Question

From Earth we can measure the radius of Mars using our telescopes. An estimate for it is 3.39 x 106 m. By sending an exploratory robot to Mars, we determined the acceleration due to gravity on its surface as 3.73 m/s2. Estimate the mass of Mars

Answer 1

$F = m_1*a$

$\text{where }m_1 \text{ -arbitrary body mass }a =3.73 \text{acceleration due to gravity}$

$\text{on the other hand, according to the law of universal gravitation:}$

$F = G\frac{m_1M}{R^2}$

$\text{where } M\text{ planet mass}$

$R =3.39*10^6\text{ distance between bodies}$

$G \approx6.67*10^{-11}\text{ gravitational constant}$

$m_1*a = G\frac{m_1M}{R^2}$

$M= \frac{a*R^2}{G}= \frac{3.73*3.39^2*10^{12}}{6.67*10^{-11}}\approx6.42*10^{23}kg$

Answer: $M \approx6.42*10^{23}kg$