Explanation:

1,2-Dibromoethane:
1,2-Dibromoethane is a compound with the molecular formula C2H4Br2. It is a halogenated organic compound that consists of two bromine atoms attached to a central ethane molecule. The two bromine atoms are attached to adjacent carbon atoms.

Gauche and Anti forms:
In the given scenario, astronauts discovered two forms of 1,2-dibromoethane on Pluto: gauche and anti. The terms gauche and anti refer to the spatial arrangement of the bromine atoms relative to each other.

1. Gauche form: In the gauche form, the two bromine atoms are on the same side of the molecule, resulting in a bent or "V" shape.

2. Anti form: In the anti form, the two bromine atoms are on opposite sides of the molecule, resulting in a linear or "I" shape.

No rotations around single bonds:
The question specifies that there are no rotations around single bonds in the given scenario. This means that the spatial arrangement of the two bromine atoms is fixed and cannot be interconverted by rotation.

Diastereomers:
Diastereomers are stereoisomers that are not mirror images of each other and have different physical and chemical properties. In the case of 1,2-dibromoethane, the gauche and anti forms are diastereomers because they have different spatial arrangements of the bromine atoms.

Explanation of the Correct Answer:
The correct answer to the question is option 'B': They are diastereomers.

The gauche and anti forms of 1,2-dibromoethane on Pluto are diastereomers because they have different spatial arrangements of the bromine atoms. Due to the lack of rotation around single bonds, these two forms cannot interconvert by simple rotation. Therefore, they exist as distinct and separate forms of the compound.

Other Incorrect Options:

a) They are enantiomers: Enantiomers are stereoisomers that are non-superimposable mirror images of each other. In the given scenario, the gauche and anti forms of 1,2-dibromoethane do not possess this mirror image relationship, so they are not enantiomers.

c) They are meso compounds: Meso compounds are stereoisomers that have an internal plane of symmetry, resulting in the cancellation of optical activity. In the case of 1,2-dibromoethane, neither the gauche nor the anti form possesses an internal plane of symmetry, so they are not meso compounds.

d) Both will show optical activity: Optical activity is observed in chiral compounds that lack internal symmetry. However, in the given scenario, neither the gauche nor the anti form is chiral, as they do not possess a stereocenter. Therefore, they do not show optical activity.