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wasi-uz-zaman

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In summary, calculating the mass of the moon is difficult, but satellites orbiting it can give you a good estimate.

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wasi-uz-zaman

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Astronomy news on Phys.org

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mfb

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Satellites orbiting the moon are a better way to determine its mass - they give direct access to the gravitational acceleration at a specific distance, together with the gravitational constant this can be used to calculate its mass.

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wasi-uz-zaman

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but how do i calculate the sum of Earth and moon mass?

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mfb

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##M+m=\frac{4\pi^2a^3}{GT^2}## with the semi-major axis a (for a circular orbit, this would be the distance)

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BobG

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I'm curious as to how you calculated the distance between the Moon and Earth. That distance might not be the semi-major axis of the Moon's orbit. It might be the sum of the Moon's semi-major axis and the Earth's semi-major axis, as measured from their combined center of mass. (The 'a' in the previous equation is actually the sum of the semi-major axes, or the distance you most likely calculated.)

In practice, calculating the mass and the semi-major axis of planets was an almost impossible task even after Newton turned Kepler's Third Law into a formula. You had a formula containing three unknown variables (the universal gravitational constant, the mass, and the semi-major axis) and the only known was the orbital period.

In fact, that's why the Earth's semi-major axis for it's orbit around the Sun was measured in astronomical units, with one AU being the distance between the Sun and the Earth. You could measure Jupiter's semi-major axis in AU's, but had no way to convert that into a more traditional measure such as kilometers.

In practice, calculating the mass and the semi-major axis of planets was an almost impossible task even after Newton turned Kepler's Third Law into a formula. You had a formula containing three unknown variables (the universal gravitational constant, the mass, and the semi-major axis) and the only known was the orbital period.

In fact, that's why the Earth's semi-major axis for it's orbit around the Sun was measured in astronomical units, with one AU being the distance between the Sun and the Earth. You could measure Jupiter's semi-major axis in AU's, but had no way to convert that into a more traditional measure such as kilometers.

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The formula for calculating the mass of the Moon from Earth is: M = (G x D^{2}) / (4 x T^{2}), where M is the mass of the Moon, G is the gravitational constant, D is the distance between the Earth and the Moon, and T is the orbital period of the Moon.

The distance between the Earth and the Moon can be determined using various methods, such as radar measurements, lunar laser ranging, and parallax measurements. These methods use different techniques to measure the distance and can provide accurate results.

The orbital period of the Moon is important because it is directly related to the gravitational force between the Earth and the Moon. The longer the orbital period, the weaker the gravitational force, and vice versa. This information is crucial in the formula for calculating the Moon's mass.

The gravitational constant, denoted by G, is a fundamental physical constant that represents the strength of the gravitational force between two objects. It is used in the formula for calculating the Moon's mass as it is a crucial factor in determining the gravitational force between the Earth and the Moon.

The calculated mass of the Moon from Earth's perspective is accurate to a certain extent, as it is based on various measurements and assumptions. There may be slight variations in the calculated mass due to factors like the Moon's irregular shape and the changing distance between the Earth and the Moon. However, the calculated mass is still considered a close estimate of the Moon's actual mass.

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