题目

相对论部分
1.The total power radiated by the sun is about 3.83 x1026 Watts.How many kilograms of protons and electrons are transformed into helium every second?Note:For a fusion reaction the fraction of mass converted to energy is about 0.007.
2.The mass of the Sun is about 1.99 x1030 kilograms.If we assume this is all hydrogen and about one tenth (0.1) is in the core,how long will the sun burn?Enter your answer in years (use yr as the unit for years).Hint:Calculate the number of seconds the Sun will last and then divide by the number of seconds in a year to get years.For comparison,the Earth is about 4.5 x109 yr old.
3.The average male in the US has a mass of about 88 kg.Interestingly,it is theoretically possible to squash the average male into a black hole.It is also possible,but extremely unlikely,that this could happen spontaneously.For curiosity,what is the Schwarzschild radius of a black hole made from a male who started with a mass of 86 kg?
4.General Relativity says

提问时间：2020-10-09

答案

1.As known,for a fusion reaction the fraction of mass converted to energy is about 0.007.So there is
△E=△mc²=0.007mc².
Here △E=P*△t=3.83×10^26(W)×1(s)=3.83×10^26(J),c≈3×10^8(m/s).We get
m=△E/(0.007c²)≈3.83×10^26/(0.063×10^16)≈6.08×10^11(kg).
So there are about 6.08×10^11 kilograms of protons and electrons are transformed into helium every second.
2.According to problem 1 and the presumption that about one tenth (0.1) mass of the Sun is in the core,we can calculate that the number of seconds the Sun will last is about
T=0.1M/(m/t)≈0.1×1.99×10^30kg/(6.08×10^11kg/s)≈3.27×10^17s,
which is
T≈3.27×10^17s/(31536000s/yr)≈1.04×10^10yr.
3.For the formular of the Schwarzschild radius is R=2GM/c² and here M=86kg,G=6.67×10^(-11m³/kgs²),we get
R=2GM/c²=2×6.67×10^(-11m³/kgs²)×86kg/(9×10^16m²/s²)≈1.275×10^(-25m).
So the Schwarzschild radius of a black hole made from a male who started with a mass of 86 kg is about 1.275×10^-25 meters.
4.Here an acceleration of 4.19 m/s² in one direction is like gravity of 4.19 m/s² in another direction.So we get
a/g=4.19(m/s²)/9.81(m/s²)≈0.427.
Now we know that this acceleration feel like 0.427 "g"s.