Speed of a rocket

[Gozzer101]

Hi

 

Might sound a silly question, but I've asked a couple of people who are unsure:

 

I read that Mecury races around the sun at around 50km a second. I also know Mercury has very long days (time it takes to spin on its axis). Knowing this I thought what would happen if a rocket was launched off the surface of Mecury (theoretically) on the side of the planet of the direction of it's orbit around the sun (Side A) against that to a rocket lifting off on the side opposite to it's suns orbital direction (Side B). To me it comes to the conclusion that to exit Mercury on side A then the rocket, when free from Mecruys gravity, had to be travelling at over 50km/sec. Else Mercury would "catch up" with the rocket bearing in mind it's on a similar sort of path as Mercury.

 

I was thinking it would be a similar situation to that off throwing a ball off a train (to person on train ball doesn't appear to go any faster than a throw while still, but to an outside observer they can see the ball travels faster).

 

If someone could explain this to me it would be brilliant. And say where I have gone wrong in my assumptions etc.

 

Also hope my question makes sense! If not I'll try to rephrase it in more detail.

 

Thanks

Edited January 2, 2012 by Gozzer101

[swansont]

Hi

 

Might sound a silly question, but I've asked a couple of people who are unsure:

 

I read that Mecury races around the sun at around 50km a second. I also know Mercury has very long days (time it takes to spin on its axis). Knowing this I thought what would happen if a rocket was launched off the surface of Mecury (theoretically) on the side of the planet of the direction of it's orbit around the sun (Side A) against that to a rocket lifting off on the side opposite to it's suns orbital direction (Side B). To me it comes to the conclusion that to exit Mercury on side A then the rocket, when free from Mecruys gravity, had to be travelling at over 50km/sec. Else Mercury would "catch up" with the rocket bearing in mind it's on a similar sort of path as Mercury.

 

I was thinking it would be a similar situation to that off throwing a ball off a train (to person on train ball doesn't appear to go any faster than a throw while still, but to an outside observer they can see the ball travels faster).

 

If someone could explain this to me it would be brilliant. And say where I have gone wrong in my assumptions etc.

 

Also hope my question makes sense! If not I'll try to rephrase it in more detail.

 

Thanks

 

 

An important concept here is that the energy or the speed is a frame-dependent quantity. You can analyze the problem from the point of view of the planet, where the planet is at rest, so the speed of the planet relative to the sun doesn't matter. If you launched a rocket that was able to escape to an arbitrary distance it would be at rest with respect to the planet. So if, according to some other observer, the planet was moving at 50 km/s (as with Mercury) then the rocket would be moving at 50 km/s as well. The planet would never catch up. These two launches require the same amount of energy, and the rockets have the same amount of energy.

 

Now, it does matter in terms of doing something with the rocket — you generally want the rocket to go faster and get somewhere. If Mercury is moving to the right, according to some observer at rest with respect to the sun, both rockets are moving with the planet. The rocket going to the right only needs a nudge to be moving away from the planet. The rocket launched to the left has to expend more energy to come to rest, and even more to go to the left. So it does matter.

 

But one would only have to wait until Mercury went around half of a revolution and it would be moving to the left, and you could launch the rocket to the left, and have it go in the same direction as the planet.

[Gozzer101]

An important concept here is that the energy or the speed is a frame-dependent quantity. You can analyze the problem from the point of view of the planet, where the planet is at rest, so the speed of the planet relative to the sun doesn't matter. If you launched a rocket that was able to escape to an arbitrary distance it would be at rest with respect to the planet. So if, according to some other observer, the planet was moving at 50 km/s (as with Mercury) then the rocket would be moving at 50 km/s as well. The planet would never catch up. These two launches require the same amount of energy, and the rockets have the same amount of energy.

 

Now, it does matter in terms of doing something with the rocket — you generally want the rocket to go faster and get somewhere. If Mercury is moving to the right, according to some observer at rest with respect to the sun, both rockets are moving with the planet. The rocket going to the right only needs a nudge to be moving away from the planet. The rocket launched to the left has to expend more energy to come to rest, and even more to go to the left. So it does matter.

