After completing The Extermination mission from Eris you will get three patrol missions from her. The Hand of Crota, Eyes of Crota and Heart of Crota are all done on Earth. Check this guide to find which areas you will need to visit to get the right patrol missions!
Eric Cosmodrome Patrol Missions
You will need to go to the area and kill the Crota minion to start the wave. After the wave spawns there will be a unit with yellow HP that needs to die to complete the mission.
Hand Of Crota – For this mission you need to go to the Lunar Complex. The Lunar Complex is the building that you go through to get to the first Loot Cave. It is also the area where you first fight a Wizard during story. When you spawn on earth go to the left through the area with all the planes and you will end up there. Once you inside you need to go the area that is pitch black and has your ghost lighting the way. In the corner of this room you can see a thrall hunched over. Kill him and the boss and his minions will spawn.
Heart Of Crota – You will need to find the Refinery for this mission. To find this area assume you are playing the Strike Mission(The Devil’s Lair) for earth. There is an area with a crashed ship right before the area that you fight three waves of enemies and defend the ghost. That area is where you will find the boss. If you go to the point where the ghost cuts through the lasers then you have gone to far!
Eyes Of Crota – This unit can be found through the Terrestrial Complex. Take the Mothyards to the Forgotten Shore and use the pathway on the left side of the area to go up to the Complex. Take the complex all the way through until you get back outside and you can see the Knight sitting near a portal on the edge. Take him down and take the vase to start the battle. You will have three mini boss units to kill this time. Use cover to avoid the drop ship shots. If you are having trouble finding the Forgotten Shore, take the canyon from the Mothyards.
After that return to Eris and you can turn all these in and you finally gain access the Strike missions.