Why is so much harder to get to Earth Orbit?

[Spaced Out]

Okay so I know to get to Kerbin orbit it starts at about 4500 delta v, and to get to Earth orbit it starts at 9400. Why is that? I know the gravity is the same but is Kerbin smaller and does Earth have a thicker atmosphere?

[Kerbart]

yes

[captainb]

You've answered your own question by your delta-V stats  (although Kerbin orbital speed is closer to 3500m/s).  Earth requires a much higher velocity to achieve orbit because it is bigger.  If you think of an Evil-Knievel motorcycle jump you need more speed to jump 10 buses than only 3 for a given ramp height.  Same with Earth/Kerbin - you need more speed to keep falling and missing with a bigger planet.

[YNM]

For starters, you should realize how fast and how near LEO is compared to KEO.

Kerbin is a weirdly-scaled object, period.

[Nibb31]

Remember Newton's hypothetical cannonball shot from a hypothetical mountain above the atmosphere ?

Remember that to reach orbit, you need to go fast. A and B don't go fast enough so they fall to Earth. Achieving orbit is about falling and missing the ground, so if you fire a cannonball fast enough it falls beyond the Earth (C and D). If you shoot it even faster, it escapes (E).

Now, because the Earth is much much bigger than Kerbin, although the gravity is the same, you need to shoot your cannonball much further to go beyond the horizon, which means it has to go much faster.

Edited August 10, 2017 by Nibb31

[tomf]

Also Kerbin's gravity drops of much more quickly with the inverse square law. Adding 100km to kerbins 600km radius means that the acceleration due to gravity there is only 7.2m/s^2 whereas adding 100km to Earths 6400km radius means gravity has only decreased to 9.5m/s^2

[NSEP]

Earth does not have a thicker atmosphere, Kerbins atmosphere is just lower, and Earths atmosphere is something like 2x higher untill you reach a good parking orbit. The reason why it takes less Delta-V is because you need to curve away from alot less surface area, than Earth, because Kerbin is alot smaller. 

[Nefrums]

Earth is 10 times bigger than Kerbin. (radius)  and is 100 times heavier.  

(You would think that the mass of Earth would be 1000 larger as the volume, but apparently Kerbin is made up of something twice as heavy as the heaviest material IRL )

If we do like in the game approximate the gravity to all be in a point at the center of the planet Earth have a 100 times greater gravity then Kerbin. The surface gravity is the same as the Earths surface is 10 times farther from the center then Kerbins surface.  (gravity decreases with r^2)

[wumpus]

10 hours ago, captainb said:

You've answered your own question by your delta-V stats  (although Kerbin orbital speed is closer to 3500m/s). 

I'm pretty sure I've seen around 2000m/s in LKO (Low Kerbin Orbit).  I suspect the 3500m/s number means that Kerbin rockets suffer similar gravity and aero-drag losses as Earth rockets (thanks to similar atmospheres and 9.08m/s**2 gravity).

[monstah]

21 minutes ago, wumpus said:

I'm pretty sure I've seen around 2000m/s in LKO (Low Kerbin Orbit).  I suspect the 3500m/s number means that Kerbin rockets suffer similar gravity and aero-drag losses as Earth rockets (thanks to similar atmospheres and 9.08m/s**2 gravity).

Precisely.

Earth orbital speed is closer to 7km/s, too, but the 9km/s figure comes in when you add gravity and aerodynamic losses.

[Tex_NL]

To put things into perspective:

[Pand5461]

Circular orbital speed is sqrt(gR), where g is gravitational acceleration, R is radius. g has the same value at surface of Earth and Kerbin, but Earth radius is about 11 times greater than Kerbin's (6400 km vs 600 km). Therefore, circular orbital speed at LEO is sqrt(11) ~ 3.3 times larger than at LKO. The overall difference in dV to orbit is a bit smaller because those dV include gravity, drag and steering losses that are comparable for both planets.

Edited August 10, 2017 by Pand5461