Earth's Rotation and Effect on Launch Altitude

[ColdFusion85]

I know that as a rocket is launched closer to the equator it gets more of a "boost" in velocity due to the Earth's rotation, but I was wondering if anyone could explain the mechanism (e.g. the mathematics) behind this. I can visualize it but I don't see how the extra velocity gets added mathematically.

 

[ColdFusion85]

And no, this isn't a homework question. Just curious.

 

[Danger]

As with any sphere, the Earth rotates at rate (rpm) which dictates how fast any particular spot upon it moves. A point just beside the north pole might move only a metre or two per second. When you extend that to a spot on the equator, you can see that it has to go over a far greater distance in order to cover the same degrees of arc that the polar spot does.

 

[rcgldr]

At the equator, the Earth rotates to the east just over 465.11m/s = 1674.4kph = 1040.4 mph. So launching from the equator, using a floating platform, such as Sea Launch, means rockets don't require as much energy (fuel) in order to achieve orbits. Once out of the atmoshpere, for the rocket it doesn't matter that the Earth is rotating below it.

 

[D H]

All of the responses to date assume an target orbit with inclination equal to the launch site's geocentric latitude. It does indeed require less energy to achieve prograde equatorial orbit from an equatorial launch site than a 29 degree orbit from Cape Canaveral launch. So why is this? The answer is in Newton's laws. The vehicle has a latitude-dependent initial velocity before firing the engines thanks to the Earth's rotation. Targeting an orbit that takes advantage of this initial velocity reduces the required delta-v needed to reach that orbit.

A plane change is needed if the target orbit inclination differs from launch site latitude. For example, achieving a retrograde polar orbit from an equatorial launch costs more than from a Vandenburg launch.

So why is this? The answer is in Newton's laws. The vehicle has a latitude-dependent initial velocity before firing the engines thanks to the Earth's rotation. Targeting an orbit that takes advantage of this initial velocity reduces the required delta-v needed to reach that orbit.

There is another factor that would help decrease fuel costs: Launching from altitude. Punching a hole through the atmosphere from sea level costs quite a bit. Adding altitude reduces this cost and reduces the change in potential energy. Launching from the top of Mount Kilamanjaro would cut fuel costs a lot. We don't do this for political and safety reasons.

 

[ColdFusion85]

I see. Since the final velocity required for a given orbit (e.g. a fixed height circular orbit of the Earth) is the same for all cases, and since we can calculate the velocity on the ground at a given latitude, we can determine the delta-V required to get the spacecraft into orbit, and therefore, we can see how the rotation of the Earth affects this needed delta-V at different geocentric latitudes. Is this correct?

 

[ColdFusion85]

I see. Since the final velocity required for a given orbit (e.g. a fixed height circular orbit of the Earth) is the same for all cases, and since we can calculate the velocity on the ground at a given latitude, we can determine the delta-V required to get the spacecraft into orbit, and therefore, we can see how the rotation of the Earth affects this needed delta-V at different geocentric latitudes. Is this correct?

 

[cngiff]

All of the responses to date assume an target orbit with inclination equal to the launch site's geocentric latitude. It does indeed require less energy to achieve prograde equatorial orbit from an equatorial launch site than a 29 degree orbit from Cape Canaveral launch. So why is this? The answer is in Newton's laws. The vehicle has a latitude-dependent initial velocity before firing the engines thanks to the Earth's rotation. Targeting an orbit that takes advantage of this initial velocity reduces the required delta-v needed to reach that orbit.

A plane change is needed if the target orbit inclination differs from launch site latitude. For example, achieving a retrograde polar orbit from an equatorial launch costs more than from a Vandenburg launch.

So why is this? The answer is in Newton's laws. The vehicle has a latitude-dependent initial velocity before firing the engines thanks to the Earth's rotation. Targeting an orbit that takes advantage of this initial velocity reduces the required delta-v needed to reach that orbit.

There is another factor that would help decrease fuel costs: Launching from altitude. Punching a hole through the atmosphere from sea level costs quite a bit. Adding altitude reduces this cost and reduces the change in potential energy. Launching from the top of Mount Kilamanjaro would cut fuel costs a lot. We don't do this for political and safety reasons.

Greetings: I wonder whether you have seen any actual launch data (from NASA or anybody else) to confirm / quantify the theoretical launch boost due to Earth's eastward rotation. I have written and e-mailed NASA, JPL, Goddard--everyone I could think of--and have never received a reply. So I am wondering whether the scientific proof of this theoretical boost is factual-- as opposed to "it is accepted scientific fact", "it is common knowledge", "everybody knows", "obviously", or some such time-honored phrase.

 

[D H]

Greetings: I wonder whether you have seen any actual launch data (from NASA or anybody else) to confirm / quantify the theoretical launch boost due to Earth's eastward rotation. I have written and e-mailed NASA, JPL, Goddard--everyone I could think of--and have never received a reply. So I am wondering whether the scientific proof of this theoretical boost is factual-- as opposed to "it is accepted scientific fact", "it is common knowledge", "everybody knows", "obviously", or some such time-honored phrase.

Everyone once in a while I get a phone call from someone I know asking if I have seen their email message. If the email message isn't in my inbox I'll see if the spam filters were a bit over aggressive. Yep. There's the message, tucked in amongst all the typical "use this growth product" and "make millions" spam -- plus the "have you met an alien" and "physics is wrong" messages that plague people with NASA email addresses.

Your messages probably hit a spam filter. TBH, your post has the look-and-feel of a crackpot.

There is no reason to "confirm / quantify the theoretical launch boost due to Earth's eastward rotation" because there is absolutely no reason to do so: We know the Earth is rotating.

Suppose that by some fluke thousands of scientists spread over hundreds of years have missed the obvious: The Earth is not rotating. Were that the case, our rockets would not get where we thought they would based on the erroneous assumption that the Earth is rotating. Our rockets, however, do get where we think they will, falisifying the conjecture that the Earth is not rotating.

 

[cngiff]

TBH, your "reply" has the look and feel of a second-rate mind. If you don't understand my inquiry--and the scientific merit of giving it serious consideration, then you should tear up your diplomas and put on a dunce cap and go sit in the corner. Why are the majority of Physicists so brain dead?

cngiff

 

[D H]

cngiff,

What exactly is your inquiry? That the Earth is not rotating? That the Earth is rotating but that this "theoretical launch boost" doesn't occur? Or is it something else? If it one of the first two, you are wrong. If it's something else, please clarify.