Take into account the Earth\'s rotational speed (1 rev/day). (a) Determine the n

Question

Take into account the Earth's rotational speed (1 rev/day).

(a) Determine the necessary speed, with respect to Earth, for a rocket to escape if fired from the Earth at the equator in a direction eastward.
_____________ m/s

(b) Determine the necessary speed, with respect to Earth, for a rocket to escape if fired from the Earth at the equator in a direction westward.
_____________ m/s

(c) Determine the necessary speed, with respect to Earth, for a rocket to escape if fired from the Earth at the equator in a direction vertically upward.
_____________ m/s

Explanation / Answer

Depending on the type of orbit, the velocity required ranges from 6.9km/s to 7.8km/s for low earth orbits. Elliptic orbits from 6.5km/s to 8.2Km/s. Geo-stationery orbits can be accomplished at a relative velocity of only 3.1km/s, but at an altitude of 42,000 km. Westward launches require additional boost to counter act the eastward rotation / velocity that the launch vehicle already has.

At the equator this difference is approximately 1700km/hour, so additional boost of approximately 3400km / hour is required to reach orbital speed when launching Westwards - which is why this is never done for commercial space craft.

For Eastwards launch, desired orbital speed less approximately 1700km/ hour.

Vertical launch - this will not put you in earth orbit, no matter what speed you achieve. Unless you reach point where the earth's gravity becomes so weak that other gravitational forces become dominant, your spacecraft will eventually fall back.

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