Question

How to calculate the value of g at surface of Earth? (5.97x10^24 kg, 6378 km) , Moon ? (7.35x1022 kg, 1738 km) and Mars? (0.642x1024 kg, 3396 km)

Answer 1

• Earth: `9.78\ "m/s"^2`
• Moon: `1.62\ "m/s"^2`
• Mars: `"3.71 m/s"^2`

Explanation:

Acceleration due to gravity `"(g)"` at surface of planet is given by the formula

`"g" = "GM"/"R"^2`

where

• `"G ="` Universal Gravitational constant
• `"M ="` Mass of planet
• `"R ="` Radius of planet

`————————`

`"(1)"` At the surface of Earth

`"g"_"earth" = (6.67 × 10^-11\ "N m"^2 "/kg"^2 × 5.97 × 10^24\ "kg")/(6378 × 10^3\ "m")^2 = "9.78 m/s"^2`

`————————`

`"(2)"` At the surface of Moon

`"g"_"moon" = (6.67 × 10^-11\ "N m"^2 "/kg"^2 × 7.35 × 10^22\ "kg")/(1738 × 10^3\ "m")^2 = "1.62 m/s"^2`

`————————`

`"(3)"` At the surface of Mars

`"g"_"mars" = (6.67 × 10^-11\ "N m"^2 "/kg"^2 × 0.642 × 10^24\ "kg")/(3396 × 10^3\ "m")^2 = "3.71 m/s"^2`

`color(blue)("g"_"earth" > "g"_"mars" > "g"_"moon")`