my original solution

since she has g, she needs re if she doesn't have G
I do have G: 6.67x10^-11

Ah. I see that now.

So, another hint: If the point is at some distance d from the center of the Earth, how far is it from the center of the Moon?
radius of the moon + distance between earth and moon + distance to point from surface of the earth

When you are on surface of the earth, force exerted by the earth,
F=ma= GMearthm/r2earth

F=6.6742x10-11 x 5.97x1024m/(6.38x106)2
F=m(9.7888) m/s2

The moon also exerted the same force according Newton's Gravitational law.
You find the radius where the forces are equal.

D H
Staff Emeritus
radius of the moon + distance between earth and moon + distance to point from surface of the earth
No! Draw a picture.

The distance between the Earth and Moon you cited in post #6 is center-to-center. You don't need the radius of the Earth or the Moon here.

I like Serena
Homework Helper
I didnt know what g for the moon was but I remembered reading somewhere that it is about one sixth of the earths g (9.81) so i calculated this figure and guessed

Of Gravitation, I posted that in my original solution

I do have G: 6.67x10^-11
Note the difference between g and G.
g is the acceleration of gravity at the surface of the earth.
G is the universal constant of gravity.
For this calculation you will not need g and if you want you can use G (which is in your formula), but you can also use your ratio of the inverse square law in which case you won't need G.

radius of the moon + distance between earth and moon + distance to point from surface of the earth
You seem to be mixing the radius of the earth itself and the distance of the equilibrium point to the center of the earth.
Both can be written as re or Re, but they are very different things.

For your problem you won't need the radius of either earth or moon.
But you do need to find the distance of the equilibrium point to the center of the earth, and also the distance of the equilibrium point to the center of the moon.

Using ratio of the inverse square laws Rm2/Re2 = Mm/Me
This is what you already wrote down and what you can use.
Note that Re and Rm are NOT the radius of either earth or moon.

simplyphysics