Energy to put space shuttle in orbit

[calculator20]

Homework Statement

The space shuttle orbits about 300km above the surface of the Earth. The shape of the orbit is circular and the mass of the space shuttle is 6.8*10⁴kg. The mass of the Earth is 6.0*10²⁴kg and the radius of the Earth is 6.4 *10⁶m. Calculate the energy needed to put the space shuttle into orbit.

Homework Equations

KE=GMm/r_p

The Attempt at a Solution

Using G=6.67*10^-11 with the mass of the Earth and shuttle and the radius of the Earth gives 4.2*10¹²J but the answer should be 2.2*10¹²J according to the book. Where am I going wrong?

 

[Astronuc]

Think about what the gravitational potential energy GMm/r means.

The shuttle lifts (or rises) from r_e to r_e+300 km, where r_e is the radius of the earth.

 

[tiny-tim]

oops!

Hi calculator20!

The space shuttle orbits about 300km above the surface of the Earth. The shape of the orbit is circular and the mass of the space shuttle is 6.8*10⁴kg. The mass of the Earth is 6.0*10²⁴kg and the radius of the Earth is 6.4 *10⁶m. Calculate the energy needed to put the space shuttle into orbit.
…
KE=GMm/r_p

erm … you can't just leave it there … it'll crash!

try giving it a shove! ​

 

[calculator20]

If I do GMm/re I get 4.2*10 to the 12, GMm/re + 300000 gives 4.06 * 10 to the 12. The difference between them isn't 2.2 *10 to the 12?
I get

 

[yesyesyes]

i am having exactly the same difficulty, its frustrating the hell out of me.
either i am not seeing something or there is an error in the answer page

 

[LowlyPion]

i am having exactly the same difficulty, its frustrating the hell out of me.
either i am not seeing something or there is an error in the answer page

Welcome to PF.

They want the total energy.

What is total energy to move from the surface of Terra to a 300km height?

What must the object have to be in orbit?

E_total = ΔKE + ΔPE

 

[yesyesyes]

so basically 2.2= KE (4.2) - PE (2.1)
allowing for roundings
?

Thanks a lot x