Take into account that the gravitational force between two object with masses mA and mB is given by the following formula:
[tex]F=\frac{Gm_Am_B}{r^2}[/tex]where,
G = 6.67*10^-11 Nm/kg
mA: mass of object A = ?
mB: mass of object B = 4.21*10^21 kg
r: distance between object A and B = 5.24*10^3 m
Moreover, consider that the force is also equal to the product of the mass by the acceleration, due to the Newton Secon Law, then, you have:
[tex]m_Aa=\frac{Gm_Am_B}{r^2}[/tex]Then, cancel out mA both sides and solve for the acceleration of object A and replace the values of the rest of the parameters, as follow:
[tex]a=\frac{Gm_B}{r^2}=\frac{(6.67\cdot10^{-11}N\frac{m^2}{\operatorname{kg}^2})(4.21\cdot10^{21}kg)}{(5.24\cdot10^3m)^2}=10226.93\frac{m}{s^2}[/tex]Hence, the acceleration of object A is approximately 10226.93 m/s^2
, as follow:
