Oberth effect - Revision history

RichardWSmith: /* Math of kinetic energy and velocity */

2024-12-30T23:45:12Z

Math of kinetic energy and velocity

RichardWSmith: /* Math of kinetic energy and velocity */

2024-12-30T23:44:06Z

Math of kinetic energy and velocity

RichardWSmith: /* Math of kinetic energy and velocity */ fixed error

2024-12-30T23:43:48Z

Math of kinetic energy and velocity: fixed error

RichardWSmith: /* Reverse gravity-drag */ Added sentence to make argument clearer.

2024-12-30T22:06:42Z

Reverse gravity-drag: Added sentence to make argument clearer.

RichardWSmith: /* Math of kinetic energy and momentum */ renamed section. Not discussing momentum now.

2024-12-30T22:04:18Z

Math of kinetic energy and momentum: renamed section. Not discussing momentum now.

RichardWSmith: /* Math of kinetic energy and momentum */ cut out discussion on momentum, as it didn't add anything.

2024-12-30T22:03:36Z

Math of kinetic energy and momentum: cut out discussion on momentum, as it didn't add anything.

RichardWSmith: /* Energy */ Fixed an error.

2024-12-30T21:59:50Z

Energy: Fixed an error.

RichardWSmith: /* Energy */ grammar

2024-12-30T21:56:42Z

Energy: grammar

RichardWSmith: Rewrote this section to make it clearer.

2024-12-30T21:56:06Z

Rewrote this section to make it clearer.

RichardWSmith: /* Energy */ fixing formatting

2024-12-30T21:43:52Z

Energy: fixing formatting

@@ Line 31: / Line 31: @@
 Let us say you fire a rocket with mass 1 kg (after the fuel has been burnt), which will give your space craft 1 m/s velocity change.
-Let us fire this rocket when you are high in an orbit moving at 1 m/s (with respect to the planet).  You get a 1 m/s change so the new velocity is 2 m/s.  What is the change KE of the ship when you fire its engines high in the gravity well?
+Let us fire this rocket when we are high in an orbit moving at 1 m/s (with respect to the planet).  We get a 1 m/s change so the new velocity is 2 m/s.  What is the change KE of the ship when you fire its engines high in the gravity well?
 The change in KE  = KE(after ) - KE(before) = (1/2 * 1kg * 2m/s ^2) - (1/2 * 1kg * 1m/s ^2)
@@ Line 41: / Line 41: @@
-Now let us fire the rocket when it has fallen much closer to the planet.  When we fire the engines, we are moving 10 meters / second (with respect to the planet).  After adding 1 m/s onto the current speed of the ship, you are moving 11 m/s.
+Now let us fire the rocket when it has fallen much closer to the planet.  When we fire the engines, we are moving 10 meters / second (with respect to the planet).  After adding 1 m/s onto the current speed of the ship, we are moving 11 m/s.
 Change in KE = KE(after ) - KE(before) = (1/2 * 1kg * 11m/s ^2) - (1/2 * 1kg * 10m/s ^2)

@@ Line 36: / Line 36: @@
 = (4J) - (1J) = 3 J
-So the change in KE is 3 Joule.
+So the change in KE is 3 Joules.
 Note that: (1kg * m^2 / s^2 ) = 1 Joule of energy = 1J.

@@ Line 36: / Line 36: @@
 = (4J) - (1J) = 3 J
-So the change in KE is 1 Joule.
+So the change in KE is 3 Joule.
 Note that: (1kg * m^2 / s^2 ) = 1 Joule of energy = 1J.

