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

Thread starter TobiasZed
Start date Nov 21, 2023
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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 :-(

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Nov 21, 2023

Hill

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Check your calculation.

Nov 21, 2023

Orodruin

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… and use units!

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

What is the formula to calculate the speed of a mass falling into a star?

The speed of a mass falling into a star can be estimated using the escape velocity formula: \( v = \sqrt{\frac{2GM}{R}} \), 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.

How does the mass of the star affect the speed of the falling mass?

The mass of the star directly affects the speed of the falling mass. A more massive star will have a stronger gravitational pull, resulting in a higher speed as the mass falls towards it. The relationship is proportional to the square root of the star's mass.

How does the radius of the star affect the speed of the falling mass?

The radius of the star inversely affects the speed of the falling mass. A larger radius means the surface is farther from the center of gravity, resulting in a lower speed. The relationship is inversely proportional to the square root of the star's radius.

Does the initial distance from the star matter when calculating the final speed?

Yes, the initial distance from the star matters. The formula \( v = \sqrt{\frac{2GM}{R}} \) assumes the mass starts from rest at the surface of the star. If the mass starts from a distance far away, you would need to account for the potential energy difference between the starting point and the surface of the star.

Can relativistic effects be ignored when calculating the speed of a mass falling into a star?

For most stars and typical distances, relativistic effects can be ignored, and Newtonian mechanics provide a good approximation. However, for extremely massive stars like neutron stars or black holes, relativistic effects become significant, and General Relativity would need to be used for accurate calculations.