DescentBB

The space shuttle reaches an altitude of up to 3.90 x 10^6 meters when it docks with Mir.

1. What is the magnitude of the acceleration due to gravity at this altitude?

2. Write a vector-valued function for the gravitational field of the earth.

3. Using the function from part 2, calculate the gravitational potential of the earth.

4. Is the gravitational field solenoidal? Irrotational? Provide proof for each answer.

You may use any resources you like. ^_~

Assume no general relativity.

<3

I'll give out cookies to whoever gets each one first. ^_~

too lazy for homework?

LOL, yeah you need to work these out yourself to get full credit and understand them for the test..... (And if it is the test, well, you should know already then )

1 is pretty easy. 2,3,4 I have no clue. Gravity acts towards the center of the earth, so if you need to write a vector equation it might be best to use a spherical coordinate system, so you just have 1 coordinate vector variable (radius).

Governing Equation

F=G(m1*m2)/r^2

G= 6.673×10−11 N m^2 kg^−2
m1 = mass of earth= 5.9742 × 10^24 kg
m2 = mass of shuttle = 2,029,203 kg
radius of earth = 6,378,100 m
elevation = 3.90 x 10^6 m
r = radius of earth + elevation

solve for F (N)

divide by mass of shuttle

== acceleration of shuttle due to gravity


Here's the wiki on gravitational potential:
http://en.wikipedia.org/wiki/Gravitational_potential

What course is this for?

--------<TANGENT>-----------
divide by 9.81 to get G-Forces (should be <1...microgravity)

The shuttle when orbiting earth is actually in constant freefall (it is still under gravity's effect, so it still falls to the earth), the reason they don't fall out of the sky is because they also have a velocity tangent to the earth. In other words the shuttle is going forward fast enough that even though its falling downwards, it doesnt change elevation.

It's actually pretty easy to solve for the shuttle's velocity tangent to gravity:
Centripetal_force

set F = force of gravity at that elevation
r = r in previous equation
m = mass of shuttle
solve for v
--------</TANGENT>-----------

/facepalm

This isn't my homework. 9_9

I just thought it would be fun to see if other people can solve them. ^_~

You don't have to believe me. :P

ccb, number 1 isn't right, but you are close. :) Your equation for F is a force equation, not one for acceleration. Hint, hint. ^_~

I'm only giving everyone a week to solve them, then I will post the answers. ^_~

I think I did get it right....

At the end I saif you had force in newtons, then I said to divide by the mass of the shuttle to get accel....

F=ma


In the end the mass of the shuttle doesnt matter

Burlyman wrote:/facepalm

This isn't my homework. 9_9

I just thought it would be fun to see if other people can solve them. ^_~

You don't have to believe me.

ccb, number 1 isn't right, but you are close. Your equation for F is a force equation, not one for acceleration. Hint, hint. ^_~

I'm only giving everyone a week to solve them, then I will post the answers. ^_~

o ^_^

Okay, so ccb056 explained how to get the answer for number one, but didn't write it. So, no cookies yet. ^_~ The answer I got is approx. 8.70 meters per second per second.


Any takers for the other ones? ^_~

Okay, I'll give you all a hint... the answer for number 1 leads into the answer for #2 :P