When Neil Armstrong took the first steps on the Moon in July 1969, his soon-to-be-legendary words crossed 230,000 miles of space to reach millions of people around the world: “That’s one small step for [a] man, one giant leap for mankind.” Armstrong’s statement acknowledged that this monumental achievement was not his alone. Those first steps were made possible by the efforts and ingenuity of multitudes that, together, made the rockets and spacecraft that had brought men to another world. And as Nathalia Holt notes in her new book about a group of women working in the American space industry, these technologies weren’t built by men alone.

In Rise of the Rocket Girls: the Women Who Propelled Us, from Missiles to the Moon to Mars, Holt – a research biologist by training – foregrounds the contributions of a cohort of women whose labour was subsumed within the “mankind” of Armstrong’s historic statement, and largely forgotten in popular recollections of the Moon effort. Focusing on the history of the Jet Propulsion Laboratory (JPL) from the mid-1930s (when it was founded by the California Institute of Technology’s “suicide squad” of rocket engineers) through to the present day, Holt builds her narrative primarily on the recollections of the women who worked there as “computers” – a term we now associate with electronic machines but that once described a (usually female) mathematician. By interspersing memories of office hijinks, technical victories and failures, and the personal lives of her subjects, Holt’s narrative conveys a palpable intimacy that reflects the close relationships maintained by this group of women over decades of professional and personal camaraderie.

Holt focuses on her subjects’ participation in (and reactions to) important moments in space history, such as the competition between US military branches to get the first American satellite into orbit and the persistent difficulty in creating a single-stage-to-orbit rocket. In describing these moments, Holt’s literary skill shines brightly. She notes, for instance, that in helping each other work through monumental challenges of physics and engineering, the women computers and their male engineer counterparts at JPL worked like a multistage rocket – segmented but ultimately successful. Milestones in the computers’ lives, from pregnancy and marriage to stillbirth and divorce, serve as signposts to punctuate the successes and failures of the rocket programmes at JPL.

In addition to retelling these personal histories, Rise of the Rocket Girls doubles as a concise, accessible introduction to various scientific and mathematical concepts, from the Coriolis effect to Doppler shift. In an artful meta conceit, Holt traces the history of the electronic computer alongside the history of human computers at JPL. Occasionally, deviations to discuss the rise of Microsoft and Apple or the causes of the Challenger accident, for example, can be a bit tangential. However, as an introduction to the American space and computing industries, Holt’s text covers a massive amount of ground – in spite of a few glaring omissions, such as the end of the Cold War and its impact on the main subjects of this narrative.

Readers should, however, be advised of some critical oversights. Holt misrepresents the range of a rocket as its altitude, and occasionally uses figures that do not correspond to most cited historical records of the launcher in question. And, frustratingly, when the computers discuss working with “data,” we never get a chance to learn more about the data in question – how they were collected, by whom, and what the data actually looked like, which would go a long way towards making the experience of these women real to readers.

At times, the intimacy and accessibility of Holt’s narrative voice becomes a double-edged sword. Basing her book on the recollections of a few, mostly white women, Holt’s narrative voice adopts the vocabulary and perspective of her subjects. For instance, Holt typically describes the JPL computers as “girls”. While this is faithful to the terminology used by both the women and the men with whom they worked, it does not conscientiously critique the infantilizing meaning of this word, both then and particularly now. As a result, Holt unintentionally recapitulates the sexism of computers’ experiences in what otherwise reads as a sympathetic historical narrative. We also see this when Holt physically describes each of the women – often focusing on their beauty or style choices – while eschewing such descriptions of men.

In another troubling aspect of the book, Holt discusses instances in which women left their jobs after getting married or pregnant, either because they were forced to leave, or because they decided to adhere to social norms. Those who did not return to JPL later in life simply disappear from the narrative – an unfortunate literary replication of the very sexism that forced these women from the lab in the first place. A particularly glaring example concerns Janez Lawson, the sole black woman of the group. Her story ends with Lawson leaving JPL largely because racial politics prevented her from living in predominantly white Pasadena – and unlike the other characters, who receive an “ever after” treatment in the final chapter, we never find out what happens to Lawson once she departs the lab. Given that two women of colour factor prominently in the narrative – and several unmentioned women of colour worked as computers at JPL during the Cold War – Holt pays only superficial attention to the compounding effects of race and gender on interpersonal relationships at JPL. The upcoming book Hidden Figures: the American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race by Margot Lee Shetterly will likely address this omission.

Perhaps surprisingly, given that this book focuses on the struggles and triumphs of women in a predominantly male institution, Holt barely mentions the women’s movement that took off at the same time as her subjects worked to get rockets off the ground. Her final conclusion, a counterpoint to other Cold War gender histories, makes a bold claim: “While protestors were demanding equal rights for women across the country, the women at JPL had created their own equality. They had formed the lab in their own image, building an environment amenable to women, where their work and contributions were every bit as valued as those of their male counterparts.” Taken at face value, and based on the contented reflections of a small group of women who lived through it, this statement is probably true. However, hindsight typically provides unstable support for sweeping historical arguments. It is likely that not all women who worked in the space industry during this period will agree.

• 2016 Little, Brown and Company £19.11/$27.00hb 304pp