100

The trouble with orbital mechanics is that it rapidly gets exceedingly complicated and hard to make intuitive sense of. However I think there is a reasonably straightforward way to show how little effect GR has on an Earth-Moon transfer orbit. But this takes a little preparation so bear with me while I give a short introduction. I hope everyone who reads ...


92

Cory, here's a different way of thinking about gravity assists that may help: First is my short answer for readers in a hurry: What is really going on is a giant game of pool, with fast-moving planets acting as massive cue balls that impart some of their energy when they whack into tiny spacecraft. Since you can't bounce a spacecraft directly off the ...


72

Start by considering what is seen by the people watching you from the Earth. Nothing can travel faster than the speed of light, $c$, so the quickest you could get to Kepler 186f would be if you were travelling at $c$ in which case it would take 490 years. In practice it would take longer than this because you have to accelerate from rest when you leave the ...


69

Can photons push the source which is emitting them? Yes. If yes, will a more intense flashlight accelerate me more? Yes Does the wavelength of the light matter? No Is this practical for space propulsion? Probably not Doesn't it defy the law of momentum conservation? No In fact that last question is the key one, because photons do carry ...


68

When an astronaut bumps against the wall of the spacecraft, the spacecraft does gain whatever momentum the astronaut transfers to the wall. However, the astronaut loses momentum-or gains it in the opposite direction. The net result is that the center of mass of astronaut- plus-spacecraft does not move, and the combined momentum does not change. It is ...


63

The Jet Propulsion Laboratory has incorporated general relativistic effects in its numerical integration of the planets since the mid to late 1960s. For example, the JPL DE19 ephemeris, released in 1967, incorporated relativistic effects in its modeling of the solar system. This didn't help much. Had they ignored relativistic effects there would have been ...


53

How do astronauts, especially those inside small spacecraft like the Crew Dragon, not “push” the spacecraft when they bounce and push off walls? You're right that when an astronaut collides with the walls of the spacecraft, some of their momentum is transferred to the spacecraft and in turn their momentum either reduces or gets reversed in direction. ...


51

Reentry speeds are fast. Astonishingly fast. The shuttle reentered at 7.8km/s. Now note the units. That's "per second." That's 28,158km/hr. And you have roughly 100 vertical kilometers to do that braking in. Yes, the braking gets to be done at a very shallow angle, which means you have more linear distance to break than the 100km would ...


43

A sailboat can make headway against the wind because of the sum of force vectors due to the wind interacting with the sail and, due to the keel interacting with the water. A sailboat without a keel can not make headway into the wind. There is no "water" out there into which a solar sailer could dip its keel. http://newt.phys.unsw.edu.au/~jw/sailing.html ...


39

Energy is in fact conserved, even in gravitational slingshots. After the slingshot, the velocity of the spacecraft may indeed change, which means its kinetic energy will also change. If this happens, the energy increase (or decrease) will be made up by a commensurate decrease (or increase) in the kinetic energy of the planet. In plain English: The planet ...


27

A few sanity checks without actually computing anything: First, the error due to neglecting general relativity is so small that it didn't affect prediction of lunar eclipses and wasn't actually noticed anywhere except in Mercury's orbit (at least not until they purpose-built experiments to detect minor discrepancies). I know this doesn't give a completely ...


26

I'll start the ball rolling on this one. My GR knowledge is probably not good enough to make this a truly satisfying answer... The gravitational acceleration for an object moving radially at non-relativistic velocities in the Schwarzschild metric is modified by a factor $(1 - r_s/r)(3[1-r_s/r] -2)$, where $r_s = 2GM/c^2 = 0.00885 m$ for the Earth. If we ...


25

Suppose that A and B are at rest relative to each other (which you have) and in their mutual rest frame are separated by 100 light years. That means that no signal can travel from A to B (or vice-versa) in less than 100 years. Signals include optical or radio signals, which travel at the speed of light, and also material projectiles like spacecraft, which ...


20

Can photons push the source which is emitting them? Yes, photons have momentum and momentum must be conserved. The source is pushed in the opposite direction of the photons. If yes, will a more intense flashlight accelerate me more? Yes, more photons means greater momentum. Does the wavelength of the light matter? Yes, shorter wavelength photons ...


