Humans are looking for a permanent home. They colonized Mars, and later terraformed it, temporarily, before being forced out of the solar system entirely when the Sun went all Red-Giant on them a few hundred years later.

Since then, they've been planet hopping. Hibernating between stops. Their terraforming ability, while impressive, is limited. Without a planet that more closely resembels Earth than, say, Mars, they keep running in to issues for long term human viability. They knew Mars was a temporary solution, a pit stop to gather materials and experience, gear up for the inevitable death of Earth. Even having terraformed it, and assuming the Sun had taken longer than expected to expand, they knew that Mars would not hold an atmosphere for long. Sure a replenishment of the atmosphere might be possible, but repeating the terraforming process only delays the inevitable. They wanted a more permanent solution.

Other planets they've stopped at along the way have had other issues. Too much gravity, too close or too far from the star, atmosphere instabilities, radiation, etc.

Each time, they would terraform it, both to make the stop more comfortable, as well as to gain knowledge and experience of the terraforming process. While at each stop, they would also replenish their resources (a long process) needed for the next terraform.

The latest stop is this planet:

1. Earthlike crust mineral content (sans water, which will be provided by the terraforming process).
2. Earthlike magnetosphere.
3. Radius of 2142 km.
4. Mass of 6.594e^23 kg.
5. Orbiting a star with properties close enough to Sun-like for the differences to be negligible for the purposes of this question.
6. If I've done my calculations correctly, and taken into consideration all relevant factors, this gives the planet an escape velocity of 3.983 miles per second (compared to Earth's 6.95 miles per second).

Unfortunately, I've been unable to find a calculator or other math reference information for determining the actual rate of atmospheric losses as a function of escape velocity, so I don't know where to start to attempt that calculation.

(If I've left off any important data, let me know in comments, I almost certainly have it available and just forgot to include it or didn't realize it was relevant)

Once the terraforming process is complete, and an Earth-analogue atmosphere is established, and assuming humans care for it, in the sense of intentionally avoiding significant damage to it, but not actively replenishing it, how long will the atmosphere remain hospitable to human inhabitants, before too much of the atmosphere bleeds off in to space due to the low escape velocity of this planet?

Humans are looking for a permanent home. They colonized Mars and later terraformed it, temporarily, before being forced out of the solar system entirely when the Sun went all Red-Giant on them a few hundred years later.

Since then they've been planet hopping and hibernating between stops. Their terraforming ability, while impressive, is limited. Without a planet that more closely resembles Earth than, say, Mars, they keep running into issues for long term human viability. They knew Mars was a temporary solution, a pit stop to gather materials and experience to gear up for the inevitable death of Earth. Even having terraformed it, and assuming the Sun had taken longer than expected to expand, they knew that Mars would not hold an atmosphere for long. A replenishment of the atmosphere might have been possible, but repeating the terraforming process only delays the inevitable. They wanted a more permanent solution.

Other planets they've stopped at along the way have had other issues. Too much gravity, too close or too far from the star, atmosphere instabilities, radiation, etc.

Each time they would terraform it the planet, both to make the stop more comfortable, as well as to gain knowledge and experience of the terraforming process. While at each stop they would also replenish their resources (a long process) needed for the next terraform.

The latest stop is this planet:

1. Earthlike crust mineral content (sans water, which will be provided by the terraforming process).
2. Earthlike magnetosphere.
3. Radius of 2142 km.
4. Mass of 6.594e^23 kg.
5. Orbiting a star with properties close enough to Sun-like for the differences to be negligible for the purposes of this question.
6. If I've done my calculations correctly, and taken into consideration all relevant factors, this gives the planet an escape velocity of 3.983 miles per second (compared to Earth's 6.95 miles per second).

Unfortunately, I've been unable to find a calculator or other math reference information for determining the actual rate of atmospheric losses as a function of escape velocity, so I don't know where to start to attempt that calculation.

Note: If I've left off any important data, let me know in comments. I almost certainly have it available and just forgot to include it or didn't realize it was relevant.

Once the terraforming process is complete, and an Earth-analogue atmosphere is established, and assuming humans care for it, in the sense of intentionally avoiding significant damage to it, but not actively replenishing it, how long will the atmosphere remain hospitable to human inhabitants, before too much of the atmosphere bleeds off in to space due to the low escape velocity of this planet?

