Question

Imagine that asteroid A that has an escape velocity of 50 m/s. If asteroid B has twice the mass and twice the radius, it would have an escape velocity ______________ the escape velocity of asteroid A.

Answer 1

Answer:

The same as the escape velocity of asteorid A (50m/s)

Explanation:

The escape velocity is described as follows:

$v=\sqrt{\frac{2GM}{R}}$

where $G$ is the universal gravitational constant, $M$ is the mass of the asteroid and $R$ is the radius

and since the scape velocity is 50m/s:

$50m/s=\sqrt{\frac{2GM}{R}}$

Now, if the astroid B has twice mass and twice the radius, we have that tha mass is: $2M$

and the radius is: $2R$

inserting these values into the formula for escape velocity:

$v=\sqrt{\frac{2G(2M)}{2R} } =\sqrt{\frac{4GM}{2R} } =\sqrt{\frac{2GM}{R} }$

and we have found that $50m/s=\sqrt{\frac{2GM}{R}}$, so the two asteroids have the same escape velocity.

We found that the expression for escape velocity remains the same as for asteroid A, this because both quantities (radius and mass) doubled, so it does not affect the equation.

The answer is

Asteroid B would have an escape velocity the same as the escape velocity of asteroid A