Speed of a mass falling into a star given the mass and radius of the star

Thread starter TobiasZed
Start date Nov 21, 2023
Tags

Mass Radius Speed

Nov 21, 2023

TobiasZed

Homework Statement: Beginning at rest at an extremely large separation, a ball is released and allowed to fall toward a star of mass 3.90E+30 kg and radius 5.70E+7 m. What is the speed of the ball when it reaches the surface?

Relevant Equations: square root of (2*G*M)/(r)

I tried the square root of ((2)(6.67*10^-11)(3.90E+30))/(5.70E+7)
I got 1.55*10^-5 and that is wrong. Maybe I am using the wrong equation but this is the one of professor gave me and I don't know what I am doing wrong :-(

Physics news on Phys.org

Nov 21, 2023

Hill

Homework Helper

Gold Member

Check your calculation.

Nov 21, 2023

Orodruin

Staff Emeritus

Science Advisor

Homework Helper

Insights Author

Gold Member

… and use units!

1. What is the formula for calculating the speed of a mass falling into a star given the mass and radius of the star?

The formula for calculating the speed of a mass falling into a star is v = √(2GM/R), where v is the speed, G is the gravitational constant, M is the mass of the star, and R is the radius of the star.

2. How does the mass and radius of the star affect the speed of a mass falling into it?

The speed of a mass falling into a star is directly proportional to the mass of the star and inversely proportional to the radius of the star. This means that as the mass of the star increases, the speed of the falling mass will also increase, while a larger radius will result in a slower falling speed.

3. Can the speed of a mass falling into a star ever exceed the speed of light?

No, the speed of a mass falling into a star cannot exceed the speed of light. According to Einstein's theory of relativity, nothing can travel faster than the speed of light.

4. How does the speed of a mass falling into a star change as it gets closer to the star?

As the mass gets closer to the star, the speed will increase due to the increasing gravitational pull of the star. However, once the mass reaches the surface of the star, its speed will be equal to the escape velocity, which is the minimum speed required for an object to escape the gravitational pull of the star.

5. What other factors may affect the speed of a mass falling into a star?

Aside from the mass and radius of the star, other factors that may affect the speed of a mass falling into a star include the initial distance of the mass from the star, the mass of the falling object, and any external forces acting on the mass (such as air resistance).