A lunar lander module has a mass of 250 slugs on earth. Calculate (a) its mass in SI units, and (b) its weight in SI units.

If the module lands on the moon, where g is 5.30 ft/s², determine (c) its weight in SI units, and (d) its mass in SI units. Calculate all the answers to four significant digits. Recall the gravitation constant, g, is 9.807 m/s² (32.17 ft/s²) on the earth's surface (average) and 1.622 m/s² (5.321 ft/s²) on the moon's surface (average).

Units table in the appendices can be used for this example. From that table 1, slug is equal to 14.59 kg.

     a) 250 slugs (14.59 kg / 1 slugs)
           = 3,647.5 kg
           = 3,648 kg

The final answer is expressed with four significant digits.

Weight is mass multiplied by the acceleration due to gravity (W = mg). In SI system g is 9.807 m/s²

     b) W = 3,647.5 kg (9.807 m/s²)
              = 35,771.01 kg-m/s²
              = 35,770 N
              = 35.77 kN

When the module is on the moon, g is 5.321 ft/s². Its weight can be found by multiplying the mass by the gravitational acceleration (both in US units)

    c) W_m = mg_m = 250 slugs (5.321 ft/s²)
                = 1,330 lb

To convert the final answer to SI unit, the units table from the appendix can be used again. 1 lb is 4.448 newton. (Please note that the final answer needs to be expressed in four significant digits)

     1,330 lb (4.448 N / 1 lb)
       = 5,915.8 N
       = 5.916 kN

The same result can be found by multiplying the weight on earth by the ration of gravitational accelerations.

    W_m=W_e (g_m / g)
           = 35.77 kN (5.321 ft/s²) / (32.17 ft/s²)
           = 5.916 kN

d) The mass is independent from the gravity and will remain constant.