Question

Mars is 7.83x10^10m [^10 is an exponent] from planet earth. The planet Earth is 5.98x10^24kg [^24 is an exponent] while Mars has a mass of 6.42x10^23kg [^23 is an exponent]. What is the gravitational attraction between the two planets? G=6.67×10^-11 (-11 is an exponent)​

Answer 1

Approximately
`4.18 * 10^(16)\; \rm N`.

Step-by-step explanation:

Consider two objects of mass
`m_(1)` and
`m_(2)`. Let
`r` denote the distance between the center of mass of each object. Let
`G` denote the gravitational constant. (
`G \approx 6.67 * 10^(-11)\; {\rm m^(3)\cdot kg^(-1)\cdot s^(-2)}`.)

By Newton's Law of Universal Gravitation, the size of gravitational attraction between these two objects would be:

`\begin{aligned}F &= (G\, m_(1)\, m_(2))/(r^(2))\end{aligned}`.

In this question,
`m_(1) = 5.98* 10^(24)\; {\rm kg}` and
`m_(2) = 6.24 * 10^(23)\; {\rm kg}` are the mass of the two planets. The distance between the two planets is
`r = 7.83 * 10^(10)\; \rm m` (approximately the same as the distance between the center of mass of planet Earth and the center of mass of Mars.)

Apply Newton's Law of Universal Gravitation to find the size of gravitational attraction between the two planets:

`\begin{aligned}F &= (G\, m_(1)\, m_(2))/(r^(2)) \\ &= \frac{1}{(7.83 * 10^(10)\; {\rm m})^(2)} \\ &\quad * (6.67 * 10^(11)\; {\rm m^(3) \cdot kg^(-1) \cdot s^(-2)}) \\ &\quad * (5.98 * 10^(24)\; {\rm kg}) \\ &\quad * (6.42 * 10^(23)\; {\rm kg}) \\ &\approx 4.18 * 10^(16)\; {\rm kg \cdot m \cdot s^(-2)} \end{aligned}`.

Since
`1\; {\rm kg \cdot m \cdot s^(-2)} = 1\; {\rm N}`, the size of gravitational attraction between the two planets would be approximately
`4.18 * 10^(16)\; {\rm N}`.