what is the value for the rate at which the moon orbits the earth assume that moon's orbit is circular

You can calculate that from the moon's distance from the earth and the gravitational forces. Here's a lecture on it. Look for "Moon".

Lecture 8

The Moon is about 239,228 miles from the Earth's center.

It makes one revolution in 27.3 days.

miles in one revolution.

Divide by 27.3 and then by 24 and we get about 2,294 mph as it travels around the Earth.

You did not say what units you were working in. metric? English?

This is approximate. Perito's site would be more precise.

Answer with the Compliments of World Book:-



MOON/How the moon moves

The orbit of the moon. The moon travels around the earth in an elliptical (oval shaped) path called an orbit. One such trip around the earth is called a revolution. The moon moves at an average speed of about 2,300 miles (3,700 kilometers) per hour along its 1.4-million-mile (2.3-million-kilometer) orbit.

The moon also travels with the earth as the earth circles the sun every 3651/4 days, an earth year. The moon actually moves from west to east in the sky. But it seems to move from east to west as it rises and sets because the earth spins much faster than the moon revolves around the earth.

Because the moon's orbit is oval, the moon is not always the same distance from the earth. The point where the moon comes closest to the earth is 221,456 miles (356,399 kilometers) away. This point is called the moon's perigee. The moon's farthest point from the earth is 252,711 miles (406,699 kilometers) away. This point is the moon's apogee.

The gravitational pull of the earth keeps the moon in its orbit. If the earth or its gravitational force were to suddenly disappear, the moon would no longer orbit the earth. But the moon would still move in orbit around the sun.

Scientists measure the moon's revolution around the earth in synodic months and sidereal months. A synodic month--which equals about 291/2 days--is the period from one new moon to the next new moon. It is the time that the moon takes to revolve around the earth in relation to the sun. If the moon started on its orbit from a spot exactly between the earth and the sun, it would return to almost the same place in about 291/2 days. A synodic month equals a full day on the moon. This lunar day is divided into about two weeks of light and about two weeks of darkness.

A sidereal month--about 271/3 days--is the time the moon takes to make one trip around the earth in relation to the stars. If the moon's revolution were to begin on a line with a certain star, it would return to the same position about 271/3 days later.

A synodic month is longer than a sidereal month because the earth travels around the sun while the moon travels around the earth. By the time the moon has made one revolution around the earth, the earth has revolved 1/13 of the way around the sun. Therefore, the moon has to travel slightly farther to be in the same position in relation to the sun.