Humans are looking for a permanent home. They colonized Mars, and later terraformed it, temporarily, before being forced out of the solar system entirely when the Sun went all Red-Giant on them a few hundred years later.

Since then, they've been planet hopping. Hibernating between stops. Their terraforming ability, while impressive, is limited. Without a planet that more closely resembels Earth than, say, Mars, they keep running in to issues for long term human viability. They knew Mars was a temporary solution, a pit stop to gather materials and experience, gear up for the inevitable death of Earth. Even having terraformed it, and assuming the Sun had taken longer than expected to expand, they knew that Mars would not hold an atmosphere for long. Sure a replenishment of the atmosphere might be possible, but repeating the terraforming process only delays the inevitable. They wanted a more permanent solution.

Other planets they've stopped at along the way have had other issues. Too much gravity, too close or too far from the star, atmosphere instabilities, radiation, etc.

Each time, they would terraform it, both to make the stop more comfortable, as well as to gain knowledge and experience of the terraforming process. While at each stop, they would also replenish their resources (a long process) needed for the next terraform.

The latest stop is this planet: Earthlike crust mineral content (sans water, which will be provided by the terraforming process). Earthlike magnetosphere. Radius of 2142 km. Mass of 6.594e^23 kg. Orbiting a star with properties close enough to Sun-like for the differences to be negligible for the purposes of this question. If I've done my calculations correctly, and taken into consideration all relevant factors, this gives the planet an escape velocity of 3.983 miles per second (compared to Earth's 6.95 miles per second). Unfortunately, I've been unable to find a calculator or other math reference information for determining the actual rate of atmospheric losses as a function of escape velocity, so I don't know where to start to attempt that calculation.

(If I've left off any important data, let me know in comments, I almost certainly have it available and just forgot to include it or didn't realize it was relevant)

Once the terraforming process is complete, and an Earth-analogue atmosphere is established, and assuming humans care for it, in the sense of intentionally avoiding significant damage to it, but not actively replenishing it, how long will the atmosphere remain hospitable to human inhabitants, before too much of the atmosphere bleeds off in to space due to the low escape velocity of this planet?

Humans are looking for a permanent home. They colonized Mars, and later terraformed it, temporarily, before being forced out of the solar system entirely when the Sun went all Red-Giant on them a few hundred years later.

Since then, they've been planet hopping. Hibernating between stops. Their terraforming ability, while impressive, is limited. Without a planet that more closely resembels Earth than, say, Mars, they keep running in to issues for long term human viability. They knew Mars was a temporary solution, a pit stop to gather materials and experience, gear up for the inevitable death of Earth. Even having terraformed it, and assuming the Sun had taken longer than expected to expand, they knew that Mars would not hold an atmosphere for long. Sure a replenishment of the atmosphere might be possible, but repeating the terraforming process only delays the inevitable. They wanted a more permanent solution.

Other planets they've stopped at along the way have had other issues. Too much gravity, too close or too far from the star, atmosphere instabilities, radiation, etc.

Each time, they would terraform it, both to make the stop more comfortable, as well as to gain knowledge and experience of the terraforming process. While at each stop, they would also replenish their resources (a long process) needed for the next terraform.

The latest stop is this planet:

1. Earthlike crust mineral content (sans water, which will be provided by the terraforming process).
2. Earthlike magnetosphere.
3. Radius of 2142 km.
4. Mass of 6.594e^23 kg.
5. Orbiting a star with properties close enough to Sun-like for the differences to be negligible for the purposes of this question.
6. If I've done my calculations correctly, and taken into consideration all relevant factors, this gives the planet an escape velocity of 3.983 miles per second (compared to Earth's 6.95 miles per second).

Unfortunately, I've been unable to find a calculator or other math reference information for determining the actual rate of atmospheric losses as a function of escape velocity, so I don't know where to start to attempt that calculation.

(If I've left off any important data, let me know in comments, I almost certainly have it available and just forgot to include it or didn't realize it was relevant)

Once the terraforming process is complete, and an Earth-analogue atmosphere is established, and assuming humans care for it, in the sense of intentionally avoiding significant damage to it, but not actively replenishing it, how long will the atmosphere remain hospitable to human inhabitants, before too much of the atmosphere bleeds off in to space due to the low escape velocity of this planet?

