How to Calculate Gravitational Field Strength at 400000m from Earth?

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SUMMARY

The gravitational field strength at a height of 400,000 meters from Earth's surface is calculated using the formula F_G/m = -GM/r². The gravitational potential at this height is -59.12 MJ/kg, while at the surface it is -62.72 MJ/kg. The correct gravitational field strength at 400,000 meters is determined to be -8.4 mega Newtons per kilogram (MN/kg). It is crucial to use the distance from the center of the Earth in calculations rather than the height above the surface.

PREREQUISITES
  • Understanding of gravitational potential energy and field strength
  • Familiarity with the formula F_G/m = -GM/r²
  • Knowledge of gravitational constants and units (e.g., mega Newtons)
  • Basic concepts of physics related to gravitational forces
NEXT STEPS
  • Study the derivation of gravitational potential and field strength equations
  • Learn about the implications of gravitational field strength variations with altitude
  • Explore the concept of gravitational potential energy in different contexts
  • Investigate the applications of gravitational calculations in aerospace engineering
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Physics students, aerospace engineers, and anyone interested in gravitational calculations and their applications in real-world scenarios.

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Distance form the Earth's surface: Gravitational potential/MJkg-1
0 : -62.72
400000 : -59.12

Deduce the Earth's gravitational field strength at a height of 400000m.

Since g=-GM/r^2 and V=-GM/r , I tried to solve this question using V/r. But I failed to get the correct answer. Any suggestion on how to approach the question?
 
Last edited:
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I don't understand your notation in the first paragraph.

However, be sure to use the distance from the center of the Earth in your calculation (and NOT the height above the surface)!
 
The gravitational field is given by
[tex]F_G/m=-\frac{GM}{r^2}[/tex]
so at the surface it is [itex]-9.8[/itex]
and at the required distance [itex]-8.4[/itex] mega Newtons per kilogram.
 
Last edited:

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