- #1
emily-
- 15
- 2
- 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.
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 Earth speed of the Moon induced orbit refers to the velocity at which the Earth travels around the Sun due to the gravitational pull of the Moon. It is measured in kilometers per hour (km/h) or miles per hour (mph).
The Earth speed of the Moon induced orbit can be calculated using the formula v = √(GM/r), where v is the velocity, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the Earth and the Moon.
The gravitational constant, denoted as G, is a fundamental constant in physics that is used to calculate the force of gravity between two objects. It is approximately equal to 6.67 x 10^-11 N*m^2/kg^2.
The mass of the Earth is approximately 5.97 x 10^24 kilograms (kg). It is one of the factors used in the calculation of the Earth speed of the Moon induced orbit.
Yes, the Earth speed of the Moon induced orbit can vary due to factors such as changes in the distance between the Earth and the Moon, variations in the gravitational force, and the presence of other celestial bodies. However, these variations are relatively small and do not have a significant impact on the overall speed of the Earth's orbit induced by the Moon.