Through how many arc minutes does the Moon move in 76 minutes to the nearest arc minute?

Question

quick astronomy q:

Q: Through how many arc minutes does the Moon move in 76 minutes to the nearest arc minute?

would this question depend on where you are in the solar system?

if possible please provide a quick explanation of how you got it

Answer 1

zanti3 has the right answer, for an observer at the center of the Earth (or more exactly, the the Earth-Moon barycenter).

For someone on the surface, the Moon would seem to move a bit faster. For example, from Cape Canaveral, FL, the moon moves 1189 arc-minutes in 76 minutes.

Answer 2

I'm assuming this question applies to an observer on the Earth. To answer your second question first, an observer on Mars would see the Earth and Moon moving at a different pace, depending on how fast Mars rotates.

On the Earth: The moon rises about 50 minutes later each day, so it takes 24 hours and 50 minutes to travel a full 360 degrees. That's 1490 minutes for 360 * 60 = 21600 arc minutes.

Figuring out 76 minutes is just setting up a ratio: x/76 = 21600/1490, or x = 76 * 21600 / 1490, about 1100 arc minutes.

Answer 3

It's all a question of perspective.

Marsh's answer come from the orbit of the Moon with respect to the stars (as seen from the Earth), what is known as the sidereal month. The Moon moves 360 degrees around its orbit in one sidereal month of 27.3 days.
This is 360/27.3 = 13.19 degrees per day.
This is 13.19/(24 x 60) = 0.0092 degrees per minute.
This is 0.0092 x 76 x 60 = 42 arc minutes in 76 minutes.

The other answer factors in the motion of the Earth. The Earth rotates with respect to the stars in 23 hours and about 56 minutes (one sidereal day). Since we think we're standing still we see the stars (and the Moon and the planets) moving in the opposite direction at the same speed.
This is 360/(23+56/60) = 15.04 degrees per hour.
This is 15.04/60 = 0.25 degrees per minute.
This is 0.25 x 76 x 60 = 1143 arc minutes in 76 minutes.

The net motion of the Moon is thus 1143 (to the west along with the stars because of Earth's rotation) - 42 (to the east along its orbit) = 1101.

And don't forget we've used the average orbital speed of the Moon by simply dividing 360 degrees by the length of the sidereal month. The Moon's orbit is an ellipse so it will move faster at some points and slower at others.

Answer 4

42 arc minutes

Answer 5

as SEEN FROM THE EARTH THE MOMMOVEVES A DISTANCE EQUAL TO ITS DIAMETERON IN ONE HOURTHAQTS ABOUT 30 MINUTES OF ARCPER HOUR