At a particular instant, two asteroids in inter-stellar space are a distance

r = 20 km apart. Asteroid 2 has 10 times the mass of asteroid 1, m2 = 10 m1.

1. If the acceleration of the asteroid 1 toward the asteroid 2 is 1.0 m/s2
, what is
the acceleration of the asteroid 2?

F = m a

F is the same on both (Third Law)

m2 a2 = m1 a1
10 m1 a2 = m 1 a1

a 2 = a1 /10
if a1 is 1
then a2 = 0.1 m/s^2

To find the acceleration of asteroid 2, given that asteroid 1 has an acceleration of 1.0 m/s^2, we can use Newton's Law of Universal Gravitation. Newton's Law states that the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

In this case, we know that asteroid 2 has 10 times the mass of asteroid 1, so we can write the equation as:

F = G * (m1 * m2) / r^2

where F is the gravitational force between the two asteroids, G is the gravitational constant, m1 and m2 are the masses of asteroid 1 and asteroid 2 respectively, and r is the distance between the two asteroids.

Since we are given the acceleration of asteroid 1, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:

F = m1 * a1

We can now set these two equations equal to each other:

G * (m1 * m2) / r^2 = m1 * a1

From here, we can solve for the acceleration of asteroid 2, a2:

a2 = G * m1 * m2 / (m1 * r^2)

Since m2 = 10 * m1 and r = 20 km, we can substitute these values into the equation:

a2 = G * m1 * (10 * m1) / (m1 * (20 km)^2)

Simplifying the equation, we get:

a2 = 10 * G / 400

Finally, the acceleration of asteroid 2 is approximately 0.025 * G.