Question

What is the weight of a 68-kg astronaut (a) on Earth, (b) on the Moon$\left(g=\mathbf{1}\mathbf{.}\mathbf{7}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}\right)$(c) on Mars$\left(g\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{7}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}\right)$(d) in outer space traveling with constant velocity?

Short answer

The weight of the astronaut (a) on Earth is $667.08\mathrm{N}$, (b) on Moon is $115.6\mathrm{N}$, (c) on Mars is $251.6\mathrm{N}$, and (d) in outer space, traveling with constant velocity is $0\mathrm{N}$.

Step-by-step solution

Step 1. Significance of the weight of the astronaut

An astronaut's weight can be evaluated with the help of his mass and the gravity of the surface. The product of the mass of the astronaut and gravity acting on him gives the weight. It can be expressed in Newton.

Step 2. Identification of given data 

The given data can be listed below as:

• The mass of the astronaut is $m=68\mathrm{kg}$.
• The acceleration due to gravity on Earth is $g_E=9.81\mathrm{m}/{\mathrm{s}}^2$.
• The acceleration due to gravity on Mars is $g_{Ma}=3.7\mathrm{m}/{\mathrm{s}}^2$.
• The acceleration due to gravity on the Moon is $g_{Mo}=1.7\mathrm{m}/{\mathrm{s}}^2$.
• The acceleration due to gravity in outer space is $g_O=0\mathrm{m}/{\mathrm{s}}^2$.

Step 3. (a) Determination of the weight of the astronaut on Earth

The weight of the astronaut on Earth can be expressed as:

$W=m{g}_E$

Here, m is the mass of the astronaut, and $g_E$is the acceleration due to gravity on the Earth’s surface.

Substitute the values as 68 kg for m, and $9.81\mathrm{m}/{\mathrm{s}}^2$for $g_E$in the above equation.

$\begin{array}{c}W=68\mathrm{kg}\times 9.81\mathrm{m}/{\mathrm{s}}^2\left(\frac{1\mathrm{N}}{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}\right)\\ =667.08\mathrm{N}\end{array}$

Thus, the weight of the astronaut on Earth is $667.08\mathrm{N}$.

Step 4. (b) Determination of the weight of the astronaut on the Moon

The weight of the astronaut on the Moon can be expressed as:

$W=m{g}_{Mo}$

Here, m is the mass of the astronaut, and $g_{Mo}$is the acceleration due to gravity on the Moon’s surface.

Substitute the values as 68 kg for m, and $1.7\mathrm{m}/{\mathrm{s}}^2$for $g_{Mo}$in the above equation.

$\begin{array}{c}W=68\mathrm{kg}\times 1.7\mathrm{m}/{\mathrm{s}}^2\left(\frac{1\mathrm{N}}{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}\right)\\ =115.6\mathrm{N}\end{array}$

Thus, the weight of the astronaut on the Moon is $115.6\mathrm{N}$.

Step 5. (c) Determination of the weight of the astronaut on Mars

The astronaut’s weight on Mars can be given as:

$W=m{g}_{Ma}$

Here, m is the mass of the astronaut and $g_{Ma}$is the acceleration due to gravity on the surface of Mars.

Substitute the values as 68 kg for m, and $3.7\mathrm{m}/{\mathrm{s}}^2$for $g_{Ma}$in the above equation.

$\begin{array}{c}W=68\mathrm{kg}\times 3.7\mathrm{m}/{\mathrm{s}}^2\left(\frac{1\mathrm{N}}{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}\right)\\ =251.6\mathrm{N}\end{array}$

Thus, the weight of the astronaut on Mars is $251.6\mathrm{N}$.

Step 6. (d) Determination of the weight of the astronaut in outer space while traveling with constant velocity

In outer space, there is no acceleration due to gravity. This means that the acceleration due to gravity in outer space is zero. Also, the astronaut traveling at constant velocity results in his acceleration being zero.

The astronaut’s weight in outer space can be given as:

$W=m{g}_O$

Here, m is the mass of the astronaut, and $g_O$is the acceleration due to gravity in outer space.

Substitute the values as 68 kg for m, and $0\mathrm{m}/{\mathrm{s}}^2$for $g_O$in the above equation.

$\begin{array}{c}W=68\mathrm{kg}\times 0\mathrm{m}/{\mathrm{s}}^2\left(\frac{1\mathrm{N}}{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}\right)\\ =0\mathrm{N}\end{array}$

Thus, the weight of the astronaut in outer space is $0\mathrm{N}$.