Identical continuous color palettes in ggplot

I am trying to plot two graphs with the same continuous color palette. In one plot the range for the color palette to represent is 0-0.48 with the vast majority of points between 0-0.18. The other plot's range is 0-0.08. I want to use the same color palette on both plots and have the same colors associated with the same value.

Below is a reproducible example (with the real data for color):

color_range_df1 <- c("0.005","0.000","0.000","0.007","0.007","0.006","0.005",
                     "0.002","0.063","0.001","0.101","0.151","0.006","0.178",
                     "0.140","0.150","0.130","0.155","0.175","0.175","0.152",
                     "0.006","0.058","0.167","0.151","0.000","0.050","0.015",
                     "0.079","0.003","0.043","0.105","0.078","0.091","0.006",
                     "0.159","0.089","0.151","0.002","0.004","0.174","0.087",
                     "0.050","0.172","0.099","0.018","0.060","0.115","0.014",
                     "0.000","0.004","0.000","0.000","0.000","0.000","0.000",
                     "0.135","0.003","0.003","0.006","0.000","0.000","0.000",
                     "0.488","0.000","0.003","0.000","0.048","0.000","0.000",
                     "0.133","0.161","0.001","0.079","0.000","0.139","0.000",
                     "0.041","0.001","0.175","0.101","0.058","0.180","0.140")

color_range_df2 <- c("0.057","0.022","0","0.009","0.049","0.048","0.055","0.048",
                     "0.031","0.049","0.043","0.047","0.06","0.059","0.049","0.045",
                     "0.042","0.049","0","0","0","0","0","0","0","0.034","0.056",
                     "0.05","0.046","0.053","0.033","0.047","0.047","0.031",
                     "0.046","0.084","0.079")


df1_bigrange_and_outlier<- data.frame(X = 1:84, y = 1:84, color = color_range_df1)
df2_smallrange <- data.frame(X = 1:37, y = 1:37, color = color_range_df2)


ggplot(data = df1_bigrange_and_outlier, aes(x = X, y = y, color = color)) +
  geom_point()

In this example, I want the 0.488 point to be a very distinct color, and there to be a visual difference between 0-0.05 and 0-0.18.

I've tried

pal <- c(colorRampPalette(c("#c9e2f6", "#95cbee", "#0099dc",
                             "#0D98BA","#4ab04a", "#C0FF02", "#ffd73e"))(10),
          colorRampPalette(c("#e29421", "#e29421", "#f05336", "#ce472e", "#8B0000"))(30))

which works well for plot 1, but I'm not sure how to translate that to the second plot, where the range only goes from 0-0.08 instead of 0-0.48.

It's buried deep in the online doc, but you can use limits to specify the range of your colour scale. However, aesthetics are going to be an issue: with disparate ranges like this, discrimination will be a problem even after you've addressed @stefan's point.

Here's something that may get close to what you want, with a small modification of your original set up:

df1_bigrange_and_outlier<- data.frame(X = 1:84, y = 1:84, color = as.numeric(color_range_df1))
df2_smallrange <- data.frame(X = 1:37, y = 1:37, color = as.numeric(color_range_df2))


ggplot(
  data = df1_bigrange_and_outlier, 
  aes(x = X, y = y, color = color)
) +
  geom_point() +
  scale_color_steps(
    limits = c(0, 0.5), 
    low = scales::muted("blue"), 
    high = scales::muted("red")
)

ggplot(
  data = df2_smallrange, 
  aes(x = X, y = y, color = color)
) +
  geom_point() +
  scale_color_steps(
    limits = c(0, 0.5), 
    low = scales::muted("blue"), 
     high = scales::muted("red")
)