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

Hint:

Escape velocity
=√(2GM/r)
G=gravitational constant
M=mass
r=radius

When mass is doubled, replace M by 2M, similarly for r.

For further reading, see for example:
http://en.wikipedia.org/wiki/Escape_velocity

25 the same

half

To determine how the escape velocity of asteroid B relates to the escape velocity of asteroid A, we need to understand the factors that influence the escape velocity of an object.

The escape velocity of an object depends on its mass and radius. The formula to calculate escape velocity (v) is given by:

v = √(2GM/r)

In this formula, G is the universal gravitational constant, M is the mass of the object, and r is the radius of the object.

Let's calculate the escape velocity of asteroid B step-by-step:

1. We know that asteroid B has twice the mass of asteroid A. So, if the mass of asteroid A is represented as Ma, then the mass of asteroid B is 2Ma.

2. We also know that asteroid B has twice the radius of asteroid A. If the radius of asteroid A is represented as Ra, then the radius of asteroid B is 2Ra.

3. Plugging these values into the escape velocity formula for asteroid B, we get:

vB = √(2G(2Ma)/(2Ra))

4. Simplifying the equation further, we have:

vB = √(4GMa/2Ra)

5. Cancelling out common terms, we have:

vB = √(2GMa/Ra)

Comparing this with the original formula for asteroid A (vA = √(2GMa/Ra)), we can see that the escape velocity of asteroid B is the same as the escape velocity of asteroid A.

In summary, if asteroid B has twice the mass and twice the radius of asteroid A, it would have the same escape velocity as asteroid A.