Find the escape speed from (a) the Sun, (b) a white dwarf star with one solar mass (same as the Sun) and radius 10,000 km, (c) a neutron star of 2.0 solar masses and radius of 10.0 km, and finally (d) a star with 2 solar masses and radius 5930 m. Comment on the speed of part (d).
To find the escape speed, we can use the formula:
escape speed = √(2 * gravitational constant * mass / radius)
where the gravitational constant is approximately 6.67430 × 10^-11 m^3 kg^–1 s^–2.
(a) Escape speed from the Sun:
The mass of the Sun is approximately 1.989 × 10^30 kg, and its radius is about 6.9634 × 10^8 m. Plugging these values into the formula, we get:
escape speed = √(2 * (6.67430 × 10^-11) * (1.989 × 10^30) / (6.9634 × 10^8))
Calculating this will give us the escape speed from the Sun.
(b) Escape speed from a white dwarf star:
In this case, the mass of the white dwarf star is equal to the mass of the Sun (1.989 × 10^30 kg), and its radius is given as 10,000 km, which is equivalent to 10^7 m. Using the formula mentioned earlier, we have:
escape speed = √(2 * (6.67430 × 10^-11) * (1.989 × 10^30) / (10^7))
Performing this calculation will give us the escape speed from the white dwarf star.
(c) Escape speed from a neutron star:
For a neutron star with a mass of 2.0 solar masses, it would have a mass of approximately 2 * 1.989 × 10^30 kg. The radius is given as 10.0 km, which is equal to 10^4 m. Using the formula:
escape speed = √(2 * (6.67430 × 10^-11) * (2.0 * 1.989 × 10^30) / (10^4))
Solving this equation will provide us with the escape speed from the neutron star.
(d) Finally, for a star with 2 solar masses and a radius of 5930 m, we can again use the formula:
escape speed = √(2 * (6.67430 × 10^-11) * (2.0 * 1.989 × 10^30) / (5930))
This will give us the escape speed from this particular star.
Comment on the speed of part (d):
The speed obtained from part (d) is likely to be extremely high due to the small radius. Since the radius is only 5930 m, the denominator in the formula will be small, resulting in a large escape speed. However, it is important to note that this scenario seems highly unlikely, as a star with such a small radius is not known to exist. It is worth double-checking the given values to ensure accuracy.