Sen. John Glenn (D-Ohio), who first rose to public acclaim in a rocket, has now soared to near presidential front-runner heights with a poll vault.

Three nationwide public opinion surveys have recorded significant gains for him in the past month, and at least for now the Democratic presidential contest has become a two-man race: former vice president Walter F. Mondale vs. Glenn.

A Gallup poll released today shows that Mondale, once far and away the front-runner, held only a modest 29-to-23 percent lead in an April 29-May 2 survey of 695 Democrats registered to vote. In mid-March, Mondale commanded a 32 to 13 percent lead.

No other Democrat was even close to the front-runners. Sen. Gary Hart (D-Colo.) was a distant third with 4 percent, Sen. Alan Cranston (D-Calif.) next with 3, followed by "others" at 10 and "none or don't know" with 31 percent. The poll had a margin or error of plus or minus 5 percentage points.

Perhaps the best news for Glenn was in trial heats against President Reagan, where Glenn scored strongly with independent voters. While Mondale led Reagan by 6 points among all voters, 49 to 43 percent, Glenn led the president by 17 points, 54 to 37 percent. The difference was among independent voters; they preferred Reagan to Mondale by 52 to 38 percent, but picked Glenn over Reagan 49 to 42 percent.

The latest Gallup poll is reflected in other recent surveys.

A poll taken for political consultant David Garth by Penn-Schoen Associates in late April showed that Glenn was gaining on Mondale and trailed 36 to 24 percent. A Los Angeles Times poll last week showed Glenn ahead of Mondale, 28 to 26 percent--but advisers in all camps, and other pollsters, tended to discount that result because a comparatively small sample of 442 Democrats was used. (A Washington Post-ABC News Poll taken between May 11 and 15 did not survey preferences for the Democratic nomination, but did find that Glenn and Reagan were tied at 44 percent while Reagan beat Mondale by 47 to 42 percent, which was little change from the previous month's survey.)

Glenn strategists figure they can cash in on the polls at campaign fund-raisers in the weeks to come, citing them to bolster Glenn's claim that he has the best chance of retaking the White House for the Democrats.

The Glenn advisers have no quick answers to explain their candidate's sudden rise, except to point out that it apparently began after the senator formally announced his candidacy on April 21. The event received the same amount of television coverage as other candidate announcements, they said, but may have made more of an impression because of Glenn's fame as an astronaut.

"Our gains come from people who were previously not willing to declare for Mondale but hadn't really thought of Glenn," said Harrison Hickman, a member of the William R. Hamilton firm that has been hired to do Glenn's private polling. "They knew him as an astronaut, and now they're beginning to consider him as a potential president."

Mondale advisers, who last week discounted the Los Angeles Times poll as out of sync with other surveys, concede now that Glenn has gained in recent polls.

"We don't ballyhoo the good ones, we don't get depressed by the bad ones," said Mondale's acting campaign chairman, James Johnson. "Our campaign is on track. At this stage, the basic question is whether a campaign is on track in positioning itself well against Ronald Reagan, in formulating its policy statements, in its political organizing, and in fund raising."

While Glenn has scored well with independents in the matchups with Reagan, Johnson expressed confidence that Mondale is doing well with those independents who will vote in Democratic primaries.

"The independents who vote in Democratic primaries are concerned about three issues: the nuclear weapons, women's issues, and the environment," Johnson said. "And those issues are pluses for Mondale more than they are for Glenn."

Mondale advisers were taking some satisfaction a few days ago in a Louis Harris survey released last Monday that showed Mondale leading Glenn by a commanding 42 to 27 percent among Democrats and independents. But it turned out that the survey was taken more than a month ago, from April 7-10.

Meanwhile, those Democrats running far behind the front-runners can take comfort in the fact that at this time in 1975, Jimmy Carter was listed only in that anonymous category of "others." Even as late as January, 1976, he had amassed only 4 percent support.