Question

What is the escape velocity (in km/s) from the surface of a 1.7 M neutron star? From a 3.0 M neutron star?

Hint: Vₑ= 2GM/r;
make sure to express quantities in units of meters, kilograms, and seconds. Assume a neutron star has a radius of 12 km and assume the mass of the Sun is 1.99 ✕ 10³⁰ kg.)

Answer 1

The escape velocity from the surface of a 1.7 M neutron star is 2.1658 × 10⁶ km/s, while the escape velocity from the surface of a 3.0 M neutron star is 3.8578 × 10⁶ km/s.

Step-by-step explanation:

To calculate the escape velocity, we use the formula Vₑ= 2GM/r, where Vₑ is the escape velocity, G is the gravitational constant (6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻²), M is the mass of the object, and r is the radius of the object.

For a 1.7 M neutron star with a radius of 12 km, the escape velocity would be:

Vₑ = 2 * 6.67430 × 10⁻¹¹ * 1.7 * 1.99 × 10³⁰ / (12 * 10³) = 2.1658 × 10⁶ km/s.

For a 3.0 M neutron star with a radius of 12 km, the escape velocity would be:

Vₑ = 2 * 6.67430 × 10⁻¹¹ * 3.0 * 1.99 × 10³⁰ / (12 * 10³) = 3.8578 × 10⁶ km/s.