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

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Homework Help Overview

The problem involves calculating the ratio of distance d above a planet's surface to the planet's radius r, given that an object's weight at that distance is 1% less than its weight on the surface. The context is centered around gravitational forces and the application of Newton's law of gravitation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of the weight change and question the relationship between distance d and radius r. There are inquiries about the application of Newton's law of gravitation and its relevance to the problem setup.

Discussion Status

Participants are actively engaging with the problem, exploring various interpretations of the gravitational equations. Some guidance has been offered regarding the formulation of the equations, but there is no explicit consensus on the approach to take.

Contextual Notes

There are discussions about the definitions of variables and the assumptions regarding the distance from the surface versus the center of the planet. The distinction between the unknown planet and Earth is also noted.

goonking
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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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