Moon without Earth: What if Earth Disappears?

[Timoothy]

If the Earth suddenly disappeared. and the moon started to travel in a straight line instead of its orbit of earth, would the moon continue to rotate on its axis every 27.3 days?

 

[tiny-tim]

Welcome to PF!

If the Earth suddenly disappeared. and the moon started to travel in a straight line instead of its orbit of earth, would the moon continue to rotate on its axis every 27.3 days?

Hi Timoothy! Welcome to PF!

Yes.

It would orbit the sun, of course, but its angular velocity would stay the same.

It is very difficult to change the angular velocity of a planet or satellite without actually colliding with it!

(You can make it lose energy through tidal forces, but that's about it.)

 

[Timoothy]

Hi Timoothy! Welcome to PF!

Yes.

It would orbit the sun, of course, but its angular velocity would stay the same.

It is very difficult to change the angular velocity of a planet or satellite without actually colliding with it!

(You can make it lose energy through tidal forces, but that's about it.)

Hi, and thanks for the welcome.

Well I've been talking to some people who say that since the moon is in a tidal-lock with earth, it doesn't rotate on its internal axis, so if Earth disappeared the moon would just orbit the sun and would not rotate on its internal axis every 27.3 days.

I'm just looking for some afferent opinions.
Thanks

 

[tiny-tim]

Well I've been talking to some people who say that since the moon is in a tidal-lock with earth, it doesn't rotate on its internal axis …

Timoothy, the rotation of the moon is a matter of geometry, not physics.

It quite obviously rotates (on an external axis by the way , not an internal one)!

 

[DaveC426913]

Hi, and thanks for the welcome.

Well I've been talking to some people who say that since the moon is in a tidal-lock with earth, it doesn't rotate on its internal axis,

They're wrong. It does. It rotates on its axis every 27.3 days. Earth disappearing will not make that suddenly stop.

Look at it from a point of view on Mars or anywhere else in the SS that's not on Earth. The Moon is most definitely rotating.

Alternately, look at it from the point of view of two dancers in a spin. They're effectively locked but if one let's go, the other will spin off into the crowd.

 

[Timoothy]

Timoothy, the rotation of the moon is a matter of geometry, not physics.

It quite obviously rotates (on an external axis by the way , not an internal one)!

So after Earth disappeared and the moon continues to rotate on an "external" axis every 27.3 (earth) days as it orbits the sun, would this "external" axis be closer to the moon or the sun?

 

[DaveC426913]

So after Earth disappeared and the moon continues to rotate on an "external" axis every 27.3 (earth) days as it orbits the sun, would this "external" axis be closer to the moon or the sun?

The Moon would proceed to rotate about its own (internal) axis.

In addition, it would also revolve around the new common barycentre of the Sun-Moon system (external axis), but it would revolve around it once per year.

So, these two would no longer be related.



I'm not sure how conservation of momentum would be preserved. Presumably, the disappearing Earth would take its momentum with it.

 

[Timoothy]

They're wrong. It does. It rotates on its axis every 27.3 days. Earth disappearing will not make that suddenly stop.

One of the arguments I've heard in favor of a moon that does not rotate on its internal axis is, since the moon is in a tidal-lock with earth, it does rotate on an axis during its orbit of earth, but this axis is the (barycenter), which is external, therefor the moon does not rotate on an internal axis.

I understand there's a barycenter, but i just can't imagine how the same side of the moon always faces Earth during its orbit of earth, unless the moon does rotate on its internal axis 1 time during its orbit of earth.

 

[Timoothy]

The Moon would proceed to rotate about its own (internal) axis.

I'm not sure how conservation of momentum would be preserved. Presumably, the disappearing Earth would take its momentum with it.

I'd guess the moon would still have the momentum it had before the Earth disappeared, and continue rotating on its internal axis every 27.3 days for a long long time, just about the same as when it orbited earth.

 

[russ_watters]

You could use the example of a ball on a string. If you swing it around your head, then release it, it will fly off in a tangent and continue to rotate at the same rate it was rotating when you were swinging it around your head.

 

[Timoothy]

You could use the example of a ball on a string. If you swing it around your head, then release it, it will fly off in a tangent and continue to rotate at the same rate it was rotating when you were swinging it around your head.

