This cannot be true. I used Newton's gravity formula ##\frac{G \cdot M_E \cdot M_0}{x^2} = \frac{G \cdot M_M \cdot M_0}{(R-x)^2}## which isn't linear and got ##x=0.9 \, R## which looks as if there were an easier argument since ##9^2 = 81.## And it violates a quote from "Armageddon", not that a movie would be a reliable source ...Charles Link said:The moon has a mass approximately 1/81 the mass of the earth. A little algebra gives ## (M_e)x=(M_e/81)(R-x) ## where ## R ## is the Earth moon distance.(from center of Earth to center of moon) ==>> ## x=R/82 =240000 ## miles ## /82=3000 ## miles approximately. With the radius of the Earth ## r_e=4000 ## miles this puts this about ## 1000 ## miles below to the surface of the Earth on the side of the Earth that faces the moon. Please double check my calculations to verify. (I didn't google this, but I believe I have it correct.)
I think you computed the zero gravity point. If I remember correctly (I computed it a few years ago), it lies 9/10 of the way to the moon. editing... yes, your calculation is for the zero gravity location... :-)fresh_42 said:This cannot be true. I used Newton's gravity formula ##\frac{G \cdot M_E \cdot M_0}{x^2} = \frac{G \cdot M_M \cdot M_0}{(R-x)^2}## which isn't linear and got ##x=0.9 \, R## which looks as if there were an easier argument since ##9^2 = 81.## And it violates a quote from "Armageddon", not that a movie would be a reliable source ...
Ah, ok. Misunderstood it.Charles Link said:I think you computed the zero gravity point. If I remember correctly (I computed it a few years ago), it lies 9/10 of the way to the moon. editing... yes, your calculation is for the zero gravity location... :-)
Yes.thetexan said:Is it that simple?
(For the OP) When the moon revolves around the Earth in 29 days or thereabouts, it is actually this dumbbell system that is rotating. Because the CG lies so near to the center of the earth, basically the moon revolves around the earth.Bandersnatch said:Yes.
The center of gravity, or the point at which the combined mass of the Earth and Moon is balanced, is located approximately 1,737 kilometers from the center of the Earth and 384,400 kilometers from the center of the Moon.
The center of gravity between the Earth and Moon is important because it determines the orbit and motion of the Moon around the Earth. It also affects the Earth's rotation and tides.
The center of gravity is calculated using the masses and distances between the Earth and Moon. The formula for calculating the center of gravity is (m1 x d1 + m2 x d2) / (m1 + m2), where m1 and m2 are the masses of the Earth and Moon, and d1 and d2 are the distances from the center of the Earth and Moon, respectively.
Yes, the center of gravity between the Earth and Moon changes slightly over time due to the varying distances between the two bodies as they orbit around each other. However, these changes are very small and have a minimal effect on the overall orbit and motion of the Moon.
The center of gravity between the Earth and Moon plays a crucial role in space missions, especially those involving spacecraft landing on the Moon. Understanding the location and strength of the center of gravity is essential for ensuring a successful landing and maintaining the stability of the spacecraft during the mission.