20

It all comes down to the fact that we are moving too. How can the bird drop down and catch the worm, if the earth and the worm are moving so quickly. It can because the tree, the bird, and the air are moving at the same speed, cancelling out. If we launch a spacecraft from Mars to the earth, the spacecraft is zooming around the sun at the same speed Mars ...


18

The question is about solar sails - I thought I would add this (too long for a comment) to clarify some confusion that is apparent in answers and comments. Solar sailing uses photon momentum, not the solar wind. The radiation force on a perfectly reflective sail of area $A$ is roughly $$ F_{rad} = 2\times\frac{L A}{4\pi r^2 c}$$ where $r$ is the distance ...


15

Deriving the relativistic equations for constant acceleration would be a formidable problem for most non-physicists. If you want to see how it's done then look at Gravitation by Misner, Thorne and Wheeler, chapter 6. For most of us the best option is just to look at John Baez's excellent article on the relativistic rocket. The relevant equation is: $$ d = \...


14

Why can't a space ship accelerate infinitely? Because a space ship needs to carry fuel, and because that fuel needs to be contained in a fuel tank. That need to carry the fuel needed to make the spacecraft accelerate leads to the very nasty ideal rocket equation, $$\Delta v = v_e \ln \left( \frac {m_{\text{initial}}} {m_{\text{final}}} \right)$$ The ...


14

An astronaut pushing against the wall of a spacecraft does cause it to move due to Newton's Third Law and conservation of momentum, as you have noted. However, the movement of the spacecraft is not that noticeable for a couple of reasons. One is that the spacecraft has much more mass than the astronaut, so any change in its velocity will be much smaller the ...


13

Yes, sort of, sometimes. As others have indicated, it is not possible for a solar sail to produce a force in the direction of the Sun. This does not, however, mean a solar sail cannot take a spacecraft to the Sun. If your spacecraft is in solar orbit, you can tilt the sail "backwards", reducing the orbital energy and lowering the orbit. The potential energy ...


12

I've talked to one of the engineers who is involved with timekeeping on the Parker Solar Probe mission. I have not yet talked with the principle timekeeping lead, so this answer may have to be revised. There seems to be two relativistic effects that will affect PSP due to the Sun's gravity well. The first is clock error due to relativistic effects near the ...


11

The link you posted refers to a design which would supposedly make use of faster than light travel. After reading this, I immediately stopped reading, since this is not possible. I don't care if it's a NASA-affiliated person who says this, it is simply misguided! Before continuing, I should draw your attention to the fact that I will not be discussing the ...


9

The one thing to keep in mind is that in order to perform a gravity-assist maneuver, you need to be able to enter a hyperbolic orbit around a given body that is moving relative to your destination. And, in order to be in such an orbit, there is a specific range of velocities for every object that you must have (dependent on mass of the object). So the ...


9

Gravity assists don't change speed in the two body problem. An object approaching a lone gravitating body will enter and leave the vicinity of that body with exactly the same speed. All that a lone gravitating body can do is change the direction in which the object is heading. The body that provides the assist needs to be moving with respect to the target ...


8

Suppose the spaceship was accelerating constantly at 1g, what would that feel like? Well Einstein gave us the answer to that: it would feel exactly like standing on the surface of the Earth where the acceleration due to gravity is 1g. This is (one statement of) Einstein's equivalence principle. If the acceleration were continued for many hours that wouldn't ...


8

1.When they travel to the watery planet, they say that 1 hour on this planet is 7 yrs om earth. How is this possible? Is the planet moving at a speed close to c? Or does strong gravitational field influence time? Sure. This is gravitational time dilation. It's due to the gravitational field of the black hole. You can calculate it using $$\frac{d \tau}{dt}=\...


7

Yes, but you'll have to go really, really fast. And even then, don't worry about the photons. The relation between velocity $v$ and the observed and "true" wavelength $\lambda_\mathrm{obs}$ and $\lambda$ of the light is $$ \lambda_\mathrm{obs} = \sqrt{\frac{1-v/c}{1+v/c}} \lambda. $$ If you consider optical (i.e. visible to humans) light with a wavelength ...


7

Even missions to Phobos have to consider relativity, but that's because of the necessary sensitivity of any instrument trying to measure Phobos's gravity. So my cop-out answer is it depends on what you consider significant. I'd assume that most instruments would be measuring pretty large properties and would not have to consider relativity, but anything that ...


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