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)

1 Answer
Apr 23, 2018
  • 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")#