Physics Gravitational Force Question

In summary, the true weight of a remote probe at a distance H above the surface of a plane is one percent less than its true weight on the surface. The ratio between H and R, the radius of the planet, can be found by multiplying both sides of the equation by r^2 and writing it as 1/(1+h/r)^2.
  • #1
neoking77
31
0
At a distance H above the surface of a plane, the true weight of a remote probe is one percent less than its true weight on the surface. The radius of the planet is R. Find the ratio H/R.

Work:
Let Mp be mass of planet and Ms be the mass of space probe

(true weight) Ft = GMpM/(r+h)^2

(surface weight) Fs = GMpM/r^2

Ft = GMpMs/r^2 - GMpMs/r^2(0.01)

Ft = GMpMs/r^2 - GMpMs/r^2(0.01) = GMpMs/(r+h)^2

i don't know where to go from here

thanks in advance.
 
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  • #2
Multiply both sides by [itex]r^2[/itex] and write

[tex]\frac {r^2}{(r+h)^2}[/tex]

as

[tex]\frac {1}{\left(1 + \frac {h}{r}\right)^2}[/tex]

You should be able to handle the rest.
 
  • #3
thank you very much for your help
 

What is gravitational force?

Gravitational force is the attractive force between two objects with mass. It is responsible for keeping planets in orbit around the sun and objects on the surface of the Earth.

How is the strength of gravitational force determined?

The strength of gravitational force between two objects is determined by their masses and the distance between them. The larger the masses and the closer the distance, the stronger the force will be.

Can gravitational force be negative?

No, gravitational force is always positive. It is an attractive force, so it always pulls objects towards each other.

What is the relationship between distance and gravitational force?

The force of gravity decreases as the distance between two objects increases. This relationship follows the inverse-square law, meaning that if the distance is doubled, the force will decrease by a factor of four.

How does gravitational force affect objects on Earth?

Gravity is what keeps objects on the surface of the Earth and gives them weight. The force of gravity between the Earth and an object is what determines the object's weight.

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