Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass mE, radius RE) and place it in a circular low earth orbit--that is, an orbit whose altitude above the earth's surface is much less than RE. (As an example, the International Space Station is in low earth orbit at an altitude of about 400 km, much less than RE

Answers

Answer 1
Answer:

The work done to launch the spacecraft in low earth orbit is  (GM_emh)/(R_e(R_e+h))

Work-energy theorem:

The gravitational force is a conservative force. So, the total energy of the system must be conserved.

According to the work-energy theorem:

work done = - change in potential energy of the system.

W = -ΔPE

Initially, the potential energy of the satellite on the surface is:

PE = -(GM_em)/(R_e)

where m is the mass of the satellite

Let the orbit be at a height of h from the surface, so the potential energy in the orbit is :

PE' = -(GM_em)/(R_e+h)

ΔPE = PE'-PE

ΔPE = -GM_em((1)/(R_e+h)-(1)/(R_e))

\Delta PE=-(GM_emh)/(R_e(R_e+h))

Now work done:

W = - ΔPE

Thus,

W=(GM_emh)/(R_e(R_e+h))

Learn more about work energy theorem:

brainly.com/question/13603991?referrer=searchResults

Answer 2
Answer:

Answer:

Work done to shift the spacecraft from Earth surface to low Earth radius is given as

W = (GM_e m)/(2R_e)

Explanation:

As we know that spacecraft is at surface of Earth initially

So we will have

U_i = -(GM_e m)/(R_e)

now when it is at low radius Earth Orbit then we have

U_f = -(GM_e m)/(2(R_e + h))

now we know that work done to shift the spacecraft from Earth Surface to Low earth orbit is change in total energy

W = -(GM_e m)/(2(R_e + h)) + (GM_e m)/(R_e)

so we have

W = (GM_e m)/(R_e) (-(1)/(2(1 + h/R_e)) + 1)

W = (GM_e m)/(R_e) (-(1)/(2)(1 - (h)/(R_e)) + 1)

W = (GM_e m)/(2R_e)(1 + (h)/(R_e))

since we know h << Re

so work done is given as

W = (GM_e m)/(2R_e)


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Answers

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Answers

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To learn more about the solar system, refer to the link;

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#SPJ2

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Based on the principles of convection, conduction and thermal radiation, which scenario below is most similar to the following situation?Heat traveling through the ceiling from your bedroom to the attic.
A) Feeling a metal wire get warmer as you roast a marshmallow over a fire.
B) Warm air rising in a room where the air is moving.
C) The sun warming up the roof on a house.
D) Cold water sinking in a pot of water being warmed up on the stove.

Answers


The situation (heat going through the ceiling) describes
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heat going from one place to another by
soaking through some material.

A).  This is the one.  Heat goes from from the marshmallow
to your hand by soaking through the wire.   This is conduction too.

B).  No.  The heat in the room goes from the floor to the ceiling
because the warm air rises and carries it there.  This is convection.

C).  No.  There's nothing for the heat to soak through between
the sun and the roof, and nothing that can move from the sun
to the roof and bring the heat with it.  This is radiation.

D).  No.  Cold water sinks from the surface to the bottom because
warm water rose from the bottom to the surface, taking heat with it. 
This is convection.

The answer is


A) Feeling a metal wire get warmer as you roast a marshmallow over a fire.


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