Gravitation Field between the Earth and Moon

[rocketgirl93]

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]

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

 

[rocketgirl93]

Thanks for the hint!

Ok, I'll try find some more, its from this horrific textbook where they don't give you all the constants/data you need at the start of the questions and its scattered throughout the chapter.

 

[HallsofIvy]

Thanks for the hint!

Ok, I'll try find some more, its from this horrific textbook where they don't 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]

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?

 

[rocketgirl93]

I take Physics, I'm not afraid to work! It makes it difficult because you don't 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

 

[rocketgirl93]

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]

Good!

Looks like you have all the ingredients you need!
Your attempt was already in the right direction.

So what do you think you should do next?

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

 

[D H]

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]

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]

I take Physics, I'm not afraid to work! It makes it difficult because you don't 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]

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]

You don't need the radius of the Earth to solve this problem.

since she has g, she needs r_e if she doesn't have G

 

[D H]

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]

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]

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?

 

[rocketgirl93]

Good!

Looks like you have all the ingredients you need!
Your attempt was already in the right direction.

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 Earth's 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 r_e 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

 

[azizlwl]

When you are on surface of the earth, force exerted by the earth,
F=ma= GM_earthm/r²_earth

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]

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]

I didnt know what g for the moon was but I remembered reading somewhere that it is about one sixth of the Earth's 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 r_e or R_e, 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 R_m²/R_e² = M_m/M_e

This is what you already wrote down and what you can use.
Note that R_e and R_m are NOT the radius of either Earth or moon.