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113 votes
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Why is it easier to escape the solar system than get to Mercury or the Sun?

Because the earth goes very fast around the sun. If you want to get to the sun, you need to slow down almost completely so that your speed relative to the sun becomes almost zero. If you don't slow ...
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65 votes
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Can a miniature Saturn V get to the moon and back?

If you could miniaturize each component uniformly, you're correct that the rocket equation terms would all balance out and the rocket would be capable of the same delta-v performance. However, the ...
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46 votes
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Do you need 0 km/s velocity to crash into the sun?

Wouldn't i inevitably spiral to sun surface even if i was faster than 0km/s ? No. On reasonable timescales, an orbit will have a fixed distance of closest approach, called "periapsis." (These ...
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45 votes
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Delta-v to hit the moon: is reaching Lunar L1 enough?

This is an excellent and fun question, bravo. First, the table is being read incorrectly, here's how to properly read it: For example, to go from LEO-Ken to EML1 is given as 3.77 km/s, not 0.77 km/s. ...
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41 votes

Can a miniature Saturn V get to the moon and back?

You've got a few problems: When a model is scaled to 1:2 it's size, its area drops by 1/4 but its volume by 1/8. This is known as the square-cube scaling problem. So you will have one quarter the ...
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37 votes
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What does `ln` mean in the Delta V equation?

ln is a math function, the "natural log" Most scientific calculators have a key for it. See https://en.wikipedia.org/wiki/Natural_logarithm
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36 votes

Why is it easier to escape the solar system than get to Mercury or the Sun?

Changing orbits requires delta-v. To reach the Sun, you need to subtract delta-v such that your velocity relative to the Sun is near zero, which allows you to "fall straight down" into the ...
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34 votes

How could a 90 m/s delta-v be enough to commit the space shuttle to landing?

Page 331 in the Shuttle Crew Operations Manual, an official NASA astronaut training document, confirms that The deorbit burn usually decreases the vehicle's orbital velocity anywhere from 200 to ...
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34 votes
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How could 99942 Apophis, in 2029, be captured and brought into a low Earth orbit?

The edge of Earth's Hill Sphere is about 929000 km, so in order to capture Apophis, it needs to decelerate from a hyperbolic orbit to an elliptical one with an apogee of at most 929000 km. In 2029, ...
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32 votes
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Why did Voyager 2's velocity drop far below escape velocity before the first gravity assist?

You are correct that Voyager did not change from above escape velocity to below escape velocity shortly after launch. The plot is misleading in that it is just not very accurate right there at 1 AU. ...
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31 votes
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How could a 90 m/s delta-v be enough to commit the space shuttle to landing?

If you're just looking for an intuitive handle on it, try this: In circular LEO, your orbital period is about 90 minutes. If you apply a velocity change of 90 m/s, then wait half an orbit -- 45 ...
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31 votes

Is it really ~648.69 km/s delta-v to "land" on the surface of the Sun?

Addressing is the sun's mass and other quantities known well enough for this to be absolutely accurate? Well, the key to this is the vis-viva equation in your question. It's not actually important ...
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29 votes
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How easy is it to take off from the Moon?

The amount of delta-V needed to get from the Moon to low Moon orbit is only 1.87 km/s or about 1/5 of that needed to get from Earth to LEO. That amount is easily attainable even if your ascent vehicle ...
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25 votes

Can a miniature Saturn V get to the moon and back?

In addition to the other answers, you'd also have to take temperature into the equation. Your cryogenics tanks have much thinner thermal insulation, primarily LH2 (LOX was "insulated" by the tank ...
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25 votes
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Does it take more energy to get to Venus or to Mars?

