a space craft at 3.2x10^5 meters given the radius of earth of 6380 Km. no more details were given. how can i find the gravitational force that act on the space craft?

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## Answers (4)

This problem may be tackled using a ratio approach. Starting with Newton's equation of universal gravitation: -

F = GMm

....._____

.........r²

And assuming that the gravitational acceleration at the Earth's surface is 9.81 m/s². We can calculate the ratio of forces for 1 kg of the spacecraft and eliminate the mass of the Earth M. Thus, at a distance R = 3.2 x 10^5 m the force due to gravity on 1 kg of spacecraft is: -

F' =............. GM.1

....._____________________

......(6.38 x 10^6 + 3.2 x 10^5)²

and at the surface of the Earth the force on 1 kg of spacecraft is

9.81 = .....GM.1

..........___________

..........(6.38 x 10^6)²

The ratio of the forces is: -

F' = ............(6.38 x 10^6)²

___...___________________

9.81..(6.38 x 10^6 + 3.2 x 10^5)²

Thus, with rearrangement and calculation. The force of each kilogramme of spacecraft is: -

F' = 8.895 N/kg

This seems a reasonable result since 3.2 x 10^5 m is only 320 km above the Earth's surface.

A check of this calculation with the mass of the Earth as 5.977 x 10^24 kg confirms the result for r = 3.2 x 10^5 + 6.38 x 10^6 m.

I hope this approach helps!

not enough info, you don't need the size of the craft you need it's mass.

You were not given enough information to find the gravitational force.

The formula for gravitational force is:

F = GMm/rÂ²

Where:

G = Universal Gravitational constant (you can find it in a table or anywhere on the internet).

M = Mass of earth (you can look that up too, although I'm surprised they did not give it to you since they told you the earth's radius.)

m = mass of spacecraft (NOT GIVEN!!)

r = distance from earth's center (this would be 6380 km + 3.2 Ã 10^5 m; or: 6700 km).

If you don't know the mass of the space craft, you can't solve this problem.

[EDIT: The method proposed by "right hand of doom" will not work. That's not how the math works. The formula he gives will tell you the space craft's acceleration; not the force.]

Newton's theory of gravity - gravitational force equals the product of the masses of the two objects, divided by the distance between them, and multiplied by a constant.

So if you have the two object's mass, the distance dividing them, and the constant, you should be able to calculate the gravitational forces.

But if they didn't give you the mass of either the craft or the Earth, I think you're screwed...