Motion in 2D astronaut orbiting moon

[knightassassin]

Homework Statement

The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 700 km above the Earth's surface, where the free-fall acceleration is 8.12 m/s2. Take the radius of the Earth as 6400 km. 2. Relevant equations
T=2(pi)radius/velocity
radial acceleration=V^2/radiusI am not sure if this is relevant, but the distance from the the satellite to the center of the Earth is 6400km+700km=7100km.
Next I try to find the time it takes the satellite to reach the center:
First I find velocity from the radial acceleration equation. I set a=8.12m/s^2 (not sure if this is right)
Next I solve for velocity=sqrt(a*r) where r=6400
v=7208m/s
Next I use the velocity to calculate the time it takes for the object to reach the center using the equation T=2(pi)radius/velocity
=2pi*6400000/7208
=92.98 min (I already converted it back to minutes from seconds)

I am not sure what I am doing wrong.

 

[djeitnstine]

Err, what is the objective of all of this? To find the time it takes for the object to reach the center? The center of what?

What does the question ask you to solve?

And just from looking at your r, you seem to be using the r that is at Earth's surface, not the actual one you calculated above.

 

[knightassassin]

whoops, sorry I forgot that part

a) Determine the speed of the satellite.
b)Determine the time interval required to complete one orbit around the Earth.

 

[LowlyPion]

whoops, sorry I forgot that part

a) Determine the speed of the satellite.
b)Determine the time interval required to complete one orbit around the Earth.

They give you gravity at that altitude, so that makes it simpler.

m*g' = m*v²/ r

Where r = 6400 + 700 = 7100 km

Careful of units.

 

[knightassassin]

what does m stand for?

 

[djeitnstine]

generally in physics m stands for mass... and usually when you see 'm' and 'g' together that is a big give away.

 

[LowlyPion]

what does m stand for?

As djeitnstine has pointed out, it is mass.

Before you ask what it is for the satellite, notice that whatever it is cancels out.