# Q & A: Gravity of Neutron Stars

Q:
How much gravity do neutron stars exert?
- mike (age 25)
A:
Good question, Mike!

Neutron Stars actually exert a lot of gravity for objects as small as they are (about 10 kilometers in radius). In fact, if you stood on the surface of a neutron star you would feel about 200 Billion times more gravity than here on Earth (which would not be healthy)!

For those interested in how to get that number, I work it out below:

Recall Newton's Equation for Gravitational Force:

F = GMm/(r^2)

We can use this classical formula to estimate the gravity on a Neutron Star. Use the fact that a Neutron Star has about 1.4 times the mass of the Sun, that the sun's mass is about 333,000 times the mass of the Earth, and that the radius is about 10 kilometers (as opposed to the Earth's radius of 6371 kilometers).

The ratio of forces is:
F(Neutron Star) / F(Earth)=(1.4)(333000)(6371^2)/(10^2)

If we run these numbers we find that the gravity on a Neutron Star is about 2 x 10^11 times that of the Earth's. That's about 200 billion times bigger!

math dan

(published on 10/22/2007)

## Follow-Up #1: What's in a neutron star?

Q:
If the massive gravitational attraction of a Neutron Star can crush the empty space out of atoms, what would happen to ordinary matter that was placed on the surface? Would those atoms also dissolve into electrons, protons, and neutrons in contact with each other. "Squish?"
- Michael (age 55)
San Diego, CA USA
A:
Neutron stars do start out as ordinary matter. Except for a thin crust, they go past the stage of being "electrons, protons, and neutrons in contact with each other" into being just neutrons. The pressure is so great that the electrons combine with the protons. This will also happen to the stuff that's added on. Squish!

Mike W.

(published on 08/03/2012)

## Follow-Up #2: neutron star gravity

Q:
is neutron star gravity greater than the parent star
- rahul kumar (age 14)
Amlatola,chaibasa(Jharkhand)
A:
At a large distance, the gravity only depends on the mass, so a neutron star would have a little less than the star it came from. However, the neutron star is much more compact than the parent star, so the surface is in much closer to the mass. That's why the gravitational field at the surface is much bigger for the neutron star.

Mike W.

(published on 01/09/2013)