Deimos, a satellite of Mars, has an average radius of 6.3 km. If the gravitational force between Deimos and a 3.0 kg rock at its surface is #2.5 * 10^-2# N, what is the mass of Deimos?

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Answer 1 · 2017-07-08T17:44:09

#5.0xx10^15# #"kg"#

We're asked to find the mass of Deimos given the gravitational force between it and a satellite with mass #3.0# #"kg"#.

We can use the equation

#F_g = (Gm_"D"m_"R")/(r^2)#

where

#F_g# is the magnitude of the gravitational force between the two objects, given as #2.5 xx 10^-2# #"N"#
#G# is the gravitational constant, equal to #6.674xx10^-11("N"•"m"^2)/("kg"^2)#
#m_"D"# is the mass of Deimos (what we're trying to find)
#m_"R"# is the mass of the rock at its surface, given as #3.0# #"kg"#
#r# is the distance between them, which, since te rock is on the surface of Deimos, is simply the radius, given as #6.3# #"km"#, or #6300# #"m"#.

Let's plug in known values, and solve for the mass of Deimos, #m_"D"#:

#m_"D" = (F_gr^2)/(Gm_"R") = ((2.5xx10^-2cancel("N"))(6300cancel("m"))^2)/((6.674xx10^-11("N"•"m"^2)/("kg"^2))(3.0cancel("kg")))#

#= color(red)(5.0xx10^15# #color(red)("kg"#

rounded to #2# significant figures.