[pburger]

How many miles or kilometres does the Earth travel in one orbit of the sun? Is it constant?

[urmod4u]

Earth's orbit around the sun is 924,375,700 km or 574,380,400 miles (figures from NASA).
You may consider it constant, keeping in mind that:
- it varies (insignificantly) over the years due to interactions with other planets
- it increases due to tidal effects by about 6 micrometer per year
- it increases due to loss of sun-mass (nuclear activity and solar wind) by about 10 to 20 cm per year (figures vary depending on the source).
This means that the distance sun-earth increases by about 1.5 to 3 cm (roughly, one inch) per year. That is 40 years for 1 meter, or 100,000 km over the age of the earth - or 0.6% of the actual distance.