The weight of an astronaut plus his space suit on the Moon is only 319 N. How much (in N) do they weigh on Earth?

Newton's second law, called the fundamental law or fundamental principle of dynamics, states that a body accelerates if a force is applied to it. This law indicates that the net force applied on a body is proportional to the acceleration that the body acquires. The constant of proportionality is the mass of the body, so Newton's second law is expressed in the following formula:

F = m*a

Where:

F is the net force. It is expressed in Newton (N)
m is the mass of the body. It is expressed in kilograms (Kg).
a is the acceleration that the body acquires. It is expressed in meters over second squared (m/s²).

The weight of an astronaut plus his space suit on the Moon is only 319 N. Then, being:

F= weight= 319 N
m= ?
a = acceleration of the Moon's gravity, whose value is 1.62 m/s²

you get:

319 N= m* 1.62 m/s²

Solving:

[tex]m=\frac{319 N}{1.62 \frac{m}{s^{2} } }[/tex]

m=196.91 kg

The mass is an invariable quantity, regardless of the planet in which the astronaut plus his space suit on the Moon is, then you have:

F= weight= ?
m= 196.91 kg
a = acceleration of the Earth's gravity, whose value is 9.81 m/s²

replacing in the definition of force:

Weight= 196.91 kg* 9.81 m/s²

Weight= 1,931.69 N

The weight of an astronaut plus his space suit on the Earth is 1,931.69 N.