Is it possible to get to the power needed to thrust a rocket so that it can escape from earth?

Question

Note: Any velocity mentioned in this question is the velocity relative to the earth.

Warning: Base your answers on formal proof and facts, moon images aren't really science...

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According to this book page in Astronomy: A Physical Perspective By Marc Leslie Kutner:

For an object going in a circular orbit around a planet the gravitational force must provide the acceleration for circular motion. If we solve this to get the orbital velocity, we get 28,000 km/h.

This means that we need that velocity to escape from the earth if we follow the earth's orbit.

Another way is to send a rocket straight up as shown in this answer:

To leave the earth, you do NOT need to go at that speed of 28,000 km/h. You simply have to be going that fast when you reach that altitude. Given enough time, something travelling at 1 m.p.h can leave the earth, or the solar system. It needs enough power so that when it stops thrusting, it's current speed exceeds it's current height's orbital velocity.

This helps explain why rockets are almost always launched east - due to the spin of the earth, they get a head start on their orbital velocity. At the Equator, you get a free boost of almost 1000 miles/hour (less so as you travel away from the equator).

So, is it possible to get to the power needed to thrust a rocket so that it can escape earth?

For the orbital way of escaping: Wikipedia mentions a velocity of 27,870 km/h which is sufficient if you count in mathematical errors, however, unless I'm incorrect I think such speeds have only been achieved by NASA. Are there any other companies that achieved this speed? And how are such speeds measured?

Someone is trying to convince me that the maximum velocity ever reached was 3,529.6 km/h by the Lockheed SR-71 Blackbird and thus space exploration does not exist because nobody has ever been there, how can I prove him wrong?

Are there any formal proofs or facts that aren't supported solely by NASA?

Answer 1

Please base your answers on formal proof and facts

I'm not sure what kind of proof or fact you will accept, but I'll add another one to the facts already given by the other posters.

The International Space Station (ISS) is clearly visible from the ground. If it is overhead on a clear night, away from the brightest city lights you can see it clearly as it sweeps across the sky. The important point is that there is nothing except a satellite that could possible have that kind of movement across the sky.

The only natural objects in the sky are stars (and galaxies), planets and meteorites. Stars sweep around in 24 hours (the rotation period of the earth). Planets move at almost the same rate as stars - with the naked eye it will take days to see them move relative to the stars. Meteorites on the other hand only take seconds to sweep across the sky, and they rarely go from horizon to horizon; they usually burn up quickly. Satellites on the other hand move majestically across the sky, at a steady pace. Satellites in low orbits (like the ISS) take a couple of minutes to cross from horizon to horizon.

If you want to know where the ISS is at any time, there are websites that tell you. There are also sites that tell when you can see it from your location, like this one. Enter your location into the website, and you'll see suitable times in the next couple of weeks. It even tells you in which direction to look.

I know that this is a NASA site, but the fact that you can see something that can only be explained by assuming it's a satellite, AND you can see it at the time that NASA tell you, is strong proof that the ISS is indeed up there.

This proves that we can travel at 28,000 km/h in orbit. It also implies that all the other, even faster spacecraft to Mars and other planets, are also real.

Answer 2

_{Neil Armstrong, standing in front of a X-15. ~ Public Domain, Wikimedia; obtained from NASA.}

The speed quote is from a Wikipedia article on the SR-71, the fastest conventional airplane (runs on jet engines) known in the US Air Force in 1998. The fastest airplane however happens to be the X-15 which is rocket powered. The simple answer is that your friend got their research mixed up a bit, and that there are things that go faster, and they are not airplanes.

But for amusement, suppose they are right, it is impossible to go faster than a few thousand miles an hour, and besides the cops would have to give out a HUGE speeding ticket.

What all does that imply? It implies a lot of ridiculous things, thats what. So, it must be possible to go that fast after all. This kind of reasoning is called an indirect proof or proof by contradiction and is a valid technique of formal logic widely used in mathematics and scientific disciplines.

