Tangential speed at equator.

[Gareth56]

In College Physics 7th Ed by Serway it states that the tangential speed of the surface of the Earth at the equator is 1700m/s!!

 

Is this correct? I thought it was more like 465m/s.

[D H]

Can you give a quote from that book in context? You are correct: 2*pi/sidereal day * 6378 km = 465 m/s.

[timo]

[math] v = \frac{2 \pi r}{24 \text{ h}} \approx \frac{6 \cdot 6 \cdot 10^3 \text{ km}}{24\text{ h}}

= \frac{36\cdot 10^3}{24} \frac{\text{km}}{\text{h}} = 1500 \frac{\text{km}}{\text{h}}.[/math]. So if "tangential speed" is defined the way I assumed, then it seems you are right. However, seeing that I did some approximations it is well possible that the actual value would be ~1700 km/h. In that case the college book might have screwed up the units (or you misread them).

[D H]

However, seeing that I did some approximations it is well possible that the actual value would be ~1700 km/h. In that case the college book might have screwed up the units (or you misread them).

Good catch. Gareth56, double-check the units in the text. Is it kilometers per hour or meters per second? 2*pi/sidereal day * 6378 km = 1674 km/hr.

 

Note well: It is 2*pi/sidereal day, not 2*pi/24 hours. There is a slight difference, probably important only to the truly pedantic. A sidereal day is 23.9344696 hours long.

[Gareth56]

Here is the exact quote from the book:-

 

"Why is the launch area for the European Space

Agency in South America and not in Europe?

 

Explanation:-

 

Satellites are boosted into orbit on top

of rockets, which provide the large tangential speed

necessary to achieve orbit. Due to its rotation, the surface

of Earth is already traveling toward the east at a

tangential speed of nearly 1700 m/s at the equator.

This tangential speed is steadily reduced further

north, because the distance to the axis of rotation is

decreasing. It finally goes to zero at the North Pole.

Launching eastward from the equator gives the satellite

a starting initial tangential speed of 1700 m/s,

whereas a European launch provides roughly half that

speed (depending on the exact latitude)."

[swansont]

I'm guessing it's the unit mistake, and should be km/hr.

 

You could contact the publisher and point that out. They might have an errata page online. Is there a URL given in the book?

[Gareth56]

I understand there's now an 8th edition so hopefully the proof reader spotted the typo.