I hope this isn't out of place, but I'm been thinking about this for a while and I'm curious to see how other people would go about it.
Imagine the following situation:
Hostile aliens have invaded the solar system with a fleet of 15 ships of the same class, each weighing 1000-tons. Experience from previous has shown these to have a sensor range of 12. 5 million km. They are armed with 1-2 missile launchers; their missiles have an approximate range of 20-30 million km with a 4 kiloton nuclear warhead but no sensors. Their ships have been observed to have a max speed of 3750 km/s and their missiles have been observed to have a speed of 16. 4k km/s.
Of these ships, 3 were destroyed unaware in a missile engagement, taking between about 6 missiles to be taken out of commission (sensors and engines down) and 9 missiles to be destroyed. Due to high training, misses were rare.
The rest of this fleet is currently near the outskirts of Mars's orbit; 5 of them have their active sensors lit up and the inner system has sufficient sensor coverage to keep them visible on passive sensors at all times.
At your disposal:
A task group composed of 3 destroyers and 6 frigates, all armed with missiles, 83 million km away from the alien fleet. They are currently undetected by the alien fleet. Active sensors can only locate the alien ships at approximately 30 million km out and only the destroyers have active sensors. All the destroyers and only one of the frigates have fire control capable of locking on to the alien ships at a range of 20 million km, these ships have an average crew training of 9. 5%. The destroyers have a maximum speed of 3015 km/s and 3 layers of amour, while the frigates have a max speed of 3797 km/s and a single layer of armour.
The Buccaneer Missile has a 59 million km range with a speed of 8900 km/s, while the Bat Missile has a 5. 9 million km range with a speed of 7700 km/s. The destroyer flagship has 2 Buccaneer launchers and a Bat launcher as well as enough ammunition for 6 salvos. The destroyer consorts have 3 Buccaneer launchers instead and hold up to 5 salvos, and the frigate with the sole appropriate fire control has a single Buccaneer launcher with 5 salvos.
As such, if the aliens wish to force an engagement, they have the speed to keep up with the task force (unless the destroyers are abandoned). Based on prior experience, there are only enough missiles in the task group's magazines to destroy 5 of the alien ships. The nearest colony with missiles stores (Earth) is 37 hours away. There is another force of 3 destroyer-consorts, with no missiles remaining, a week away from Earth. There is also a destroyer-consort being overhauled on Earth as well as 4 PDCs armed with similar missiles and sensors.
What would you do? Force an engagement right away? Try to lure the alien fleet to Earth? Await the arrival of the second task group?
My apologies if this is overly long, I tried to put in only the relevant information, but there was so much which I thought could sway one's decision.
For full information on the ship classes available:
The destroyer flagship
Vanguard Mk. IIA class Destroyer 9,750 tons 210 Crew 1112.8 BP TCS 195 TH 600 EM 0
3076 km/s Armour 3-40 Shields 0-0 Sensors 60/1/0/0 Damage Control Rating 2 PPV 17
Maint Life 0.8 Years MSP 143 AFR 380% IFR 5.3% 1YR 179 5YR 2680 Max Repair 150 MSP
Intended Deployment Time: 6 months Spare Berths 1
Flag Bridge Magazine 98
Prototype Commercial Ion Drive (4) Power 150 Fuel Use 10.61% Signature 150 Exp 5%
Fuel Capacity 150,000 Litres Range 26.1 billion km (98 days at full power)
Buccaneer Launcher (2) Missile Size 7 Rate of Fire 105
Bat Launchers (1) Missile Size 4 Rate of Fire 120
Buccaneer Fire Control FC54-R90 (1) Range 54.6m km Resolution 90
Missile Fire Control FC20-R1 (1) Range 20.2m km Resolution 1
Bat Missile (7) Speed: 7,700 km/s End: 11.1m Range: 5.1m km WH: 4 Size: 3.5025 TH: 48/29/14
Buccaneer Missile (12) Speed: 8,900 km/s End: 110.7m Range: 59.1m km WH: 4 Size: 6.05 TH: 62/37/18
Small Ship Sensor (1) GPS 5120 Range 48.6m km Resolution 40
Active Search Sensor MR6-R1 (1) GPS 112 Range 6.7m km Resolution 1
Large Passive Thermal Sensors (1) Sensitivity 60 Detect Sig Strength 1000: 60m km
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes
The destroyer consort
Vanguard Mk. IIB class Destroyer 9,950 tons 207 Crew 1003.6 BP TCS 199 TH 600 EM 0
3015 km/s Armour 3-41 Shields 0-0 Sensors 60/1/0/0 Damage Control Rating 2 PPV 24
Maint Life 0.73 Years MSP 126 AFR 396% IFR 5.5% 1YR 173 5YR 2594 Max Repair 128 MSP
Intended Deployment Time: 6 months Spare Berths 2
Magazine 121
Prototype Commercial Ion Drive (4) Power 150 Fuel Use 10.61% Signature 150 Exp 5%
Fuel Capacity 150,000 Litres Range 25.6 billion km (98 days at full power)
Buccaneer Launcher (3) Missile Size 7 Rate of Fire 105
Bat Launchers (1) Missile Size 4 Rate of Fire 120
Buccaneer Fire Control FC54-R90 (1) Range 54.6m km Resolution 90
Missile Fire Control FC20-R1 (1) Range 20.2m km Resolution 1
Bat Missile (7) Speed: 7,700 km/s End: 11.1m Range: 5.1m km WH: 4 Size: 3.5025 TH: 48/29/14
Buccaneer Missile (16) Speed: 8,900 km/s End: 110.7m Range: 59.1m km WH: 4 Size: 6.05 TH: 62/37/18
Small Ship Sensor (1) GPS 5120 Range 48.6m km Resolution 40
Active Search Sensor MR6-R1 (1) GPS 112 Range 6.7m km Resolution 1
Large Passive Thermal Sensors (1) Sensitivity 60 Detect Sig Strength 1000: 60m km
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes
The sole frigate with proper fire control
Warrior class Frigate 3,800 tons 71 Crew 310.6 BP TCS 76 TH 300 EM 0
3947 km/s Armour 1-21 Shields 0-0 Sensors 1/1/0/0 Damage Control Rating 1 PPV 7
Maint Life 1.06 Years MSP 51 AFR 115% IFR 1.6% 1YR 45 5YR 680 Max Repair 112 MSP
Intended Deployment Time: 3 months Spare Berths 1
Magazine 39
Prototype Commercial Ion Drive (2) Power 150 Fuel Use 10.61% Signature 150 Exp 5%
Fuel Capacity 70,000 Litres Range 31.2 billion km (91 days at full power)
Buccaneer Launcher (1) Missile Size 7 Rate of Fire 105
Missile Fire Control FC20-R1 (1) Range 20.2m km Resolution 1
Bat Missile (2) Speed: 7,700 km/s End: 11.1m Range: 5.1m km WH: 4 Size: 3.5025 TH: 48/29/14
Buccaneer Missile (5) Speed: 8,900 km/s End: 110.7m Range: 59.1m km WH: 4 Size: 6.05 TH: 62/37/18
Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s
This design is classed as a Military Vessel for maintenance purposes