- #1
Mikestone
- 21
- 9
- How did you find PF?
- Google Search
I am a retired civil servant, but have been into Science Fiction, Astronomy and Astronautics since childhood. I am also into history(esp American history), and since 1995 have been an active member of the Church of Jesus Christ of Latter-day Saints, which I first encountered through the works of Robert A Heinlein.
As a lifelong space enthusiast, I was familiar with the theorem that the energy required to escape from the Earth was the same at that acquired by falling 4000 miles at a constant acceleration of 1g. I first learned this from Arthur C Clarke’s The Exploration of Space (my ninth birthday present) and from another book (title forgotten but I think the author was American) where this was referred to as “Gravity Mountain”. So I was aware of this, but didn’t give it a lot of thought. More recently however, (just over 60 years on!) I recalled this matter, and realized I had never learned how the relationship was arrived at.
It would be mean-spirited to blame Sir Arthur for this, but I found some of his figures confusing. He had also given depths for the gravity wells of the Moon and sun as 170 and 12 million miles respectively, and try as I might, I couldn’t come up with a calculation which produced these results.
Googling took me to a number of sites including PF, where I found a thread stating the energy required to escape from any planet was the same as acquired by a fall at constant acceleration from an altitude equal to the radius of the planet concerned. This threw me for a while as I was still using Clarke’s figures, but finally it clicked when I realized that he had been assuming a constant 1g acceleration for all the bodies concerned, rather than the different gravitational acceleration of each one.
That realized, It only took a bit of algebra to produce the result which I just submitted. I couldn’t send it to the first thread I found, as comments on it were closed, but after a bit of looking around I found another to which it seemed relevant, and sent it there. Don’t know when I’ll contribute next, but will continue to follow.
As a lifelong space enthusiast, I was familiar with the theorem that the energy required to escape from the Earth was the same at that acquired by falling 4000 miles at a constant acceleration of 1g. I first learned this from Arthur C Clarke’s The Exploration of Space (my ninth birthday present) and from another book (title forgotten but I think the author was American) where this was referred to as “Gravity Mountain”. So I was aware of this, but didn’t give it a lot of thought. More recently however, (just over 60 years on!) I recalled this matter, and realized I had never learned how the relationship was arrived at.
It would be mean-spirited to blame Sir Arthur for this, but I found some of his figures confusing. He had also given depths for the gravity wells of the Moon and sun as 170 and 12 million miles respectively, and try as I might, I couldn’t come up with a calculation which produced these results.
Googling took me to a number of sites including PF, where I found a thread stating the energy required to escape from any planet was the same as acquired by a fall at constant acceleration from an altitude equal to the radius of the planet concerned. This threw me for a while as I was still using Clarke’s figures, but finally it clicked when I realized that he had been assuming a constant 1g acceleration for all the bodies concerned, rather than the different gravitational acceleration of each one.
That realized, It only took a bit of algebra to produce the result which I just submitted. I couldn’t send it to the first thread I found, as comments on it were closed, but after a bit of looking around I found another to which it seemed relevant, and sent it there. Don’t know when I’ll contribute next, but will continue to follow.