To flyby or impact Venus varies from 3.45 to 3.6 km/s from LEO for the optimal time every 19 months. Mars varies from 3.55 to 3.9 km/s for the optimal time every 26 months. So on average, getting to ...
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24 votes
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Maximum speed reachable by Saturn V

The amount by which a spacecraft is able to change its velocity is called it's Δv (delta-velocity) budget. You can calculate the Δv-budget of each stage of a rocket using the Tsiolkovsky rocket ...
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24 votes

Is it really ~648.69 km/s delta-v to "land" on the surface of the Sun?

The Vis-viva equation is $$ v = \sqrt{ GM \left(\frac{2}{r} - \frac{1}{a} \right) }, $$ The $GM$ product for the Sun is 1.327E+20 m^3/s^2. If 1 AU is 150E+09 meters, then when you are in a ...
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22 votes

Why is it easier to escape the solar system than get to Mercury or the Sun?

Escaping the solar system requires adding orbital velocity to the spacecraft. Similarly, getting closer in the solar system requires removing orbital velocity. It turns out Earth is more out of the ...
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20 votes
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How much delta-v can we squeeze out of a gravitational slingshot and what factors limit it?

Yes, those are the three factors. Your third factor shows up as the $v_\infty$ of the spacecraft relative to the object. The first two are the GM of the object, $\mu$ and the closest approach ...
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20 votes
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What would it cost to bring a 1 gram payload to the CMBR rest frame (i.e. Δv 368 km/s ?)

With current technologies, this is unfortunately well outside our reach. However, there is promise on the horizon! Chemical Engines The Tsiolkovsky equation is always your friend when calculating Δv ...
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20 votes
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What are the benefits of supersynchronous transfer orbits?

This is a partially copied answer from this closely-related question: The other answerer focuses on the straight-up dV savings which occur when you're launching from a very inclined launched site. I'm ...
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  • 9,790
19 votes

Do you need 0 km/s velocity to crash into the sun?

You need below 2866 m/s of orbital velocity at 1 AU to crash into the Sun. You technically don't need to slow down exactly to 0 m/s relative to the Sun in order to crash into it. Let's calculate the ...
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19 votes
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What is the equation that relates delta v of a rocket to time taken to complete an orbit?

There is actually no relationship between the two. In a simple 2-body problem, each orbit starts and ends in the same place with the same velocity vector. The "delta" in "delta-v" ...
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18 votes
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Delta-v to move from GEO to GEO

Theoretically, you can go anywhere in GEO for an arbitrarily small ∆v - you raise your apogee a little bit, which slows you down, wait until you've phased to your destination latitude, then re-...
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18 votes
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Will crewed vehicles ever follow multi-flyby trajectories?

Given the mass costs in terms of consumables and the risk and support costs of keeping humans in space for longer, it seems unlikely that the multiple Earth-Venus flybys used by a lot of robot probes ...
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18 votes

Has there ever been a completely solid fuelled orbital rocket?

There have been a few purely solid-fuel orbital rockets over the years. The first was the Scout from 1961; the only ones in current use are the Long March 11 and the Minotaur/Minotaur-C family. ...
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17 votes

Why did Voyager 2's velocity drop far below escape velocity before the first gravity assist?

The image (original at Wikimedia Commons) is only an approximation, as evidenced by the noticeable change in shape of the solar system escape velocity line at 14AU. The line is only defined with three ...
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17 votes

Do you need 0 km/s velocity to crash into the sun?

And note that if you want to hit the sun the cheaper (but slow!) way to do it is to head out. 12.32km/sec will take you to infinity, at infinity a burn of 0m/sec will kill your orbital velocity and ...
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16 votes

How could a 90 m/s delta-v be enough to commit the space shuttle to landing?

I think that something visual may be of help This is a bit more to scale than most peoples pictures, but the shuttle only orbits at 200 miles, while the earth itself is almost 8000 miles across, so ...
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16 votes

What would it cost to bring a 1 gram payload to the CMBR rest frame (i.e. Δv 368 km/s ?)

Jack did a great job describing how to do it using propulsive engines. I have a different answer: We already (almost) planned to do it (inadvertently). The original plan for the recently launched ...
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