Answer to Question #103559 in Astronomy | Astrophysics for Emma Tarr

Question

A space traveler weighs 540.0 N on earth. Calculate what the travelers will weigh on another planet whose radius is four that of the earth and whose mass is five times that of earth ?

Answer 1

Let's write the formula for the gravitational acceleration on Earth:

$$g_E = \dfrac{GM_E}{R_E^2},$$

here, $G$ is the gravitational constant, $M_E$ is the mass of the Earth, $R_E$ is the radius of the Earth.

Then, we can write the gravitational acceleration on another planet in terms of $g_E$ :

$$g_{p} = \dfrac{GM_p}{R_p^2} = \dfrac{5GM_E}{(4R_E)^2} = \dfrac{5GM_E}{16R_E^2} = \dfrac{5}{16}g_E.$$

Finally, we can find the weight of the space traveler:

$$W_{traveler, p} = mg_p = \dfrac{5}{16}mg_E = \dfrac{5}{16}W_{traveler,E} = \dfrac{5}{16} \cdot 540N = 169N.$$

Answer:

$W_{traveler, p} = 169N.$