There is no direct instrument to measure the mass of the Earth. However, the mass of the Earth can be estimated using various indirect methods. One common method is to use the gravitational constant (G) and the acceleration due to gravity (g) at the Earth's surface.

The formula to calculate the mass of the Earth (M) is:

M = (g * R^2) / G

Where:

g = acceleration due to gravity (approximately 9.81 m/s²)

R = radius of the Earth (approximately 6.371 × 10^6 meters)

G = gravitational constant (approximately 6.674 × 10^-11 N·m²/kg²)

By substituting these values into the formula, we can estimate the mass of the Earth to be approximately 5.972 × 10^24 kilograms.

It's important to note that while this calculation provides an estimate of the Earth's mass, there may be some variations and refinements to the estimated value based on different measurement techniques and models.