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When we send satellite into space using a rocket, logically we consider the shortest path which is a straight line perpendicular to Earth's surface. My question is do rocket takes the shortest path to reach outer space or stray off intentionally at an angle from Earth's surface?

Mark Eichenlaub
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user6760
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  • See http://physics.stackexchange.com/q/5979/37364 – mmesser314 Apr 27 '15 at 04:24
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    I'm not a rocket scientist, but when a satellite is launched it needs to reach about 17,500 MPH, which is the orbital speed at satellite altitude. It would probably be inefficient to go straight up the whole way, though they probably go straight up at first to reduce air resistance. I'm sure they've got a pretty good idea on how to do it with efficiency. – userLTK Apr 27 '15 at 04:24
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    The center of mass of the rocket's trajectory will acquire an angle to the surface of the earth due to the earth's rotation below it , anyway. Intentional changes in direction have to happen if the satellite is to reach a specific orbit . – anna v Apr 27 '15 at 04:27
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    What the rocket scientist wants is tangential velocity. Working against gravity is costly (you are losing 600m/s for every minute you are going straight up). Thanks to vectorial addition of acceleration and velocity this gets much better once the thick part of the atmosphere is left behind. Inside the atmosphere it's the aerodynamic forces that force rockets on their gradual change in direction. A small tilt from vertical has to become a large one over time, because rockets are very sensitive to shear forces, so they always have to fly "straight" in air once they pass a certain airspeed. – CuriousOne Apr 27 '15 at 04:41
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    See my answer to this question, which is almost but not quite a duplicate of yours. If you send the rocket and satellite straight up the satellite is going to fall straight back down again! – John Rennie Apr 27 '15 at 05:45
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    If you want to get an intuitive feeling for how this works, it's impossible not to recommend Kerbal Space Program :) – Luaan Apr 27 '15 at 06:57
  • Nobody mentioned this, but this is called a gravity turn. – Superbest Apr 27 '15 at 20:09
  • Hopefully not to add confusion, if the question was more about getting somewhere beyond Earth and not about launching satellites into orbit. Those who grew up during the "space race" should know that every mission to the Moon went partially around the Earth first. It's not the shortest distance but it's the most efficient because of what was called a slingshot effect of building up momentum till it finally breaks free. –  Apr 27 '15 at 19:32
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    Anyone who wants to understand orbital mechanics should start by playing Kerbal Space Program. – Qwerky Apr 28 '15 at 16:07
  • The not-quite-true (due to Earth's rotation) but almost answer: Yes, it's that the rockets and their cargo would then come straight down. –  Apr 29 '15 at 10:09

5 Answers5

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It sounds like you are imagining that what satellites do is go up through the atmosphere, break through into outer space, and hang there. That is not right. If you simply go straight up to outer space (say 300 km above Earth's surface), gravity will pull you right back down, even if you've left the atmosphere, and you'll crash back into the Earth. Gravity is only about 10% weaker at 300km (which is well above the bulk of the atmosphere) than it is on the surface of the Earth

Satellites are not only ~300 km above the surface of the Earth, they are also orbiting. For a low-Earth orbit, satellites need to travel some 7,000 meters/sec horizontally (17,000 mph) in order to orbit.

Because getting to an orbit is a combination of getting through the atmosphere, getting up to the desired height, and getting the desired orbital velocity, (all while their mass is changing because they carry their fuel with them) rockets do not simply go straight up. Early on in a satellite launch, rockets usually go roughly straight up because the atmosphere is thick near the surface of the Earth and they're trying to get through it as quickly as possible. Later on, rockets tilt over and perform a combination of horizontal and vertical motion as they reach their orbit. The optimal path is a combination of avoiding drag and mixing height and orbital velocity together appropriately.

This is also why most satellites orbit in the same direction the Earth spins; by orbiting that way, they get a bit of free sideways velocity from Earth's rotation during launch.

Mark Eichenlaub
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    tl;dr first images of this – ratchet freak Apr 27 '15 at 09:15
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    As always, xkcd covers this well. https://what-if.xkcd.com/58/ – Bill Michell Apr 27 '15 at 12:55
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    I wonder if for a given rocket configuration the optimal path to orbit is unique. – Jorge Leitao Apr 27 '15 at 17:47
  • @J.C.Leitão Yes, the orbital insertion routine is slightly different for each rocket based on it's individual capabilities. – EtherDragon Apr 27 '15 at 20:44
  • A sentence or paragraph about the problems with lifting fuel you are just going to burn higher in the gravity well might be worthwhile. (You already mention the "get out of the thick atmosphere quickly to reduce drag" requirement, and this is the opposing one, and why even an interplanetary craft might thrust sideways while in Earth orbit. – Yakk Apr 28 '15 at 14:04
  • Yakk, yes, good point. – Mark Eichenlaub Apr 28 '15 at 15:50
  • If a rocket launched from the equator were targeting a geosynchronous orbit directly over the launch site (implying that in the rotating reference frame it would appear to be going "straight up"), how would the fuel required to stay precisely over the launch site compare with the most fuel efficient path (and what would that path be)? – supercat Apr 28 '15 at 18:07
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I highly recommend you download Kerbal Space Program and see for yourself (there's a free demo version)!

Typically the goal of a satellite is to orbit, and thus as the other answers address, you must build significant horizontal velocity. Indeed if the Earth didn't have an atmosphere, you could orbit a few km above the surface, so the main goal is building enough orbital (horizontal) velocity somewhat above the dense regions of the atmosphere.