Humans are looking for a permanent home. They colonized Mars, and later terraformed it, temporarily, before being forced out of the solar system entirely when the Sun went all Red-Giant on them a few hundred years later.

Since then, they've been planet hopping. Hibernating between stops. Their terraforming ability, while impressive, is limited. Without a planet that more closely resembels Earth than, say, Mars, they keep running in to issues for long term human viability. They new Mars was a temporary solution, a pit stop to gather materials and experience, gear up for the inevitable death of Earth. Even having terraformed it, and assuming the Sun had taken longer than expected to expand, they knew that Mars would not hold an atmosphere for long. Sure a repleneshment of the atmosphere might be possible, but repeating the terraforming process only delays the inevitable. They wanted a more permanent solution.

Other planets they've stopped at along the way have had other issues. Too much gravity, too close or too far from the star, atmosphere instabilities, radiation, etc.

Each time, they would terraform it, both to make the stop more comfortable, as well as to gain knowledge and experience of the terraforming process. While at each stop, they would also replenish their resources (a long process) needed for the next terraform.

The latest stop is this planet: Earthlike crust mineral content (sans water, which will be provided by the terraforming process). Earthlike magnetosphere. Radius of 2142 km. Mass of 6.594e^23 kg. Orbiting a star with properties close enough to Sun-like for the differences to be negligible for the purposes of this question. If I've done my calculations correctly, and taken into consideration all relevant factors, this gives the planet an escape velocity of 3.983 miles per second (compared to Earth's 6.95 miles per second). Unfortunately, I've been unable to find a calculator or other math reference information for determining the actual rate of atmospheric losses as a function of escape velocity, so I don't know where to start to attempt that calculation.

(If I've left off any important data, let me know in comments, I almost certainly have it available and just forgot to include it or didn't realize it was relevant)

Once the terraforming process is complete, and an Earth-analogue atmosphere is established, and assuming humans care for it, in the sense of intentionally avoiding significant damage to it, but not actively replenishing it, how long will the atmosphere remain hospitable to human inhabitants, before too much of the atmosphere bleeds off in to space due to the low escape velocity of this planet?

Humans are looking for a permanent home. They colonized Mars, and later terraformed it, temporarily, before being forced out of the solar system entirely when the Sun went all Red-Giant on them a few hundred years later.

Since then, they've been planet hopping. Hibernating between stops. Their terraforming ability, while impressive, is limited. Without a planet that more closely resembels Earth than, say, Mars, they keep running in to issues for long term human viability. They knew Mars was a temporary solution, a pit stop to gather materials and experience, gear up for the inevitable death of Earth. Even having terraformed it, and assuming the Sun had taken longer than expected to expand, they knew that Mars would not hold an atmosphere for long. Sure a replenishment of the atmosphere might be possible, but repeating the terraforming process only delays the inevitable. They wanted a more permanent solution.

Other planets they've stopped at along the way have had other issues. Too much gravity, too close or too far from the star, atmosphere instabilities, radiation, etc.

Each time, they would terraform it, both to make the stop more comfortable, as well as to gain knowledge and experience of the terraforming process. While at each stop, they would also replenish their resources (a long process) needed for the next terraform.

The latest stop is this planet: Earthlike crust mineral content (sans water, which will be provided by the terraforming process). Earthlike magnetosphere. Radius of 2142 km. Mass of 6.594e^23 kg. Orbiting a star with properties close enough to Sun-like for the differences to be negligible for the purposes of this question. If I've done my calculations correctly, and taken into consideration all relevant factors, this gives the planet an escape velocity of 3.983 miles per second (compared to Earth's 6.95 miles per second). Unfortunately, I've been unable to find a calculator or other math reference information for determining the actual rate of atmospheric losses as a function of escape velocity, so I don't know where to start to attempt that calculation.

(If I've left off any important data, let me know in comments, I almost certainly have it available and just forgot to include it or didn't realize it was relevant)

Once the terraforming process is complete, and an Earth-analogue atmosphere is established, and assuming humans care for it, in the sense of intentionally avoiding significant damage to it, but not actively replenishing it, how long will the atmosphere remain hospitable to human inhabitants, before too much of the atmosphere bleeds off in to space due to the low escape velocity of this planet?