Surface Gravity of a Neutron Star

In summary, the conversation discusses finding the distance a satellite must be from a neutron star with a mass five times that of Earth and a 10 KM radius in order to stay in a circular orbit at a speed of 50000 km/min. The process involves converting units and using the formula v = squareroot GM/R. However, there is a discrepancy in determining the mass of the neutron star, with different units and values being used. The correct units and value for the mass must be determined in order to accurately solve the problem.
  • #1
scoles
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A neutron star has a mass five times that of Earth and a 10 KM radius. Find the distance from this star's surface a satellite must be at to stay in a circular orbit if the satellite is moving at 50000 km/min.

First, I changed the 10 KM to meters and found the mass of this neutron star. Then, I changed the 50000 km/min to 833,333 m/s (tell me if this is incorrect). Next, I used the equation v = squareroot GM/R and plugged in (6.67 x 10 to the negative eleventh power) for G and (10 to the 31st power) for M and the radius is unknown. I came up with -10,000 m, which is obviously incorrect. Am i doing something wrong?
 
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  • #2
How did you get 10^31 for M? And what units? g or kg? What unit does the formula require?
 
  • #3


I would first like to commend you for attempting to solve this problem on your own. However, it seems that you may have made a mistake in your calculations. The equation you used, v = squareroot GM/R, is for calculating the orbital velocity of a satellite. In order to find the distance from the surface of the neutron star that the satellite must be at, we need to use the equation for centripetal force, F = ma = GMm/R^2.

Using this equation, we can rearrange it to solve for R, the distance from the surface of the neutron star. We know the mass of the neutron star (5 times that of Earth, or approximately 3 x 10^31 kg) and the mass of the satellite (unknown, but not relevant for this calculation). We also know the speed of the satellite (833,333 m/s) and we can assume that it is in a circular orbit, so the acceleration is equal to the centripetal acceleration, which is v^2/R.

Plugging in all of these values, we get R = 6.25 x 10^6 m, or approximately 6,250 km. This means that the satellite must be at a distance of 6,250 km from the surface of the neutron star in order to maintain a circular orbit with a speed of 833,333 m/s.

It's also worth noting that this calculation is based on the assumption that the neutron star has a uniform mass distribution, which may not be the case in reality. There may also be other factors, such as the effects of general relativity, that could affect the actual distance from the surface that the satellite needs to be at. However, for the purposes of this calculation, the result of 6,250 km should be a good estimate.
 

Related to Surface Gravity of a Neutron Star

1. What is the surface gravity of a neutron star?

The surface gravity of a neutron star is incredibly strong, measuring approximately 2x10^11 times the gravity on Earth's surface. This means that if you were standing on the surface of a neutron star, you would be crushed under the intense gravitational pull.

2. How does the surface gravity of a neutron star compare to other celestial bodies?

The surface gravity of a neutron star is much stronger than any other known object in the universe. For comparison, the surface gravity of a black hole is even stronger, but only at the event horizon. The surface gravity of a neutron star is stronger than that of a white dwarf, which is the remnant of a low-mass star.

3. What causes the intense surface gravity of a neutron star?

The intense surface gravity of a neutron star is due to its incredibly high mass and compact size. Neutron stars are formed when a massive star collapses in on itself during a supernova explosion, causing the core to become extremely dense. This leads to a highly concentrated mass, resulting in strong gravitational pull on the surface.

4. How is the surface gravity of a neutron star measured?

The surface gravity of a neutron star is measured by observing the curvature of spacetime around the star. This can be done through the study of pulsars, which are rapidly rotating neutron stars that emit beams of electromagnetic radiation. By measuring the pulsar's rotation and mass, scientists can calculate the surface gravity of the neutron star.

5. Can the surface gravity of a neutron star be escaped?

Due to its incredibly strong gravitational pull, it is virtually impossible to escape the surface gravity of a neutron star. Even if an object were able to reach the escape velocity, the intense gravitational force would still pull it back towards the star. This is why neutron stars are often referred to as "cosmic traps".

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