@@ Line 6: / Line 6: @@
 ==Reverse gravity-drag==
-Gravity-drag is when you are launching a rocket in a gravity well.  Not only do you have to lift the rocket & payload, you have to lift the fuel which will be used higher up in the launch.  You have fuel low in a gravity field, and are burning it higher.  Effectively this acts as an energy 'tax' when you are lifting fuel higher in a gravity field.
+Gravity-drag is when you are launching a rocket in a gravity well.  Not only do you have to lift the rocket & payload, you have to lift the fuel which will be used higher up in the launch.  You have fuel low in a gravity field, and are burning it higher.  Instead of all of the energy of your fuel going into increasing your speed, you are using some of your chemical energy to increase the potential energy of the unburnt fuel.  Effectively this acts as an energy 'tax' when you are lifting fuel higher in a gravity field.
-Look at it the other way, let us say that you have fuel high in a gravity well, and burn it when you are lower.  That fuel has potential energy, which turns into kinetic energy as you fall closer to the central body.  When it is burnt lower, you have already converted some of that potential energy into kinetic energy, so the burn is more efficient.  This is the reverse gravity-drag 'tax refund'.
+Look at it the other way; let us say that you have fuel high in a gravity well, and burn it when you are lower.  That fuel has potential energy, which turns into kinetic energy as you fall closer to the central body.  When it is burnt lower, you have already converted some of that potential energy into kinetic energy, so the burn is more efficient.  This is the reverse gravity-drag 'tax refund'.
 ==Proportion of KE used to accelerate exhaust==

@@ Line 21: / Line 21: @@
 Since the reference frame we care about is the planet's (we want the ship to move away from the planet), the Oberth effect gives us a bonus.
-==Math of kinetic energy and momentum==
+==Math of kinetic energy and velocity==
 Energy can be stored in several forms.  There is chemical energy, potential energy (the energy of being high in a gravity field) and Kinetic energy (the energy of motion).  The energy of a system does not change, but we can change the form which this energy takes.

@@ Line 22: / Line 22: @@
 ==Math of kinetic energy and momentum==
 Energy can be stored in several forms.  There is chemical energy, potential energy (the energy of being high in a gravity field) and Kinetic energy (the energy of motion).  The energy of a system does not change, but we can change the form which this energy takes.
@@ Line 53: / Line 52: @@
 Now you might say, "won't the speed gained when we fell in towards the planet be balanced by the speed we lose when we rise up further from the planet?"  No.  We are moving faster, so we move away from the planet faster.  We spend less time in the deep gravity well, (when the planet is pulling harder), and more time far from the planet (where gravity is weaker).  After our boost, we spend less time in the planet's gravity, and so less speed is lost.
 ==Summary==

@@ Line 30: / Line 30: @@
 What we are interested in is the ''change'' in KE.
-Let us say you fire a rocket with mass 1 (after the fuel has been burnt), which will give your space craft 1 m/s velocity change.
+Let us say you fire a rocket with mass 1 kg (after the fuel has been burnt), which will give your space craft 1 m/s velocity change.
-Let us fire this rocket when you are high in an orbit moving at 1 m/s (with respect to the planet).  You get a 1 m/s change so the new velocity is 2 m/s.  (We will assume that the ship masses 1 kg.). What is the change KE of the ship when you fire its engines high in the gravity well?
+Let us fire this rocket when you are high in an orbit moving at 1 m/s (with respect to the planet).  You get a 1 m/s change so the new velocity is 2 m/s.  What is the change KE of the ship when you fire its engines high in the gravity well?
 The change in KE  = KE(after ) - KE(before) = (1/2 * 1kg * 2m/s ^2) - (1/2 * 1kg * 1m/s ^2)
-= (2J) - (1J) = 1 J
+= (4J) - (1J) = 3 J
 So the change in KE is 1 Joule.
@@ Line 46: / Line 46: @@
 Change in KE = KE(after ) - KE(before) = (1/2 * 1kg * 11m/s ^2) - (1/2 * 1kg * 10m/s ^2)
 = (60.5 J) - (50 J) = 10.5 Joules.
 Now this is an extreme case where the ships is moving 10 times faster near the planet than far from it, but it illustrates the point.  The energy of motion of the this rocket is much higher when the fuel is burnt after you have fallen from a point of high potential energy to a point of lower potential energy.  You are taking the potential energy of the fuel high in the gravity well, and converting it more efficiently to kinetic energy.

@@ Line 23: / Line 23: @@
 ==Math of kinetic energy and momentum==
 ===Energy===
-Energy can be stored in several forms.  There is chemical energy, potential energy (the energy of being high in a gravity field) and Kinetic energy (the energy of motion).  The energy of a system does not change, but we can change the form of this energy takes.
+Energy can be stored in several forms.  There is chemical energy, potential energy (the energy of being high in a gravity field) and Kinetic energy (the energy of motion).  The energy of a system does not change, but we can change the form which this energy takes.
 Kinetic Energy (KE) is the energy of motion.  Its value is calculated with this formula: