An asteroid through a massive of
The relationship between force and acceleration is Newton"s 2nd law:
We know the mass, but we will need to discover the force. Because that this calculation, usage the law of global gravitation:
We are offered the value of each mass, the distance (radius), and also the gravitational constant. Making use of these values, we deserve to solve because that the pressure of gravity.
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Now the we understand the force, we can use this value through the mass of the asteroid to discover its acceleration.
Two asteroids exert a gravitational force on one another. By what factor would this force adjust if one asteroid doubles in mass, the various other asteroid triples in mass, and also the distance in between them is quadrupled?
The equation for the pressure of gravity between two objects is:
Using this equation, we can choose arbitrary worths for our initial masses and also distance. This will make it easier to solve when these values change.
We have the right to use our very first calculation to check out the how the pressure has changed.
We can use the preservation of momentum to solve. Due to the fact that the satellites rod together, there is just one last velocity term.
We know the masses because that both satellites space equal, and also the second satellite is at first stationary.
Now we need to discover the velocity that the very first satellite. Because the satellite is in orbit (circular motion), we require to find the tangential velocity. We have the right to do this by recognize the centripetal acceleration native the centripetal force.
Recognize the the force because of gravity that the planet on the satellite is the exact same as the centripetal force acting ~ above the satellite. That means
Remember the r is the distance between the centers the the two objects. That means it will be equal to the radius the the planet PLUS the orbiting distance.
Use the provided values because that the masses the the objects and distance to solve for the force of gravity.
Now that we recognize the force, us can discover the acceleration. Remember that centripetal force is Fc=m∗ac. Collection our two pressures equal and also solve for the centripetal acceleration.
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Now us can discover the tangential velocity, utilizing the equation because that centripetal acceleration. Again, remember that the radius is equal to the amount of the radius of the Earth and also the elevation of the satellite!
This value is the tangential velocity, or the initial velocity that the an initial satellite. We can plug this into the equation for conversation of momentum to settle for the last velocity that the two satellites.