Neutron stars, such as the one at the center of the Crab...

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but have a much smaller diameter. If you weigh 675 $\mathrm{N}$ on the earth, what would you weigh at the surface of a neutron star that hat has the same mass as our sun and a diameter of 20 $\mathrm{km}$ ?

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but have a much smaller diameter. If you weigh 675 $\mathrm{N}$ on the earth, what would you weigh
at the surface of a neutron star that hat has the same mass as our sun and a diameter of 20 $\mathrm{km}$ ?

Key Concepts

Scaling Relations in Astrophysics

Scaling relations in astrophysics involve comparing physical quantities such as mass, radius, and gravitational acceleration between different celestial bodies. When an object has a similar mass but a much smaller radius, as is the case with neutron stars compared to the sun or Earth, these scaling laws predict significantly stronger gravitational effects, thereby drastically increasing the apparent weight at the surface.

Neutron Stars

Neutron stars are extremely dense remnants of massive stars that have undergone supernova explosions. They contain masses comparable to that of the sun compressed into a sphere with a radius of only a few kilometers, resulting in an incredibly strong gravitational field at their surfaces.

Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation states that the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This principle is fundamental in calculating how weight, which is the force of gravity acting on a mass, varies based on the mass of the celestial body and the distance from its center.

Surface Gravity Calculation

Surface gravity is the acceleration due to gravity that a body exerts at its surface and is calculated using the formula g = GM/R², where G is the gravitational constant, M is the mass of the body, and R is its radius. This concept is essential for understanding how a person’s weight would change when moving from Earth’s surface to the surface of a compact object like a neutron star.

Transcript

00:01 So in this question, we're told that neutron stars, such as the one at the center of the crab mambula, have about the same mass as our sun, but a much smaller diameter.

00:13 They are very, very dense astronomical objects.

00:17 We are asked to calculate what a person who weighs 675 newtons on earth would weigh on the surface of a neutron star that has the same mass as our sun, but a diameter of only 20 kilometers.

00:36 So in order to calculate the weight at the surface of the neutron star, we do need to know the mass of the person.

00:45 So we're not given the mass of the person.

00:47 We're given their weight on earth.

00:50 So we need to convert between that weight, i .e.

00:55 The force of gravity and the mass.

00:58 So we know that the force of gravity is equal to mass times the acceleration due to gravity.

01:07 And so we can calculate the mass just by dividing that 675 by g 9 .81.

01:16 And when we do that, we get a mass of, for the person, of 68 .8 kilograms.

01:23 So this represents, you know, the actual amount of stuff in the person, not necessarily the weight.

01:29 Or the gravitational force experienced by the person due to any object.

01:36 So now that we have that, we can go ahead and calculate what is the force of gravity if this person is located on the surface of the neutron star...

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