Space Help (1 Viewer)

[mrzeidan1]

Imagine that you were to travel in a spacecraft of mass 10,000kg from the Earth to the Moon. After liftoff, you intend to orbit the Earth at an altitude of 40,000km and then proceed to the moon.

I am asked in this question to investigate the acceleration due to gravity acting upon the spacecraft during its journey...

Do I need to take both the gravitational force of the Earth and the Moon into account?

If so, how can I work them out?

Thanks in advance

 

[Heart.O.Gold]

Imagine that you were to travel in a spacecraft of mass 10,000kg from the Earth to the Moon. After liftoff, you intend to orbit the Earth at an altitude of 40,000km and then proceed to the moon.

I am asked in this question to investigate the acceleration due to gravity acting upon the spacecraft during its journey...

Do I need to take both the gravitational force of the Earth and the Moon into account?

If so, how can I work them out?

Thanks in advance

I am guessing there are a few parts to this question;
---------------

At lift-off- the acceleration due to gravity is 9.8ms^-2
To work it out to equal 9.8ms^-2
g= G X (mass of Earth / Radius of Earth^2)

G= 6.67X10^-11 Mass of Earth = 5.97X10^24 Radius of Earth = 6.3X10^6)

------------------
Orbiting Altitude- acceleration due to gravity is 0.19ms^-2
g = G X (mass of Earth/ [radius of Earth + altitude]^2)

G= 6.67X10^-11, Mass of Earth = 5.97X10^24 Radius = 6.3X10^6 + 40 000 000

Therefore g = 0.19ms^-2
---------------
g at the moon - acceleration due to gravity is 1.6ms^-2
g= GX (mass of moon / Radius of moon^2)

G=6.67X10^-11 Mass of Moon = 7.35X10^22 Radius of moon = 1738
g=1.6ms^-2
----------------

Hope that is what you were looking for...

 

[mrzeidan1]

Thanks mate. We also have to graph results taking 5 points into consideration. Does this mean that i need to calculate 2 points between the orbit and takeoff/landing?

 

[Forbidden.]

I am guessing there are a few parts to this question;
---------------

At lift-off- the acceleration due to gravity is 9.8ms^-2
To work it out to equal 9.8ms^-2
g= G X (mass of Earth / Radius of Earth^2)

G= 6.67X10^-11 Mass of Earth = 5.97X10^24 Radius of Earth = 6.3X10^6)

------------------
Orbiting Altitude- acceleration due to gravity is 0.19ms^-2
g = G X (mass of Earth/ [radius of Earth + altitude]^2)

G= 6.67X10^-11, Mass of Earth = 5.97X10^24 Radius = 6.3X10^6 + 40 000 000

Therefore g = 0.19ms^-2
---------------
g at the moon - acceleration due to gravity is 1.6ms^-2
g= GX (mass of moon / Radius of moon^2)

G=6.67X10^-11 Mass of Moon = 7.35X10^22 Radius of moon = 1738
g=1.6ms^-2
----------------

Hope that is what you were looking for...

Now I'll modify that a little and I'll use these tags to make it look easier ...

[sup][/sup]

Throughout all the working out, g will be the acceleration due to gravity in meters per second squared (ms^-2) and G will be the universal gravitational constant (i.e 6.67x10^-11 Nm² kg^-2)

At lift-off- the acceleration due to gravity is 9.8ms^-2
To work it out to equal 9.8ms^-2

m_e is the mass of Earth
r_e is the radius of Earth

Data:

g = ?
G = 6.67x10^-11 Nm² kg^-2
Mass of Earth = m_e = 5.97x10²⁴ kg
Radius of Earth = r_e = 6.3x10⁶ m

g = Gm_e/r_e²



------------------

Hey, is this finding the acceleration due to gravity at 40,000km above the earth ?

Orbiting Altitude- acceleration due to gravity is 0.19ms^-2

Data

Let r_o be orbital radius of Earth
Orbital Radius of Earth = r_o = r_e + r_a
Where r_a is the altitude


g = ?
G = 6.67x10^-11 Nm² kg^-2
Mass of Earth = m_e = 5.97x10²⁴ kg
Radius+Orbital Altitude of Earth = r_o = 6.3x10⁶ m + 40 000 000 m
(Don't forget your units.) (4.0x10⁷ m)

g = Gm_e/r_o²

Therefore g = 0.19ms^-2

Therefore the higher the altitude the weaker the acceleration due to gravity, they are inversely proportional.
Sub in a big value for Orbital Altitude, you get a small acceleration
Sub in a small value for Orbital Altitude, you get a larger acceleration
Sub in no value for Orbital Altitude, you get the planet's original acceleration due to gravity on its surface (e.g on Earth's surface it's 9.8ms^-2)
---------------

g at the moon - acceleration due to gravity is 1.6ms^-2

G = 6.67x10^-11 Nm² kg^-2
Mass of Moon = m_m = 7.35x10²² kg
Radius of Moon = r_m = 1738 m

g = Gm_m/r_m²

g =1.6ms²

I assume this is at the Moon's surface
---------------

By the way, which formula is the
g = Gm/r² derived from ?

It has to do with escape velocity and centripedal acceleration ...

 

[Heart.O.Gold]

just got two questions.
1. how did you manage to use subsript and superscript?
2. Where the hell do u get off on remodeling my working weirdo?

 

[airie]

just got two questions.
1. how did you manage to use subsript and superscript?
2. Where the hell do u get off on remodeling my working weirdo?

There's no need to call him a weirdo, he's just trying to grasp it o.0

Check out the link to vB codes under "Posting Rules" down the bottom. Just use the tags [sub ]-text-[/sub ] (without spaces) for subscripts and [sup ]-text-[/sup ] for superscript.

 

[Heart.O.Gold]

There's no need to call him a weirdo, he's just trying to grasp it o.0

Check out the link to vB codes under "Posting Rules" down the bottom. Just use the tags [sub ]-text-[/sub ] (without spaces) for subscripts and [sup ]-text-[/sup ] for superscript.

Thanks for that;

I guess he isn't a weirdo, just taking my information and making it much more clearer.

I withdraw my comment

 

[Forbidden.]

Now I know where g = Gm/r² is derived from ...

F = mg
F = Gm₁m₂/r²

So F = mg = Gm₁m₂/r²

Therefore:

g = Gm/r²

Cancel out the m from mg and remove either m₁ or m₂, does not matter which one then remove the subscript and thats it.

Thanks for that;

I guess he isn't a weirdo, just taking my information and making it much more clearer.

I withdraw my comment

Good.

There's no need to call him a weirdo, he's just trying to grasp it o.0

Check out the link to vB codes under "Posting Rules" down the bottom. Just use the tags [sub ]-text-[/sub ] (without spaces) for subscripts and [sup ]-text-[/sup ] for superscript.

hi airie, yes i am grasping it, what I need to really grasp is projectile motion.
Projectiles are objects which move only under the influence of gravity, and can be projected in many different ways.
For example when an object is thrown into the air at time t, it will arrive back on the floor at time 2t, that is alone enough to throw me off track. Projectile motion is not all just "subbing in the values given" all the time, let alone not even knowing when to use the correct formula

 

[alcalder]

For my derivation of the projectile motion equations look HERE:
http://community.boredofstudies.org/263/space/127193/projectile-motion-help.html