Io gets most of its heat flow from tidal pulling and pushing as it orbits Jupiter. Europa also orbits Jupiter

and gets quite a bit of tidal pulling. The heat flow on Europa is around 100 times less than that on Io. The
latent heat of melting from solid ice to liquid water is 3.4 × 105 J/kg. If, as some people have proposed, the
uppermost 100 km of Europa is a thick water ice layer, what is the timescale to melt this layer? Do you
expect Europa to have no, few, some, or many craters on its surface, and why? This surface/interior ocean,
some people think, is the reservoir of water that life on Europa could survive in – but only if there is enough
liquid water that persists for long enough. (Note: The density of ice is around 1000 kg/m3.)

To calculate the timescale to melt the 100 km thick water ice layer on Europa, we need to determine the amount of heat required to melt the ice and then consider the heat flow from tidal pulling.

First, let's calculate the amount of heat required to convert solid ice to liquid water. The latent heat of melting from solid ice to liquid water is given as 3.4 × 10^5 J/kg.

To find the total amount of heat needed, we multiply the latent heat of melting by the mass of the water ice layer. The density of ice is approximately 1000 kg/m^3, and the thickness of the ice layer is 100 km (or 100,000 m), so the volume of the ice layer is:

Volume = area × thickness = (100,000 m) × (1 m^2) = 1 × 10^10 m^3

The mass of the ice layer can be calculated by multiplying the volume by the density:

Mass = volume × density = (1 × 10^10 m^3) × (1000 kg/m^3) = 1 × 10^13 kg

Now, we can calculate the total heat required:

Total heat = mass × latent heat of melting = (1 × 10^13 kg) × (3.4 × 10^5 J/kg) = 3.4 × 10^18 J

Next, we need to consider the heat flow from tidal pulling on Europa. Since Europa experiences tidal pulling similar to Io, but at a slower rate, we can assume the heat flow is proportional but reduced by a factor of (1/100).

The timescale to melt the ice layer can be calculated by dividing the total heat required by the heat flow:

Timescale = Total heat / Heat flow = (3.4 × 10^18 J) / [(1/100) × heat flow of Io]

It is not explicitly mentioned what the heat flow is for Io, but we can assume a value for reference. According to NASA, the estimated heat flow from Io is approximately 1.6 × 10^14 W (watts).

Using this value:

Timescale = (3.4 × 10^18 J) / [(1/100) × (1.6 × 10^14 W)]

Simplifying the equation:

Timescale = (3.4 × 10^18 J) / (1.6 × 10^12 J/s) = 2.125 × 10^6 seconds

So, the timescale to melt the 100 km thick water ice layer on Europa is approximately 2.125 × 10^6 seconds or about 24.6 days.

As for the craters on Europa's surface, we can expect to see few craters. The reason is that the presence of an active, convecting icy shell on Europa would cause any craters to be erased over time. Since Europa has a subsurface ocean, and the ice layer is believed to be undergoing constant changes due to tidal forces, any impact craters would likely be smoothed out or filled in relatively quickly compared to a static surface. Therefore, we would expect Europa's surface to have relatively few craters compared to other solid bodies with more stable surfaces.