Calculating the Ratio of d/r for an Object Above a Planet Surface

AI Thread Summary
An object located a distance d above a planet's surface experiences a weight reduction of 1% compared to its weight on the surface, prompting the need to calculate the ratio d/r. The discussion emphasizes that d must be significantly smaller than the planet's radius r, suggesting that d/r will yield a large number. The relevant equation derived from Newton's law of gravitation is 0.99g = GMe/(D+R)^2, where g represents the gravitational force at the surface. Participants clarify that the mass should be denoted as Mp for the unknown planet rather than Me for Earth. This analysis highlights the relationship between gravitational force and distance from the planet's surface.
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Homework Statement


An object is located a distance d above the surface of a large planet of radius r. At this position, its true weight is one percent (1.000 %) less than its true weight on the surface. What is the ratio of d/r?

Homework Equations

The Attempt at a Solution


so if something weights 100 kg on the earth, at 'that' distance, it should weigh 99k.

so d should be extremely small compared to R.

D/R should be a big number then. But I have no idea how to put this into calculations.
 
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goonking said:


so d should be extremely small compared to R.

Based on what?
What is Newton's law of gravitation?
 
billy_joule said:
Based on what?
What is Newton's law of gravitation?
D is just the distance from the surface to the point in space, it is not the distance from the center of the Earth to the point in space.
So if a person would only get 1% lighter in terms of weight at that point, it shouldn't be very far away from the surface of the earth.

Newton's law of gravitation is g = GMe / R^2e

Me = mass of earth

Re = radius of earth
 
That's half of it. The right side of your equation is the force of gravity a distance D above the surface of the unknown planet. The left hand side is 99 percent of the force of gravity at the surface of the unknown planet. You are correctly equating the two numbers.

Now can you express the surface gravity of the unknown planet in terms of Newton's universal law of gravitation?

On a cosmetic note... it's not the earth. So the mass should probably be symbolized as ##M_p## (mass of the unknown planet) rather than ##M_e##.
 

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