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

## 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.

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

Related Introductory Physics Homework Help News on Phys.org
PeroK
Homework Helper
Gold Member
2020 Award
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
Homework Helper
Gold Member
2020 Award
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!

• shk
haruspex
Homework Helper
Gold Member
2020 Award
true weightlessness
True weightlessness, with no other forces present, would produce what acceleration?

##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 !

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

haruspex
Homework Helper
Gold Member
2020 Award
zero?!
Right... and the acceleration of the astronaut is...?

Right... and the acceleration of the astronaut is...?
I think the downward acceleration is g !

haruspex
Homework Helper
Gold Member
2020 Award
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.

• SammyS, shk and gneill
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
Homework Helper
Gold Member
2020 Award
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?

##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
Homework Helper
Gold Member
2020 Award
sorry but I need the answer to this question. Do you by any chance know the answer to help me with this. many thanks

contact force/ normal reaction force

haruspex
Homework Helper
Gold Member
2020 Award
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.

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
Homework Helper
Gold Member
2020 Award
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.

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
Homework Helper
Gold Member
2020 Award
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.

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

haruspex