So let's be brave, and assume it is impossible to go "20,000 km/hr" or whatever speed is required for escape velocity. Then what?

Then:

• There are no well worked out principles of escape velocity or orbits -- allowing for the construction of space probes -- that could be reduced to physics, algebra and calculus and then taught at the university level to prospective engineers.
• The Space Shuttle Columbia would have never burned up and broke apart on reentry, killing all 7 crew, because gaps in the heat shielding allowed the friction of the metal skin against the air at 20,000+ km/hr and burned through the hull. The news of fragments spread out over a large area wouldn't have occurred. NASA could have made everyone send back all the pieces to make the cover up complete, but then where did the pieces come from again? Did NASA put them out there surreptitiously then ask people to pick them up?

Also, it implies no one has ever explored beyond Earth:

• There isn't any good evidence that the US sent men into space or to the moon, is there?
• The US, Soviet, and ESA space programs would be frauds. Nothing ever sent back pictures from the Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune, or a comet. I would post all of the pictures, but you said you didn't want to see them. The pictures some people thought they saw would then have to be hoaxes [one could claim the scifi channel can do as well, but why such a complex hoax when a simple one might do?] and all the scientists who looked at them were negligent in noticing these hoaxes. Or it was quite the cover up...
• There would never have been any Mars rovers.
• Independent radio amateurs would not be able to detect the signal of a Mars probe on the expected frequency and position in the sky, because space probes don't exist. But they did detect the probe's signals.

Sorry if the bits of sarcasm here and there offend some people.

Can you reasonably explain all of these examples?

If you believe the objective reality of any of these examples, then using proof by contradiction it refutes the claims that speeds for orbit or escape (as appropriate) from Earth are impossible.

Answer 3

According to NASA the Space Shuttle can reach a speed of 27,875 kph.

I defy Earth's gravity daily, by walking up three flights of stairs to my apartment. As someone else has already pointed out, you don't necessarily need escape velocity to leave this planet, just "continuous thrust".

If there were a pole reaching into orbit, even a snail could eventually escape from earth.

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EDIT:

a Space Elevator is an example of "low speed, but continuous thrust/acceleration".

Answer 4

To address the subquestion

Someone is trying to convince me that the maximum speed ever reached was 3,529.6 km/h and thus space exploration does not exist because nobody has ever been there, how can I prove him wrong?

That is a velocity of nominally 1 km/s (3600 seconds in an hour), or about 3280 feet per second.

There are several ammunition loads (available for both military and non-military purposes) which achieve velocities greater than this - as high as 5700 m/s (or 5.7 km/s).

Achieving velocities higher than that which the SR-71 is confirmed to have achieved in flight is, therefore, possible.

For larger objects, even excluding orbital vehicles, Wikipedia has a list of airspeed records, including a substantially higher speed attained by the X-15 (5500-6200 kmh).

For non-US vehicles, you could look at the history of the Buran, too.

Answer 5

Good answers, but let me just chime in with what might be an intuitive explanation. The Earth, or any massive object, creates a "gravity well". Think of it as a big funnel, with the planet at the bottom. It's a smooth funnel, like the bell of a horn, like a tuba or trumpet. I'm sure you've seen this in a museum. A small round ball, like a marble or ball bearing, is injected tangentially at the top, and it goes around and around, until because of rolling friction it finally goes lower and faster until it falls through the hole.

What the ball does depends on how much energy it has. If it is injected with not much speed, it goes into a low orbit, probably eliptical, maybe circular, but it stays in orbit (forever if there is no friction). If it is injected too energetically, it flies right out.

The speed it needs to fly right out and never come back is the escape velocity.

When NASA sends a rocket to the moon, it's sending it almost all the way out of the gravity well. To send a rocket to another planet takes only a little more energy, and then it basically never comes back. With more energy still, it has enough to escape the sun's gravity well, and it will just keep going out of the solar system. We've done that too.

Here's an explanation.

... and a video.

... and some math.