Question

Compare the value of $g$ between earth and moon.

Answer 1

Hint: The net acceleration given to objects by the combined action of gravitation (from mass distribution within Earth) and centrifugal force (from the Earth's rotation) is indicated by the letter g. Newton's second law of motion, or $F = ma$ which means $\text{Force = mass} \times \text{acceleration}$, defines the weight of an item on Earth's surface as the downward force on that item.

Complete answer:
This acceleration is expressed in SI units as metres per second squared (in symbols\[m{s^{ - 2}}\]) or newton per kilogram (\[Nk{g^{ - 1}}\]). Gravitational acceleration at the Earth's surface is around 9.81\[m{s^{ - 2}}\], which implies that, excluding the effects of air resistance, the speed of an item falling freely will increase by roughly 9.81\[m{s^{ - 2}}\]. This amount is frequently referred to as "small g" informally (in contrast, the gravitational constant G is referred to as big G).
The acceleration due to gravity on the Moon's surface is around 1.625\[m{s^{ - 2}}\], or 16.6 percent of the acceleration due to gravity on Earth's surface, which is 0.166. The variance in gravitational acceleration throughout the entire surface is around 0.0253\[m{s^{ - 2}}\] (1.6 percent of the acceleration due to gravity). Things on the Moon will weigh just 16.6% (= 1/6) of what they weigh on Earth since weight is exactly proportional to gravitational acceleration.
By following the radio signals transmitted by circling satellites, the gravitational field of the Moon has been determined. The principle relies on the Doppler effect, which allows the line-of-sight spacecraft acceleration to be determined by minor variations in radio signal frequency, as well as the determination of the distance between the spacecraft and a ground station. Because the Moon's gravitational field impacts a spacecraft's orbit, this tracking data can be used to identify gravity anomalies. However, because of the Moon's synchronous rotation, spacecraft cannot be tracked much beyond the limbs of the Moon from Earth.

Note:
A non-rotating perfect sphere with uniform mass density or whose density changes only with distance from the centre (spherical symmetry) would provide a uniform gravitational field at all places on its surface. The Earth rotates and is not spherically symmetric; instead, it is somewhat flatter in the poles and bulges at the Equator, resulting in an oblate spheroid. As a result, there are minor variations in gravity magnitude over its surface.