Gravity on Earth: 70% Value Above Surface?

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SUMMARY

To determine the altitude above Earth's surface where gravity is reduced to 70% of its surface value (9.8 m/s²), one must utilize the gravitational force equation Fg = G*m1*m2/r². The solution involves understanding the inverse square law of gravity, which states that as distance from the center of the Earth increases, the gravitational force decreases proportionally to the square of the distance. By establishing the relationship between the radius of the Earth (R) and the desired gravitational force, one can calculate the necessary height above the surface.

PREREQUISITES
  • Understanding of gravitational force equations, specifically Fg = G*m1*m2/r²
  • Familiarity with the concept of inverse square law in physics
  • Knowledge of Earth's radius and its approximate value (6,371 km)
  • Basic algebra skills for manipulating equations and ratios
NEXT STEPS
  • Calculate the height above Earth's surface where gravity equals 0.70 times its surface value
  • Explore the implications of gravitational force changes with altitude
  • Investigate the relationship between mass, distance, and gravitational force in different celestial contexts
  • Learn about gravitational potential energy and its dependence on height
USEFUL FOR

Students studying physics, educators teaching gravitational concepts, and anyone interested in understanding the effects of altitude on gravitational force.

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Homework Statement



How far above the surface of the Earth do you need to be for the force of gravity to be reduced to 70% of its value on the surface.

Homework Equations


g on surface is 9.8 m/s^2

Fg=G*m1*m2/r^2


The Attempt at a Solution



Is there a way to do this without knowing the mass of the earth? It seems as though the gravity equation I have above could only be useful if you knew either the mass of the Earth or the radius of the earth. I was just wondering if there is a way to approach this without knowing either of those. Thanks!
 
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Instead of plug and chug into the gravitational force equation, try working with ratios.
Everything drops out except for the radii between the masses.
 
Since you are being asked for the specific distance, then you will ultimately need to know the Earth's radius, which is easy enough to find.

Remember that "r" is not zero at Earth's surface, but "R" (let that represent the Earth's radius.

Think about the "inverse square proportionality" of force with distance. If distance doubled (that is, if you went a distance of R above the surface so the distance from Earth's center is "2R"), the field and therefor the force would be (1/4)F , or (0.25)F (compared to F on the surface). If distance was 3R, the force would be (1/9)F , or (0.111)F .

You need to figure out what factor of R would produce (0.70)F
 

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