Calculate the force of gravity on a spacecraft

[mathcrzy]

1. Homework Statement

Calculate the force of gravity on a spacecraft 19200 km (3 Earth radii) above the Earth's surface if its mass is 1500 kg.


2. Homework Equations

Fg=[(G)(M spacecraft )(Mearth)]/r^2=ma.

3. The Attempt at a Solution

a=[(6.67e-11)(1500)(6e24)]/19200000^2(convert km to m)=1628.4

 

[dynamicsolo]

1. Homework Statement

Calculate the force of gravity on a spacecraft 19200 km (3 Earth radii) above the Earth's surface if its mass is 1500 kg.


2. Homework Equations

Fg=[(G)(M spacecraft )(Mearth)]/r^2=ma.

3. The Attempt at a Solution

a=[(6.67e-11)(1500)(6e24)]/19200000^2(convert km to m)=1628.4

Whoops! Ya fell into the pit -- they catch lots of students this way (especially on multiple choice questions). What does r represent in Newton's gravitational force equation? The distance you are given is measured from the surface of the Earth, that is, it is an altitude... (Oh, and don't forget to put units on your answers!)

 

[mathcrzy]

r represents the radius and so it would be 4 Earth radii because they only talk about from the surface? so if that is the case i would do a=[(6.67e-11)(1500)(6e24)]/25600000^2(convert km to m)=915.98N

 

[dynamicsolo]

r represents the radius and so it would be 4 Earth radii because they only talk about from the surface? so if that is the case i would do a=[(6.67e-11)(1500)(6e24)]/25600000^2(convert km to m)=915.98N

That looks fine! Be sure to read exam problems carefully because little traps like this are frequently set for the unwary. (Altitude is more convenient for describing orbits, and people who work with Earth satellites do so all the time, but the value always has to be adjusted to distance from the center of Earth for use in equations.)