Sun-Earth gravitational force

Problem

Using the law of universal gravitation, calculate the magnitude of the gravitational force the Sun exerts on the Earth. Data: $M_S = 2{,}0\cdot 10^{30}\ \text{kg}$, $M_T = 6{,}0\cdot 10^{24}\ \text{kg}$, $r = 1{,}5\cdot 10^{11}\ \text{m}$, $G = 6{,}67\cdot 10^{-11}\ \text{N}\,\text{m}^2/\text{kg}^2$.

Solution

Law of universal gravitation. $F = \frac{G\,M_S\,M_T}{r^2}$

Numerical substitution. $F = \frac{6{,}67\cdot 10^{-11}\cdot 2{,}0\cdot 10^{30}\cdot 6{,}0\cdot 10^{24}}{(1{,}5\cdot 10^{11})^2} = \frac{8{,}0\cdot 10^{44}}{2{,}25\cdot 10^{22}}$

$\ev{F \approx 3{,}5\cdot 10^{22}\ \text{N}}$

It is this force that keeps the Earth on its orbit: it acts as the centripetal force of the (nearly) circular motion around the Sun.

Links

Topics: Gravitation Concepts: Law of universal gravitation Skills: Symbolic setup