This episode's coordinates point to an object named NGC 1501 in the constellation Camelopardalis, which is a constellation representing a giraffe. However, the first two syllables in the constellation's name are clearly the word "camel". Apparently, the Greek word for "giraffe" is "camel leopard" [1]. Also, this is not a constellation created by the ancient Greeks but instead created by a Dutch theologian and astronomer named Petrus Plancius in 1612 [1]. The constellation basically consists of a bunch of faint stars, the brightest of which is magnitude 4.0 (or only one to two magnitudes brighter than what can be seen without a telescope) [1].
Anyhow, that concludes the part of the episode where I rant about a stupid constellation. Now, back to the astronomical object. NGC 1501 is a planetary nebula, as in the type of nebula that is formed when a star about the size of the Sun dies and blows off its outer atmosphere and not the type of nebula associated with actual planets. The nebula is kind of a weird oval shape, and in fact this object has the nickname of the Oyster Nebula because it extremely vaguely looks like the shape of an oyster. Very specifically, it has the shape of an abnormally symmetric oyster. Most oysters are asymmetric, or at least they look asymmetric to me.
Anyway, stars the size of the Sun have the mass to trigger the fusion of helium into carbon and oxygen in their cores, but the stars are not massive enough to trigger the fusion of carbon and oxygen into heavier elements, so when the stars die and blow away their outer atmospheres, they leave behind these cores of carbon and oxygen, which are sometimes still surrounded by residual amounts of helium. These cores thus become white dwarfs. Such a white dwarf has been found in the center of NGC 1501. However, the star is very young. It's also not an ordinary white dwarf.
First of all, this white dwarf is extremely hot. The temperature is listed as 134000 degrees Kelvin (which is about 134000 degrees Celsius because the 273 degree difference between the two temperature scales doesn't matter when things are that hot) [2]. Because the temperature is so high and because the white dwarf formed relatively recently, the star is also producing really strong stellar winds that are helping to blow away the remaining gas surrounding the white dwarf and shape the surrounding planetary nebula. Additionally, the star is really bright; it produces 3.85 times more light than the Sun does [2]. However, the star is located at a distance of 5630 light years (1730 pc), so it doesn't look that bright as seen from Earth [3, 4].
More notably, though, the star at the center of NGC 1501 pulsates. It actually has several different pulsation periods; the strongest pulsations have a period of between 19 and 33 minutes [5]. In fact, this star belongs to a class of pulsating white dwarf stars named GW Virginis stars after the first star identified with this type of variability [2]. A bunch of other terms are also used to describe this class of variable stars, which could get really confusing very quickly because most variable star classifications are based on the names of individual stars, so I'll just go with GW Virginis stars. In any case, the star at the center of NGC 1501 is one of the more notable and well-studied GW Virginis stars.
The pulsations in the central white dwarf in NGC 1501 come from gravitational waves propagating through the white dwarf, which is still cooling off. After a while, the star should have settled down and stabilized and stopped pulsing. For now, though, the pulsations are very interesting, as they are a form of what is called astroseismology, and astronomers have used astroseismological models to estimate the mass of the star, which is about 0.61 times the mass of the Sun [2].
It is possible to see NGC 1501 with an amateur telescope. Unfortunately, I can't really give good instructions on how to find the nebula because it's in a constellation that consists of a bunch of really faint stars, so you'll just need to either use a good star chart or a telescope with a computerized mount. The nebula is apparently barely visible as a faint oval shape in telescopes with diameters of 10 to 12.5 cm (4 to 5 inches) [6]. In 20 cm (8 inch) or larger telescopes, it's possible to see the central star as well as more structure in the nebula [6, 7, 8]. High magnification is recommended for viewing the star [8].