Can you clarify the question? Are you trying to calculate the speed of the moon in its orbit about the Earth? Or the Earth in its orbit about the Earth-moon barycenter? The speed of the Earth's tidal bulge as it "orbits" the Earth's surface?emily- said:Homework Statement:: How to calculate earth speed of the moon induced orbit?
Relevant Equations:: I thought of using F = ma along with momentum p =mv to get the v for earth
It didn't work and I don't know how to do it.
Drakkith said:Sorry, what is an 'induced' orbit? A quick google search didn't give me any results for that term.
I am thinking about the speed that earth has to have due to its gravitational interaction with the moon. I know that the moon's orbital velocity is approximately 1.022 km/sjbriggs444 said:Can you clarify the question? Are you trying to calculate the speed of the moon in its orbit about the Earth? Or the Earth in its orbit about the Earth-moon barycenter? The speed of the Earth's tidal bulge as it "orbits" the Earth's surface?
What inputs do you have to play with?
Since the only work you have shown is a pair of equations that "didn't work", I'll leave it there. We need you to show more work than that.
OK. So it is the Earth's orbital speed about the Earth-moon barycenter that you are hoping to calculate.emily- said:I am thinking about the speed that earth has to have due to its gravitational interaction with the moon. I know that the moon's orbital velocity is approximately 1.022 km/s
Yes indeed. If we knew ##a_\text{moon}## we could solve for ##a_\text{earth}##. Though we do have the pesky problem of finding ##a_\text{moon}## if we attack the problem that way.emily- said:Now according to Newton's third law, the force is equal for both of the bodies meaning that F = m_earth * a_earth = m_moon * a_moon
m_earth, m_moon and a_moon are known. By replacing the variables with values we get the value for a_earth.
That is not a correct formula. ##F\ dt = dp##. Force is the rate of transfer of momentum. But that rate is an incremental change, not a final total. It is not equal to ##p## and hence, is not equal to ##mv##.emily- said:Now according to this formula F * dt = p = mv:
The speed of the Earth induced by the Moon's orbit can be calculated using the formula v = (2πr) / T, where r is the radius of the Earth-Moon barycenter orbit and T is the orbital period of the Moon around the Earth.
The radius of the Earth-Moon barycenter orbit is the distance from the center of the Earth to the barycenter of the Earth-Moon system. This distance is approximately 4,671 kilometers (2,902 miles).
The orbital period of the Moon around the Earth is approximately 27.32 days, which is the time it takes for the Moon to complete one full orbit around the Earth.
To convert the orbital period from days to seconds, multiply the number of days by the number of seconds in a day (86,400 seconds/day). For the Moon's orbital period of 27.32 days, this would be 27.32 * 86,400 = 2,359,488 seconds.
Using the formula v = (2πr) / T, with r = 4,671,000 meters and T = 2,359,488 seconds, the speed v is approximately 0.012 meters per second (m/s). This is the average speed of the Earth's motion induced by the gravitational influence of the Moon.