Question

The escape velocity from the sun surface today is 618 km/s. What will the escape velocity be when the sun becomes a red giant with a radius 60 times greater and a mass only 0.8 times that of today?

Answer 1

The escape velocity from the sun's surface will be approximately 101 km/s when it becomes a red giant.

Step-by-step explanation:

To calculate the escape velocity when the sun becomes a red giant, we need to consider the changes in mass and radius. The escape velocity formula is given by:

v = sqrt(2GM/r)

where v is the escape velocity, G is the gravitational constant, M is the mass of the object, and r is the distance from the center of the object.

In this case, the mass of the sun becomes 0.8 times its current mass, so we can substitute 0.8M for M in the formula. The radius becomes 60 times greater, so we can substitute 60r for r in the formula. Substituting these values into the formula, we get:

v' = sqrt(2G(0.8M)/(60r))

Simplifying, we find:

v' = sqrt(0.0267v)

Therefore, the escape velocity when the sun becomes a red giant will be approximately 0.1637 times the current escape velocity, or 0.1637 * 618 km/s = 101 km/s.

Answer 2

The escape velocity from the Sun's surface today is 618 km/s. When the Sun becomes a red giant with a radius 60 times greater and a mass only 0.8 times that of today, the escape velocity will be approximately 597 km/s.

Step-by-step explanation:

The escape velocity from the surface of the Sun can be calculated using the formula:

v = √(2GM/R)

where v is the escape velocity, G is the gravitational constant, M is the mass of the Sun, and R is the radius of the Sun.

Given that the escape velocity from the Sun's surface today is 618 km/s, we can use this equation to find v:

`618 = \sqrt{(2GM/R)`

Solving for GM, we get -

`GM = (v^2R)/2 = (618^2 * R)/2.`

When the Sun becomes a red giant with a radius 60 times greater and a mass only 0.8 times that of today, we can substitute these new values into the equation:

`v' = \sqrt(2GM'/R')`

Substituting the new values, we get v'

`= \sqrt{(2*0.8*GM/R*60)`

`= \sqrt{(0.96 * GM/R*60).`

Therefore, the escape velocity when the Sun becomes a red giant will be √(0.96) times the current escape velocity:

`v' = \sqrt{(0.96) * 618 km/s`

= 597 km/s.