Surface Gravity of a Neutron Star

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SUMMARY

The discussion focuses on calculating the orbital distance from the surface of a neutron star, which has a mass of 5 times that of Earth and a radius of 10 kilometers. The user converted the radius to meters and the satellite's speed to 833,333 m/s. They attempted to apply the formula v = √(GM/R) using the gravitational constant G as 6.67 x 10-11 m3kg-1s-2 and the mass M as 1031 kg. However, the user encountered an incorrect result of -10,000 m, indicating a misunderstanding in the application of the formula or unit conversions.

PREREQUISITES
  • Understanding of gravitational physics and orbital mechanics
  • Familiarity with the gravitational constant (G) and its units
  • Knowledge of mass units, specifically converting between kilograms and solar masses
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Review the concept of gravitational force and its application in orbital mechanics
  • Learn about the properties and characteristics of neutron stars
  • Study unit conversions, particularly between different mass and distance units
  • Explore the derivation and application of the orbital velocity formula v = √(GM/R)
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in the physics of neutron stars and orbital mechanics.

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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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How did you get 10^31 for M? And what units? g or kg? What unit does the formula require?
 

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