Class 10 Science I Gravitation

The masses of the earth and moon are 6 x 10²⁴ kg and 7.4x10²² kg, respectively. The distance between them is 3.84 x 10⁵ km. Calculate the gravitational force of attraction between the two?

the data can be listed as

mass of earth , M = 6 x 10²⁴ kg

mass of moon , m = 7.4 x 10²² kg

distance , r = 3.84 x 10⁵ km = 3.84 x 10⁵ x 10³m = 3.84 x 10⁸ m

$G=6.7\textrm{x}10^{-11}Nm^{2}/kg^{2}$

To find, gravitational force F = ?

Solution -

As per Newtons law of gravitation, the gravitational force can be written as,

$F=\frac{GMm}{r^{2}}$

substituting all the values in it we have

$F=\frac{6.7\textrm{x}10^{-11}\textrm{x}6\textrm{x}10^{24}\textrm{x}7.4\textrm{x}10^{22}}{(3.84\textrm{x}10^{8})^{2}}$

$F=\frac{6.7\textrm{x}6\textrm{x}7.4\textrm{x}10^{35}}{3.84^{2}\textrm{x}10^{16}}$

$F=\frac{297.48\textrm{x}10^{35}}{14.7456\textrm{x}10^{16}}$

by rounding off the last digits we have,

$F=\frac{297.5\textrm{x}10^{19}}{14.75}$

$F=20.169\textrm{x}10^{19}=2.0169\textrm{x}10^{20}=2.02\textrm{x}10^{20}N$

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?