 

But one would only have to wait until Mercury went around half of a revolution and it would be moving to the left, and you could launch the rocket to the left, and have it go in the same direction as the planet.

 

Okay. So as a stationary observer in Space. If we were to launch a Rocket off Mercury it would be travelling at around 50km/sec (plus the extra negligible speed of the rocket to exit the surface of Mercury). At around 50km/sec that works out to 180000km/hour or 4320000km/day. Assuming that to reach orbital path of the furtherest planet in the solar system, Neptune (4.45billion km away from Mecury?), it would take 1028 days. I know that is far too quick of a rocket (e.g. Voyager). I take into account that the rocket wont follow the direct path from Mercury to Neptune, but it wont be too much of a change?

 

Is that correct?

 

EDIT: Voyager 1 travels at around 13km/sec far slower than the orbital speed of the Earth (29km/sec). I assume it has used the gravity sling shot method of planets to propel it further out and to gain speed. But 13km.sec is still slower than the Earth rotation speed around the sun...

 

The only thing I can think of is when exiting Earth, the gravity of Earth will slow it down? As once free from the gravity of Earth it will never lose speed (assuming no other things collide or any other gravity forces act on it)

Edited January 2, 2012 by Gozzer101

[Janus]

Okay. So as a stationary observer in Space. If we were to launch a Rocket off Mercury it would be travelling at around 50km/sec (plus the extra negligible speed of the rocket to exit the surface of Mercury). At around 50km/sec that works out to 180000km/hour or 4320000km/day. Assuming that to reach orbital path of the furtherest planet in the solar system, Neptune (4.45billion km away from Mecury?), it would take 1028 days. I know that is far too quick of a rocket (e.g. Voyager). I take into account that the rocket wont follow the direct path from Mercury to Neptune, but it wont be too much of a change?

 

Is that correct?

Assuming that you rocket leaves with just enough velocity to escape Mercury, it will be moving at 50 km/sec relative to the Sun (there is no such thing a "stationary observer in space".) This is equal to Mercury's orbital velocity. Mercury moves at this speed as this is the speed that it needs to be moving in order to orbit the Sun at the distance it does. Since your rocket will be just about the same distance from the Sun, it will need to move 50 km/sec to just stay in the same orbit. IOW, it will just enter its own orbit around the Sun along with Mercury. In order to escape the Sun's gravity, it will need an additional ~20.7 km/sec.

 

To reach Neptune, it won't have to move quite that fast at it doesn't have to escape from the Sun entirely, just enter an elliptical orbit around the sun with a aphelion at Neptune's distance. (this is call a Hohmann transfer orbit.) Such a trip will take 10843 days or 29.7 years. To enter such an orbit you will need to have a velocity of ~67.5 km/sec or another 17.5 km/sec more than Mercury's orbital speed. Upon reaching Neptune your rocket will be moving at a bit under 1 km/sec. The difference in speed is due to the fact that the rocket loses speed as it climbs away from the Sun. It trades kinetic energy doe potential energy.

EDIT: Voyager 1 travels at around 13km/sec far slower than the orbital speed of the Earth (29km/sec). I assume it has used the gravity sling shot method of planets to propel it further out and to gain speed. But 13km.sec is still slower than the Earth rotation speed around the sun...

 

The only thing I can think of is when exiting Earth, the gravity of Earth will slow it down? As once free from the gravity of Earth it will never lose speed (assuming no other things collide or any other gravity forces act on it)

 

The point is that there is another gravitational force to consider, that of Sun. The 13 km/sec that Voyager is moving at now is much slower than what it left the vicinity of Earth with. It lost speed fighting the Sun's gravity.

Edited January 2, 2012 by Janus

[Gozzer101]

Good answers thanks

[JohnStu]

Launching a rocket on a planet is like firing an arrow on a moving ship. The arrow gets the velocity of moving ship added to it before launch.