Ground speed of moon on earth

[Saber]

Whats the   ground speed of moon on the  surface of earth ? i mean the speed of the point that the moon  is exactly  above it ?

 

Is it the speed of earth rotating around its self   minus the ground  speed of moon orbiting earth ? As  both  revolutions are towards east  ?

Thanx

To calculate that  do we have to subtract the  angular speed of moon  rotating earth  from the  angular speed of earth rotating its self    then  project that  angular speed on to  earth  radius ?

Edited June 14, 2023 by Saber

[Genady]

This question is the same as to ask, what is the speed of the Moon's shadow on the Earth's surface. This has been discussed here: https://www.scienceforums.net/topic/131698-moon-shadow/

 

The simple case answer, on the equator, with a back-of-the-envelope calculation was: (https://www.scienceforums.net/topic/131698-moon-shadow/?do=findComment&comment=1240426)

The Earth spins from West to East making a full circle in 1 day. The Moon rotates around the Earth from West to East making a full circle in 30 days. OTOH, the radius of the Moon's circle is about 300000 km while the Earth's radius is about 6000 km. This makes the Moon's circle 50 times longer. The Moon makes 50 times longer way in 30 times longer time, i.e., it moves from West to East 50/30 times faster than the Earth surface. Thus, its shadow should move to the East faster than the Earth surface does, hence its shadow on the Earth surface moves to the East.  

 

[Saber]

Are these calculations  right ?  
The moon  orbits earth  every   27.3 days ( 655.2 hours )    so   its  360/ 655.2  =  0.549 Deg per hour

And earth  rotates around its self every 24  hours   so its   15 Deg per hour    and so moons projection on  earths  surface moves 14.451 Deg per hour

And the  earth's Circumstance is 40075 Km   and that makes every Deg equal to 111.319 Km

So 14.451  Deg   =1607.67    So   moons projection on  earths  surface   aka moons  ground speed is  1607.67  Km/H   

Are   these calculations  right ?

Moons  orbit also has a 5.142 Deg incline    do we have to  take that into the calculations as well ?

[Genady]

The other comments in that thread show the complications in real situation. The answer depends where on Earth is the point above which the Moon is in zenith.

15 minutes ago, Saber said:

Are these calculations  right ?  
The moon  orbits earth  every   27.3 days ( 655.2 hours )    so   its  360/ 655.2  =  0.549 Deg per hour

And earth  rotates around its self every 24  hours   so its   15 Deg per hour    and so moons projection on  earths  surface moves 14.451 Deg per hour

And the  earth's Circumstance is 40075 Km   and that makes every Deg equal to 111.319 Km

So 14.451  Deg   =1607.67    So   moons projection on  earths  surface   aka moons  ground speed is  1607.67  Km/H   

Are   these calculations  right ?

Moons  orbit also has a 5.142 Deg incline    do we have to  take that into the calculations as well ?

No, these calculations are incorrect. The Moon's projection on the Earth surface doesn't move 14.451 degrees per hour. You need to compare linear velocities rather than the angular ones.

[Saber]

15 minutes ago, Genady said:

The other comments in that thread show the complications in real situation. The answer depends where on Earth is the point above which the Moon is in zenith.

No, these calculations are incorrect. The Moon's projection on the Earth surface doesn't move 14.451 degrees per hour. You need to compare linear velocities rather than the angular ones.

The thing  you  are talking about  (  the moons  shadow )   is like  this

 

 

That  varies  according to where the shadow  is on  earth  surface........it moves faster when it enters or  want to  exit   the surface  that  when  it  on the middle

 

The thing  i  have in mind is  like this ............

 

 

The point that  moon is right above its  head......

 

[Genady]

4 minutes ago, Saber said:

The thing  you  are talking about  (  the moons  shadow )   is like  this

 

 

That  varies  according to where the shadow  is on  earth  surface........it moves faster when it enters or  want to  exit   the surface  that  when  it  on the middle

 

The thing  i  have in mind is  like this ............

 

 

The point that  moon is right above its  head......

 

Yes, I see now that your question is different. You're right then, the distance to the Moon does not matter. However, you can add the angles only if they are aligned, which they generally are not. Also, the Earth circumference is only important if the point is on the equator, which it generally is not.

[Saber]

So  i guess i had to  use another word  instead of ( projection )

 

Maybe   radial  projection  ?

Edited June 14, 2023 by Saber

[Genady]

17 minutes ago, Saber said:

So  i guess i had to  use another word  instead of ( projection )

 

Maybe   radial  projection  ?

Sublunar point.

[Saber]

So  for  the  subsolar  point  are these right ?

One year = 8766 hours   so  360/ 8766    so   0.041 Deg/H   Subsolar point travels W to E

One day..... 360/24 so  15Deg/H   Subsolar point  travels E to W

So speed of SS point =  15.041 Deg/H  =  1674.64 Km/H

[Genady]

34 minutes ago, Saber said:

So  for  the  subsolar  point  are these right ?

One year = 8766 hours   so  360/ 8766    so   0.041 Deg/H   Subsolar point travels W to E

One day..... 360/24 so  15Deg/H   Subsolar point  travels E to W

So speed of SS point =  15.041 Deg/H  =  1674.64 Km/H

I think that because you calculate for the solar day, i.e., 24 hours, you need to add the annual movement of the Sun.

OTOH, if you calculate for a sidereal day, which is 23 h 56 minutes, you get directly 360/(23h56min) = 15.041.

