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I am a high school student. I saw the latest Indian spacecraft "CHANDRYAANN 2", which was in orbit around the Earth for 14 days.....

I am so curious to know how a spacecraft changes its orbit. I have done some research on Google and it says "velocity first increases then decreases"; I do not know why the velocity increases. Can anyone explain this if I have read it correctly?

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    $\begingroup$ Firing the rockets momentarily (or for a short duration) changes the height of the opposite side of the orbit. Doing this again on the opposite side of the orbit completes the orbit change. This is the most common way for a spacecraft to change it's orbit. It's called a Hohmann transfer orbit. Search on that for more information. $\endgroup$
    – Wayne Goode
    Oct 28, 2019 at 21:48
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    $\begingroup$ Yet another question which can be answered "Play Kerbal Space Program" :) $\endgroup$
    – IMil
    Oct 28, 2019 at 23:10
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    $\begingroup$ @yuvrajsingh You might want to search up "The Oberth Effect" as it relates to your question of why "velocity increases". $\endgroup$
    – Star Man
    Oct 29, 2019 at 1:21
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    $\begingroup$ If you are willing to spend some dollars for a commercial game, Kerbal Space Program is well recognized as an amazing way to learn how orbital mechanics actually works. (or at least learn enough that you're not totally confused when they introduce real physics). We can tell you the answer, but sometimes playing around with the mechanics is required before you can feel it. $\endgroup$
    – Cort Ammon
    Oct 29, 2019 at 2:27
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    $\begingroup$ @yuvrajsingh "The Oberth Effect" combines the simple adage of "what goes up, must come down" with the secret to flying: Throw yourself at the ground, and miss $\endgroup$
    – Chronocidal
    Oct 29, 2019 at 8:56

4 Answers 4

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To answer your title question: By using its engines.

However you seems to be quite puzzled by the fact that velocity of an object can decrease and increase over the course of an orbit.

If the orbit is perfectly circular, the speed will always remain the same (until thrusters are used).

However, as is the case with Chandrayaan-2, most orbits are elliptical (so they have a high altitude and a low altitude points)

On an elliptical (i.e., not circular) orbit, the altitude curve looks a bit like this (1):

    _       _       _
   / \     / \     / \
  /   \   /   \   /   \
_/     \_/     \_/     \...

The altitude of the spacecraft goes up and down. When the spacecraft altitude increases, it slows down, and when the spacecraft altitude decreases, it accelerates.

This is exactly the same as riding over small hills on a bicycle (except there is no friction so you don't need to pedal at all).

[1]: It's a bit more complicated, since the altitude change is not linear with time, but you get the idea.

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    $\begingroup$ It seems the OP wants to know about Keplerian orbits and the equal area law. The altitude graph looks helpful, combined with a picture of an elliptical orbit and references to a good description. $\endgroup$
    – Bit Chaser
    Oct 28, 2019 at 23:17
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    $\begingroup$ Or rather, very small friction that gets abstracted to zero. The ISS has to perform an orbital boosting maneuver every month or so due to the drag from the microatmosphere at its altitude. $\endgroup$
    – Draco18s no longer trusts SE
    Oct 29, 2019 at 15:18
  • $\begingroup$ Slight nitpick - the speed of a body in a circular orbit is constant, but the velocity vector is constantly changing direction because of the centripetal acceleration due to gravity. $\endgroup$
    – Nuclear Hoagie
    Oct 29, 2019 at 15:37
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    $\begingroup$ @uhoh It would have been better if it was screenshotted from the message preview then annotated with freehand circles in paint, but yeah the graphics are adequate... $\endgroup$
    – corsiKa
    Oct 30, 2019 at 3:48
  • $\begingroup$ @NuclearWang Is there no coordinate system that defines your velocity in a rest state as following an orbital path? A satellite-centric coordinate system? $\endgroup$
    – corsiKa
    Oct 30, 2019 at 3:50
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Hohmann transfer orbit

After reading all your answers I'd like to summarise the situation.

The black circles are the circular orbits and the red ellipse is the transfer orbit.

Consider a spacecraft in the elliptical orbit. At the point P the velocity is greater than the circular orbital velocity, and that's why the distance from the centre increases. And at the point A the velocity is less than the orbital velocity, which is why the spacecraft falls back towards the centre.

