Where between the Moon and the Earth is the gravitational potential=0 ?

[shk]

Homework Statement

Somewhere between the Earth and the Moon there is a point where the gravitational potential due to the Earth exactly equals that due to the Moon.
i)At what distance from the Earth is this point?
Mass of Earth = 5.98x10^24 kg
Mass of Moon= 7.35x10^22 kg
Distance between Earth and Moon = 3.84x1^8

ii) Is this the point at which the combined gravitational field is zero?Explain

b)
i) Explain why an astronaut in a spacecraft orbiting the Earth appears to be weightless?
ii)State the condition necessary for true weightlessness.

Homework Equations

V=GM/r
g=Gm/r^2

The Attempt at a Solution

I think
for part a ) i)
i need to equate the potential of moon and Earth to find the distance from the Earth.
for part a) ii)
I think the answer is no . because g is inversely proportional to r^2 and not r. but this pat is 3 marks so I may need to find that point by equation the g from moon and Earth. I am not really sure.
for b)i)
I think g is nearly zero in space so resultant force is zero. but this also doesn't make sense as there must be some forces as the astronaut is orbiting the Earth.
plus this is also 3 marks.
ii)I think weightlessness is when g is nearly zero

 

[PeroK]

For part a) you need to do some equations.

For part b), what does "apparently" weightless mean? In physics, something is what it is measured to be. How would you measure the weight of an astronaut in orbit?

This also helps to say what "true" weightlessness is.

 

[shk]

For part a) you need to do some equations.

For part b), what does "apparently" weightless mean? In physics, something is what it is measured to be. How would you measure the weight of an astronaut in orbit?

This also helps to say what "true" weightlessness is.

so your saying that what I have said for part a) i and ii are correct and I just need to add the equations and find those points!

for part b, i
probably this is what I need to do:

w=mv^2/r

as weight is the only force acting on the astronaut.
w=mg so by canceling the g's I'll get
g=v^2/r

but r is very big so g will be zero.
but I still don't know how to explain the apparent weightlessness and the true weightlessness

 

[PeroK]

so your saying that what I have said for part a) i and ii are correct and I just need to add the equations and find those points!

for part b, i
probably this is what I need to do:

w=mv^2/r

as weight is the only force acting on the astronaut.
w=mg so by canceling the g's I'll get
g=v^2/r

but r is very big so g will be zero.

$v$ might be big as well!

 

[haruspex]

true weightlessness

True weightlessness, with no other forces present, would produce what acceleration?

 

[shk]

$v$ might be big as well!

you are right.
so maybe I should put it this way:
g is less than 9.8 in space but surely is not still zero so the astronaut still has weight and the weight is the centripetal force . this explains the speed.
but because the person is not pushing on anything so there won't be a reaction on him so he feels weightless. like in a lift.
and the true weightless is probably at that point between Moon and Earth where the g's cancel each other out !

 

[shk]

True weightlessness, with no other forces present, would produce what acceleration?

zero?!

 

[haruspex]

zero?!

Right... and the acceleration of the astronaut is...?

 

[shk]

Right... and the acceleration of the astronaut is...?

I think the downward acceleration is g !

 

[haruspex]

I think the downward acceleration is g !

Little g is conventionally used for (average) gravitational acceleration at Earth's surface.

As for "downward", probably better to say "Earthward". My favourite Isaac Newton cartoon has him sitting under a tree contemplating an apple on the ground and observing "It fell down." The caption: Newton discovers tautology.

 

[shk]

Little g is conventionally used for (average) gravitational acceleration at Earth's surface.

As for "downward", probably better to say "Earthward". My favourite Isaac Newton cartoon has him sitting under a tree contemplating an apple on the ground and observing "It fell down." The caption: Newton discovers tautology.

I understand. I'd better say Earthward ;) thanks
But I still don't know what is the answer to this question. I need it for tomorrow. Can you please help me with this?
Thanks

 

[haruspex]

I understand. I'd better say Earthward ;) thanks
But I still don't know what is the answer to this question. I need it for tomorrow. Can you please help me with this?
Thanks

Think about how you are aware of your own weight. What force do you feel?

 

[shk]

$v$ might be big as well!

sorry but I need the answer to this question. Do you by any chance know the answer to help me with this. many thanks

 

[haruspex]

sorry but I need the answer to this question. Do you by any chance know the answer to help me with this. many thanks

Please try to answer post #12.

 

[shk]

Please try to answer post #12.

contact force/ normal reaction force

 

[haruspex]

contact force/ normal reaction force

Right! So apparent weightlessness consists of feeling no applied forces, so the only applied force is gravity. Real weightlessness consists of there being no gravity.

 

[shk]

Right! So apparent weightlessness consists of feeling no applied forces, so the only applied force is gravity. Real weightlessness consists of there being no gravity.

so you're saying that apparent weightlessness is when normal reaction force is zero. like in free fall. when the only force acting on the object is it's weight . but the true weightless only happens when g=0 ?

 

[haruspex]

so you're saying that apparent weightlessness is when normal reaction force is zero. like in free fall. when the only force acting on the object is it's weight . but the true weightless only happens when g=0 ?

Yes.

 

[shk]

Yes.

so the astronaut's feeling weightless because he is in free fall meaning there is no reaction force (N=0) .
and the condition of true weightlessness is when g=0.
fir the second one can i say this point can be somewhere between Moon and Earth where g's cancel each other out like we do for part a?
although i am not if it is ok to ignore the g of sun

 

[haruspex]

fir the second one can i say this point can be somewhere between Moon and Earth where g's cancel

Do you mean for b ii)?
You are only asked to state the condition. You are not asked for any specific example of where such a condition could arise, though you would not lose marks for adding that.

 

[Ravensong]

Isn't that L1? or am I getting my numbering order wrong on the moon's LaGrange points?

 

[haruspex]

Isn't that L1? or am I getting my numbering order wrong on the moon's LaGrange points?

No. It is a common misunderstanding that a Lagrange point is where gravitational fields cancel.
Rather, they are points where the net field leads to the same orbital period as the larger pair of bodies.
E.g. for the Earth and Sun as the major bodies, a Lagrange point is where a much smaller body would stay at constant distances from those two.