[Janus]

A factor you need to consider is that the Moon does not orbit over the Equator, and it's orbital plane is ~ 5 degrees from the ecliptic. 

This video gives an idea of the Moon's path over the Earth.  The camera tracks wit the Moon, and the Red dot shows where the "Earth-Moon joining line intersects the Earth's surface.  It not ~100% accurate as I made the Moon's orbit exactly 28 sidereal days long to keep it simple.

The path starts North of the Equator, drifts South and then back again.

[Saber]

4 minutes ago, Janus said:

A factor you need to consider is that the Moon does not orbit over the Equator, and it's orbital plane is ~ 5 degrees from the ecliptic. 

This video gives an idea of the Moon's path over the Earth.  The camera tracks wit the Moon, and the Red dot shows where the "Earth-Moon joining line intersects the Earth's surface.  It not ~100% accurate as I made the Moon's orbit exactly 28 sidereal days long to keep it simple.

The path starts North of the Equator, drifts South and then back again.

Thanx    i mentioned  that  incline in the 3rd post

Why  dont posts have numbers here ?

[iNow]

They do, they’re just not presented via the UI outside of the URL

[Airbrush]

On 6/14/2023 at 8:46 AM, Saber said:

Whats the   ground speed of moon on the  surface of earth ? i mean the speed of the point that the moon  is exactly  above it ?

 

Is it the speed of earth rotating around its self   minus the ground  speed of moon orbiting earth ? As  both  revolutions are towards east  ?

Thanx

To calculate that  do we have to subtract the  angular speed of moon  rotating earth  from the  angular speed of earth rotating its self    then  project that  angular speed on to  earth  radius ?

Interesting question.  The Earth rotates about 1,000 miles per hour at the equator.  According to Wikipedia the Moon's average orbital speed is about 1 km/second, or 2237 miles per hour.  So, the Moon's orbital speed is a over twice as fast as the Earth rotates.  That is easy to understand and remember.

Moon - Wikipedia

Edited June 29, 2023 by Airbrush

[Janus]

On 6/29/2023 at 4:43 PM, Airbrush said:

Interesting question.  The Earth rotates about 1,000 miles per hour at the equator.  According to Wikipedia the Moon's average orbital speed is about 1 km/second, or 2237 miles per hour.  So, the Moon's orbital speed is a over twice as fast as the Earth rotates.  That is easy to understand and remember.

Moon - Wikipedia

I really don't think that's a useful way of looking at it.  Consider this, The orbital speed of a geostationary satellite is 6.6 times that of the equatorial speed at the surface.  But a geostationary satellite stays in exactly the same position relative to any point on the ground at all times, so in effect, its "ground speed" is zero.

[Airbrush]

On 7/1/2023 at 9:56 AM, Janus said:

I really don't think that's a useful way of looking at it.  Consider this, The orbital speed of a geostationary satellite is 6.6 times that of the equatorial speed at the surface.  But a geostationary satellite stays in exactly the same position relative to any point on the ground at all times, so in effect, its "ground speed" is zero.

I wish you could explain this a little bit more, because I don't understand your point.  A geostationary satellite is moving a little faster than 1,000 miles per hour, because it is covering a little more distance than the ground that it hovers over, and the ground is already moving 1,000 mph.  "Ground speed" is never zero in my understanding.  But I am not an expert.

[swansont]

32 minutes ago, Airbrush said:

I wish you could explain this a little bit more, because I don't understand your point.  A geostationary satellite is moving a little faster than 1,000 miles per hour, because it is covering a little more distance than the ground that it hovers over, and the ground is already moving 1,000 mph.  "Ground speed" is never zero in my understanding.  But I am not an expert.

It’s covering more distance by a lot. A geostationary orbit is ~35,800 km in altitude (~42,200 km from center) as opposed to the 6400 km radius. As Janus says, that’s 6.6 times further out, so it covers a circumference 6.6 times as big in the same time - it’s moving 6.6 times faster. But its ground speed is basically zero.

 

[Airbrush]

Wow!  I never realized that a geostationary orbit was so high an altitude.  35,800 km means over 22,000 miles high, which is almost one tenth the distance to the moon.  Anyone have an idea of how many geostationary satellites the US has hovering over North Korea?

[swansont]

19 minutes ago, Airbrush said:

Wow!  I never realized that a geostationary orbit was so high an altitude.  35,800 km means over 22,000 miles high, which is almost one tenth the distance to the moon.  Anyone have an idea of how many geostationary satellites the US has hovering over North Korea?

None. Geostationary orbits are equatorial 

[Janus]

In addition to swansot's comment, putting a spy satellite that high would make it pretty useless as its image resolution would not be very good.

Generally, they would be put into much lower polar orbits.

So the Earth rotates under it, allowing it to observe pretty much any point on the surface over time. The particular orbit in the image is a Sun synchronous one. This means that as the satellite passes over a particular point of the Earth's surface, it is being lit the same by the Sun. This assures that differences in images between successive passes aren't due to different lighting angles from the Sun.

[Airbrush]

On 7/15/2023 at 9:22 AM, Janus said:

In addition to swansot's comment, putting a spy satellite that high would make it pretty useless as its image resolution would not be very good.

Generally, they would be put into much lower polar orbits.

So the Earth rotates under it, allowing it to observe pretty much any point on the surface over time. The particular orbit in the image is a Sun synchronous one. This means that as the satellite passes over a particular point of the Earth's surface, it is being lit the same by the Sun. This assures that differences in images between successive passes aren't due to different lighting angles from the Sun.

Very interesting, thanks for the info!