Account for planetary incoming and outgoing energy

Choose a boundary before adding the arrows

Sketch a planet inside a circle labeled top of atmosphere. Draw sunlight entering, reflected sunlight leaving, and thermal radiation leaving. The budget in this lab concerns exchange across that outer boundary, averaged over the entire planet. It does not separately assign energy to the ground, ocean or atmospheric layers.

NASA’s Earth energy-budget explanation distinguishes incoming sunlight, reflection and thermal radiation. The lab turns these categories into a controlled arithmetic exercise. Its outputs are calculated scenarios, not a loaded set of satellite measurements.

A watt is a joule per second. W/m² therefore measures energy-transfer rate per area, not stored energy and not temperature. Keep that unit on every arrow. If you add an arrow with units of kelvin to an arrow measured in W/m², the calculation has lost its physical meaning.

Explain the factor of four with areas

The solar irradiance S is 1361 W/m² on a surface perpendicular to the arriving rays, a representative value from the NASA Earth fact sheet. A spherical planet intercepts sunlight over a disk of area πR², where R is its radius. Its entire surface area is 4πR².

Total intercepted power is SπR². Dividing that power by the full spherical area gives global mean incoming flux S/4 = 340.25 W/m². Radius cancels. The four comes from the disk-to-sphere area ratio; counting day and night twice is not a derivation.

For a paper activity, draw a disk and sphere with the same radius. Write their areas and cancel the common πR² explicitly. Then explain why 340.25 W/m² is not the sunlight at every location at every moment. A global mean summarizes uneven illumination rather than removing the unevenness from the real planet.

Partition the sunlight once

Planetary albedo α is the fraction of incoming solar energy reflected back to space. The slider displays percent, so 30% must become α = 0.30 in the equations. Reflected flux is αS/4; absorbed flux is (1 − α)S/4.

At 30%, reflection is 0.30 × 340.25 = 102.075 W/m² and absorption is 0.70 × 340.25 = 238.175 W/m². Their sum is 340.25 W/m². Reflection has already been removed when you calculate absorption; subtracting it again from absorbed energy would count the same loss twice.

Construct a three-column ledger for incoming, reflected and absorbed flux at albedos 0%, 30% and 80%. Predict whether incoming sunlight changes before touching the control. The source remains fixed in all three cases. Only the allocation between reflection and absorption changes.

Compare absorption with thermal emission

Outgoing thermal flux is calculated from the selected effective emitting temperature. At the default 255 K it is about 239.758 W/m². Define signed net flux N as absorbed sunlight minus outgoing thermal radiation. The default net is 238.175 − 239.758, about −1.583 W/m².

A positive net indicates energy accumulation for the defined system; a negative net indicates energy loss. A zero net means balanced radiative exchange. This sign convention does not supply a temperature change per year. That requires additional information about stored energy, heat capacity and evolution through time, none of which is calculated here.

Hold temperature at 255 K and change albedo. Then hold albedo at 30% and change temperature. In your ledger, name which flux each control changes directly. This separates two mechanisms that could otherwise be hidden inside one net number.

Transfer to a different solar input

For a paper-only planet with normal solar irradiance 1200 W/m², albedo 25% and outgoing thermal flux 220 W/m², calculate global incoming, reflected, absorbed and signed net flux. State whether the result gives a heating rate in kelvin per year.

Check the energy-budget transfer

Incoming is 300 W/m², reflected is 75 W/m² and absorbed is 225 W/m². Net is +5 W/m², indicating energy accumulation. It does not provide a temperature-change rate without a storage and heat-capacity model.