Is Launching a Satellite Eastward More Efficient Due to Earth's Rotation?

[Soaring Crane]

1. A newspaper article discussing the space program noted that it is easier to launch a satellite into an eastward orbit tan into a westward orbit. Is this true?

a.No, this is not true because it is the upward component of velocity that is important in reaching an orbit, not the horizontal component east and west.

b.No, this is not true because the kinetic energy of the launch vehicle is independent of the direction in which it is launched.

c.No, this is not true because launching toward the east means an event greater speed needed to attain orbiting speed due to the earth’s rotation.

d.Yes, this is true because launching in the east reduces wind resistance.

e.Yes, this is true because the earth’s rotation toward the east gives the satellite added speed, thereby reducing the speed required with respect to the Earth if orbital velocity is to be attained.

I am uncertain of this one. Is the answer E.? I know the Earth's rotation is eastward, but I do not know if the Earth's rotation affects the satellite as described in E.



2. Satellite A has twice the mass of satellite T, and rotates in the same orbit. Which of the following is true?
a.The speed of T is one-fourth the speed of A.
b.The speed of T is half the speed of A.
c.The speed of T is twice the speed of A.
d.The speed of T is three-fourths the speed of A.
e.The speed of T is equal to speed of A.

I used the circular orbit formula v = sqrt(G*m_earth)/r. The mass of the satellite is not included, so will it be E. both speeds are equal to each other?

Thanks.

 

[stenbro]

1E. The Earth is a sphere, and rotates with a certain angular velocity. Thus, launching objects with the direction of velocity due to rotation gives it a "free" extra velocity in that direction. The velocity of rotation is greatest where the Earth's radius is largest, which is at the equator. So that's why many launch sites are places as close to the equator as possible.

2E. Write the equation for v for both satellites. Turns out it's the same and thus independent of the mass. The speeds will therefore also be the same.

 

[QuantumCrash]

1st one seems alright. For the 2nd 1 equate centripetal force on the individual satellites and the gravitational force exerted on them since they are 1 and the same. You should find that for each case the masses cancel out.