So if you start at the inner circular orbit then at the point P you have to increase your velocity to change to the red elliptical orbit. When you get to the point A your velocity has fallen because you slow down as you move away from the centre. So you now have to increase your velocity once again to change to the outer circular orbit.

So there are three changes to the velocity:

  1. you fire your engines at point P to increase velocity

  2. your velocity decreases as you coast away from the Sun

  3. you fire your engines at point A to increase velocity again

So in fact both times you fire you engine it is to increase your velocity. The total velocity change is the sum of the two increases when you fire your engine minus the decrease that happens as you coast away from the Sun.

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To simplify the explanation and terminology, let's consider the case of a spacecraft orbiting Earth.

All orbits are elliptical, with the center of mass of the system (Earth, in our example) at one focus. Circular orbits are a special case where the ellipse has no eccentricity and the focii are coincident.

The orbit of our spacecraft has a perigee (closest point to Earth) and apogee (farthest point from Earth). As an aside: the terms "perigee" and "apogee" are used specifically for orbits around Earth; around an unspecified object, we use the terms "periapsis" and "apoapsis". As our spacecraft completes one orbit around Earth, it will pass through perigee once, and apogee once.

Kepler worked out that an object in orbit (our spacecraft) will not travel at a uniform speed, but instead carve equal areas in equal time as it orbits. This means that it will have its highest speed at perigee and lowest speed at apogee. A truly circular orbit is a special case where its speed actually is uniform.

Let's consider a spaceship in a circular orbit. It wants to climb to a higher orbit. It briefly fires its engine to speed up along its current trajectory. It is now no longer in circular orbit; it is now at the perigee of an elliptical orbit, and as it travels to apogee, it must slow down. If it does nothing else, it will return to that same perigee point after one complete orbit. On the other hand, when it gets to the apogee point, it can fire its engine again to speed up again. This will raise the perigee point; the right change in speed at apogee will raise the perigee to make the orbit circular again, at the new altitude.

The "velocity increases then decreases" would refer to either an interpretation of Kepler's second law, or what typically happens when a spacecraft makes an adjustment to its orbit, such as I've described.

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  • $\begingroup$ Thanks, one question as we move outwards shouldn't, t orbit be circular, and earth is spherical and symmetrical why orbit need to be circular sir. $\endgroup$
    – आर्यभट्ट
    Oct 29, 2019 at 2:45
  • $\begingroup$ @yuvrajsingh Not sure how to answer that question. I think the best way to understand what is going on will come from the underlying mathematical description - newtonian motion and calculus. I don't remember enough of it anymore. I'll have to defer to someone else better versed in it. $\endgroup$
    – Anthony X
    Oct 29, 2019 at 2:52
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    $\begingroup$ @yuvrajsingh When you accelerate in orbit, you're moving the opposite side of the orbit; which also means you're changing the eccentricity ("circular-ness") of your orbit. When you reach the new "highest" point, you can accelerate again to bring up the other side, making the orbit circular again. But regardless, orbits certainly don't need to be circular. We use orbits for a given purpose. Each orbit has different benefits and drawbacks. The main benefit of circular orbits is that they are much simpler. $\endgroup$
    – Luaan
    Oct 29, 2019 at 7:26
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Imagine your spacecraft is on elliptical orbit around space body. The body is inside ellipse (in the focus, if more specifically). When spacecraft is on the vertex of ellipse and speed up in direction of movement, another vertex of trajectory is moving far from body. Vice versa, if the spacecraft is braking (by turning engines forward and burning) in the one vertex, second vertex moves to the space body.

This is simplest scenario, without orbit precession and other things, but it illustrate the idea.

If you really want to know, just find demo of Kerbal Space Program game, it will help for sure.

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  • $\begingroup$ The demo of KSP isn't all that useful - it doesn't contain many parts, and while you can get to orbit, it lacks a lot of the display to project orbits etc. It's from a very old build (pre release) $\endgroup$
    – Baldrickk
    Oct 30, 2019 at 15:16
  • $\begingroup$ @Baldrickk : I would recommend "Spaceflight Simulator", you can land on every planet and return, even with only the equipment found in the free version. Also, it's 2d, and easier to learn and use. $\endgroup$
    – vsz
    Oct 30, 2019 at 20:06

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