How Does Distance from Earth Affect Spacecraft Weight?

[Coco12]

Homework Statement

The radius of the Earth is 6400km. A 7200n spacecraft travels away from the earth. what would be the weight of the spacecraft at the following distances from the Earths surface: 6400km, 12800km

Homework Equations

Fg=mg
F=Gm1m2/r^2

The Attempt at a Solution

Just want to confirm I'm doing this right
So first I want to find the mass of the spacecraft so I use the fg=mg formula. I know that the mass of the Earth is 5.98*10^24kg.

Gravitational constant is 6.67*10^-11

I use the universal gravitation formula

The r will just be the radius of the Earth PLUS the distance from the Earth's surface. (Converted to m)

Then just plug into the equation. Am I doing this right?

 

[nasu]

It is not wrong but too complicted. They give these nice numbers for a reason.
Look at the numbers. By what factor increases the distance? What does this tell about the change in force?

 

[Coco12]

The factor increases by 2 (6400+6400) then 3 (6400+12800)

So u mean I would just multiply 7200 by 1/4 for the distance 12800 from th Earth's center
And 1/9 for the distance 19200 ?

 

[BOAS]

The factor increases by 2 (6400+6400) then 3 (6400+12800)

So u mean I would just multiply 7200 by 1/4 for the distance 12800 from th Earth's center
And 1/9 for the distance 19200 ?

You have what is known as 'an inverse square law'

ie

Force due to gravity decreases with 1/r^2

 

[nasu]

The factor increases by 2 (6400+6400) then 3 (6400+12800)

So u mean I would just multiply 7200 by 1/4 for the distance 12800 from th Earth's center
And 1/9 for the distance 19200 ?

Yes. This will do it.