# Speed of Moon without Sun gravity.

(1) If you want a slightly bigger challenge on the first question, rather than just average speed, you can calculate the moon’s speed at a particular point on its orbit, using the vis viva equation.

Taking the moon’s current distance from http://www.wolframalpha.com/input/pod.jsp?id=MSP84219d1c35216ihb377000043gf3i5i495496cb&s=54 [Broken], I googled

sqrt(G((mass of earth)+(mass of moon))(1/m)(2/364717584-1/384472282)) in km/h

to get 3 882.96569 km/h. A bit faster than your average value, which seems reasonable, since the moon is currently closer than its average distance.

(2) There are some figures relating the movement of sun and earth to the cosmic microwave background (CMB) here:

The speed of the Sun relative to the CMB is now 1,328,000 km/h (plus or minus 9000 km/h) in the direction of the constellation of the Cup [Crater] (just south of the Lion [Leo]). Contributions 2 - 4 make your speed relative to the CMB up to about 105,000 km/h greater (greatest around 15 December, if my calculations are correct) or smaller (least around 12 June) than the speed of the Sun “relative to the CMB”, mostly depending on the season.
So the speed of the moon about the earth is a couple of orders of magnitude smaller than the seasonal difference due to differences in the earth’s linear direction of motion, and also somewhat smaller than the uncertainty given here for the sun’s speed relative to a coordinate system where the CMB is isotropic (the same in all directions).

Suppose we have a figure for the moon’s current speed relative to anything. What will it be without gravity? Well, if the only thing we change is to remove gravity, the moon’s speed will be exactly the same until its motion is effected by some other force such as the pressure of the solar wind. If we remove all external forces, its velocity shouldn’t change at all.

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Hello,
I have similar question: Can we calculate the velocity of the moon relative to EARTH without the gravitational pull of the sun??,or the velocity shouldn’t change at all?(i think this called three-body problem,how to solve these bodies?).
thank you.

D H
Staff Emeritus
The result of an imaginary scenario can be anything you choose to imagine. There is no formula for that.
What he said.

russ_watters
Mentor
Hello,
I have similar question: Can we calculate the velocity of the moon relative to EARTH without the gravitational pull of the sun??,or the velocity shouldn’t change at all?(i think this called three-body problem,how to solve these bodies?).
thank you.
Since the sun has very little effect on the average orbital speed of the moon around the earth, removing it will have very little effect.

Since the sun has very little effect on the average orbital speed of the moon around the earth, removing it will have very little effect.
Thank you, that's what im looking for! What he said.
Hello D H,
you didn't understand me, as i said:

the moon makes 360 degrees around Earth with respect to stars the Earth-moon system moves 26.92952225 degrees around the sun.We can calculate ø from the period of one heliocentric revolution of the Earth-moon system (365.2421987 days):
ø = (360 degrees / 365.2421987 synodic days) x 27.32166088 synodic days = 26.92952225 degrees. So,the speed of moon without Sun gravity should be like this:
V = (2 * pi * R / T)*cos[26.92952225]
Is this CORRECT?
then you said:
No.

Assuming no other bodies are present, Newton's law of gravity yields an equation for the period of a pair of bodies orbiting their common center of mass. You need to use that equation.
I will tell you a simple example:
The velocity vector is defined by the speed and also by the direction of motion. Objects experiencing no net force do not accelerate and, hence, move in a straight line with constant speed: they have a constant velocity. However, even an object moving in a circle at constant speed has a changing direction of motion. The rate of change of the object's velocity vector in this case is the centripetal acceleration.

The centripetal acceleration varies with the radius of the path and speed of the object, becoming larger for greater speed (at constant radius) and smaller radius (at constant speed). If an object is traveling in a circle with a varying speed, its acceleration can be divided into two components, a radial acceleration (the centripetal acceleration that changes the direction of the velocity) and a tangential acceleration that changes the magnitude of the velocity.
So, this formula V = (2 * pi * R / T)*cos[26.92952225] is right,that should find speed of moon without sun gravity from Earth-Moon System(i think the orbit of moon would be very close to circle).
The Speed of Moon Relative to Earth without the gravitational pull of the sun from Earth-Moon System is 3282.9 km/h (roughly).

Thank you.