I actually did that experiment a couple of days ago with a two foot length of steel pipe with the string attached to one end of the pipe, and I was surprised that it started to rotate the instant I released the string, but just while ago I read the explanation for it in a different thread, and I now understand the velocity of the leading edge of the pipe was greater than the trailing edge, causing it to continue to rotate when the string was released.

 

[tiny-tim]

… external axis …

One of the arguments I've heard in favor of a moon that does not rotate on its internal axis is, since the moon is in a tidal-lock with earth, it does rotate on an axis during its orbit of earth, but this axis is the (barycenter), which is external, therefor the moon does not rotate on an internal axis.

I understand there's a barycenter, but i just can't imagine how the same side of the moon always faces Earth during its orbit of earth, unless the moon does rotate on its internal axis 1 time during its orbit of earth.

Hi Timoothy!

You're quite right … it is an external axis!

But that doesn't matter … the angular momentum is conserved irrespective of the axis … remember the pipe on the string spinning about an external axis first, then about an internal axis!

 

[Janus]

One of the arguments I've heard in favor of a moon that does not rotate on its internal axis is, since the moon is in a tidal-lock with earth, it does rotate on an axis during its orbit of earth, but this axis is the (barycenter), which is external, therefor the moon does not rotate on an internal axis.

A problem with this argument is that it neglects the fact that the Moon does not keep exactly the same face pointing at the Earth thoughout its orbit. The Moon's orbit around the Earth is slightly elliptical. As such its orbital speed varies as it moves in and out from the Earth. At perigee it takes less time for the Moon to cross 1 degree of the sky than it does at apogee. The Moon's rotation around its axis however is constant. It takes the same amount of time to rotate 1 degree through all points of its orbit. So the Moon, from the Earth, appears to rock slowly side to side a little so that we end up seeng a little more than half the Moon's surface. (this motion is called libration).

Also, the Moon's internal axis of rotation is tilted by 6 degrees from the axis of its orbit, much the way the Earth's axis is tilted with respect to the axis of its orbit. (So the Moon also appears to nod up and down a little as seen from the Earth.)

Put together, it is clear that the Moon's rotation around its internal axis and its orbit around the Earth-Moon barycenter are two separate motions that have the same period.

 

[Timoothy]

Hi Timoothy!

You're quite right … it is an external axis!

But that doesn't matter … the angular momentum is conserved irrespective of the axis … remember the pipe on the string spinning about an external axis first, then about an internal axis!

Yes, the axis was not the center of the pipe while it was attathed to the string and being spun overhead.

But that is, of course, a different condition from when the string was released.

And it's been my point of view all along that the moon rotates on its internal axis, and the earth-moon barycenter is an external axis, which doesn't change the fact that the moon does rotate one time on its internal axis each time it orbits earth.

When the string is released the pipe still has its angular momentum and will then rotate on its own internal axis, and if the moon was "released" from its orbit of Earth by the Earth disappearing, since the moon does rotate on its internal axis, it would continue to rotate on its internal axis every 27.3 days as it orbits the sun.

 

[russ_watters]

I actually did that experiment a couple of days ago with a two foot length of steel pipe with the string attached to one end of the pipe, and I was surprised that it started to rotate the instant I released the string, but just while ago I read the explanation for it in a different thread, and I now understand the velocity of the leading edge of the pipe was greater than the trailing edge, causing it to continue to rotate when the string was released.

Yes, I saw the thread after I posted the previous post. I don't like the way you worded it here, though. You should simply say that the pipe did not start to rotate when released, it merely continued to rotate when released. That stuff about the velocity of the leading and trailing edges is just going to confuse you. It is unnecessary. From your above post, it is really better to model the pipe's motion as two separate motions. I believe someone explained this in your other thread. One motion has the pipe modeled as a point mass, revolving around you, attached to the string. The other motion is the pipe's rotation around its axis. Using this method, it is easy to see that the two motions need not be considered one motion and if one is discontinued (ie, by releasing the string), the other need not also be discontinued. The same principle applies to the moon.

Janus - good point about libration. I tend to like to keep things simple and ignore complexities like that, but in this case, that minor complication adds a lot to the picture of how the motions are separate.