Oops!
Slight correction to my post. (I've mis-read the National Rail website. I ought to know that the Underground from Heathrow doesn't go directly to Victoria!). By rail, either take the Underground to South Kensington and then change for another Underground train to Victoria (fares as above) OR take the Heathrow Express to Paddington, then the Circle Line (Underground) to Victoria. The through fare from Heathrow to Gatwick is �27.40 (US$55, �40) if you use the Southern Trains service or �33.40 (US$67, �48) if you take the Gatwick Express.
Chris