Question

\two small asteroids are separated by a distance 250 meters. the mass of one asteroid is 300 kg; the mass of the other asteroid is 400 kg. what is the gravitational force between the two asteroids?

Answer 1

Approximately
`1.28* 10^(-10)\; {\rm N}`.

Step-by-step explanation:

The gravitational attraction between two point masses is:

`\begin{aligned}F &= (G\, M\, m)/(r^(2))\end{aligned}`,

Where:

• 
  `G \approx 6.67 * 10^(-11)\; {\rm N\cdot kg^(-2)\cdot m^(2)}` is the gravitational constant,
• 
  `M` and
  `m` are the mass of the two objects, and
• 
  `r` is the distance between the two objects.

Verify that all quantities are provided in standard units: mass in kilograms, and distance in meters. In this question, it is given that
`M = 300\; {\rm kg}`,
`m = 400\; {\rm kg}`, and
`r = 250\; {\rm m}`. Using the equation for the gravitational force between the two:

`\begin{aligned}F &= (G\, M\, m)/(r^(2)) \\ &\approx ((6.67 * 10^(-11))\, (300)\, (400))/((250)^(2))\; {\rm N} \\ &\approx 1.28 * 10^(-10)\; {\rm N}\end{aligned}`.