Question

The graph above plots gravitational force versus distance for two asteroids of equal mass (10 billion kg). When the distance between the asteroids is 1,000 km, the gravitational force between them is about 6,700 N.
Based on the trend shown in the graph, predict the force between the asteroids when the distance between them decreases to 850 km.
A.
about 6,700 N
B.
about 74 N
C.
about 9,200 N
D.
0 N

Answer 1

Explanation:

Given parameters:

Mass of the asteroid = 10 x 10⁹kg

Distance between the asteroid = 850km

Unknown:

Force = ?

Solution:

We can predict the outcome of this reduction in distance between the two masses using the newton's law of universal gravitation.

The law states that "the gravitational force of attraction between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distances between them".

  Mathematically, we have;

           F = $\frac{Gm_{1} m_{2} }{r^{2} }$

F is the gravitational force

G is the universal gravitational constant = 6.67 x 10⁻¹¹Nm²kg⁻²

m is the mass of the body

r is the distance between them.

 From this, we know that as the separation increases, the force of gravitation will reduce since the mass is constant.

The distance between the two asteroids decreased from 1000km to 850km, this will increase the force of attraction between them and we expect the force to be higher than 6700N.

  At 1000Km, force = 6700N,

 since as the distance reduces the force increases, we expect the force to be about 9200N.

Let us verify this by plugging the values into the equation:

        F = $\frac{6.67 x 10^{-11} x 10 x 10^{9} x 10 x 10^{9} }{(850 x 10^{3})^{2} }$

       F = 9200N

learn more:

Asteroid brainly.com/question/12785992

Universal gravitation brainly.com/question/1724648

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