If you only burned vertically with respect to the Earth, you will follow a trajectory similar to the one below:

Straight Up Trajectory

I did want to add why you might WANT to travel 'vertically' only:

  1. Your goal is to smash into something that is in orbit; you just want to reach a desired altitude at a given time (say, to destroy a satellite or an orbiting alien craft)
  2. You want to crash land back on earth, say for Kinetic Bombardment ("Rods from The Gods")
  3. You want to smash into other celestial bodies. In theory, the lowest energy trajectory to lunar bombardment is to launch 'straight up' at the right time to just beyond the Earth-Moon L1 Lagrange Point.

To get to the moon (well, smash into or flyby the moon), for example, you could 'launch straight up' and follow a trajectory like the one below. Note that you will have some horizontal velocity if you 'launch straight up', as you will inherit the rotational velocity at the surface depending on your launch site's latitude (~500 m/s at the equator, 0 m/s at the poles).

Lunar Flyby

In the above scenario, I was a bit late on the launch timing and thus trailed behind the Mun (in game 'Moon'). The purple post-encounter trajectory would have landed me back onto the surface of the planet, with no stable orbit established, and launched from the equivalent of the equator.

Bottom line is, if you want to orbit, you need horizontal and (and initially some vertical) velocity with respect to the surface. You can save a bit of fuel if you just want to 'get there' (and then smash into something).

Ehryk
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  • Agreed, I'll look for an Earth-Moon one and I'll draw in a trajectory – Ehryk Apr 27 '15 at 17:13
  • Picture posted showing the trajectory for a 'straight up' burn. I might try this in KSP later and post the video. – Ehryk Apr 27 '15 at 18:46
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    I was just going to suggest Kerbal Space Program (if you're into computer games, and rocket science!)

    https://kerbalspaceprogram.com/en/

     – EtherDragon Apr 27 '15 at 20:46
  • Also, here is a video that explains why rockets go sideways (and Kepler's First Law in general):

    https://www.youtube.com/watch?v=jkWhVd6TjCI

     – EtherDragon Apr 27 '15 at 20:46
  • Maybe even add a link to KSP in the main body of the post? (or did I miss it?) – Yakk Apr 28 '15 at 14:09
  • I've learned so much about rockets and physics in general from KSP. – Josh Apr 28 '15 at 14:27
  • Note that KSP does not in fact simulate Lagrange points (it uses spheres of influence instead of n-body dynamics) – Sanchises Apr 29 '15 at 10:55
  • Right, but crossing into the Moon's SOI is roughly equivalent to what I meant by crossing the Earth - Moon L1. – Ehryk Apr 29 '15 at 14:35
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Rockets take the shortest path to reach their orbit.

If all we want to do is pop up to LEO and come back down again, then we do go straight up. See the first two Mercury missions for an example - they landed north of Nassau.

If you want to end up in orbit, you need substantial horizontal speed. Turning at right angles is the least fuel-efficient way to do this, so the launch trajectory is a complex function of where you are now compared to where you want to be, and "where" includes velocity and direction, not just position.

paul
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    pop up to the altitude of LEO, but I would argue that to go "to LEO" means the same as "achieving LEO". (Unless maybe you are thinking of Ehryk's example, where you want your payload to "rendezvous" with an orbiting spacecraft for the purpose of destroying it.) – Solomon Slow Apr 27 '15 at 13:45
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I'm sure this is an incomplete answer, and would only add to those already excellent, more knowledgeable answers, but I do know that rocket scientists try to situate their launch site as close to the equator as they can, so the Earth's diameter gives some extra "throw" as compared to higher latitudes. I expect when the rocket tilts toward the horizontal, it is leaning in the direction of the Earth's rotation, so it can simply accelerate the motion it already has.

some more explanation, because I love to explain: That's one reason why the United States' facility is at Cape Canaveral, almost the southernmost point in the continental United States. You could liken it to those tennis ball throwers dog owners use --the longer the stick (the distance from the center of the Earth), the more velocity you get. If denser atmosphere slows down a rocket, the ideal launch site might be on a mountain in Colombia. Unfortunately the logistics to launch any sizable satellite from there would be prohibitive.

Haggisbreath
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  • Another reason to put launch sites close to the equator: Geosync orbits must always be in the equatorial plane. A launch from anyplace not on the equator means some kind of maneuver (more fuel burned) will be required to change the orbital plane. The further the launch site is from the equator, the more the cost. Just imagine the worst case: Trying to achieve an equatorial orbit by launching from one of the poles! – Solomon Slow Apr 27 '15 at 20:22
  • Launch Site latitude is dependent on the orbit desired and chosen to minimize fuel. For a Polar orbit, the equator is the worst place to launch as you'll have to spend $500 m/s \Delta v$ extra fuel to cancel this effect, and the north or south poles would be ideal. For equatorial orbits the direction of Earth's rotation (including geostationary), indeed the equator is the ideal place to launch and has the minimum fuel requirements, but these 'ideal' locations have to be tempered against the practicality of getting a rocket and launch facility there. – Ehryk Apr 28 '15 at 16:50
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It's not efficient that way. There is something called gravity turn. You need sideways velocity to stay in orbit and gravity turn essentially assists the rocket to turn sideways.

Alp
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