Formula of measuring celestial body density in high school

Formula of measuring celestial body density in high school

Let the mass of the celestial body be m, the acceleration of surface gravity be a, and the radius be r
Let's say there's an object on the surface with a mass of M
Then f = GMM / R ^ 2
Moreover, f = ~ g = ma
∴ma=GMm/R^2 --->M=aR^2/G
Volume v = (4 / 3) π R ^ 3
Density ρ = m / v = 3A / (4 π GR)
∴ ρ= 3a/(4πGR)
This is a derivation method, which is based on the known data of celestial bodies

Is there a strict derivation of the law of gravitation?
High school textbooks give us the idea of approximating the motion of a planet to a uniform circular motion, which is derived in combination with Kepler's third law. But this is not rigorous at all. What's the difference between guessing and guessing?
Can we give rigorous proof by using mathematical tools such as conic curve?

The meaning of law is the summary of objective facts, and its proof also needs experiments

If ∠α and ∠β are both opposite vertex angles and complementary angles, then ∠β = ()

Because the opposite vertex angles are equal, and the sum is 180 degrees
So α = β = 90 degrees

(1) if two angles are equal, then they are opposite vertex angles; (2) the complement angles of opposite vertex angles are equal
③ Two angles with common vertex are opposite vertex angles;
④ If two angles are opposite vertex angles, then the two angles are equal
A.①③
B.②④
C.①④
D.②③

B. It is correct

If ∩ A and ∩ B are antiparietal angles, the complementary angle of ∩ A is 80 degrees, and what is ∩ B

∠b=∠a=180°-80°=100°.

The angle formed by the intersection of two straight lines is the opposite vertex angle, right? The complementary angle to the vertex angle is equal, right? 30 seconds, it's so urgent
Only one of the two sentences is right, and the other two are excluded by me, definitely not

The complement to the vertex angle is equal
The angle formed by the intersection of two lines may be the same side of a line

If an angle is 40 degrees smaller than its adjacent complementary angle, the opposite vertex angle of the angle is

The answer is 70 degrees

If angle 1 and angle 2 complement each other, and angle 1 = 3 times angle 2, then angle 1 = -- degree, angle 2 = -- degree

∵∠1+∠2=180° ∠1=3∠2 ∴∠1+∠2=3∠2+∠2=180° ∴∠1=135° ∠2=45°

The condition that two angles are adjacent complements

The condition that two angles are adjacent complements
1. The sum of the two angles is 180 degrees;
2. The two corners have a common edge

If angle 1 and angle 2 satisfy the following conditions, they are complementary to each other: (why?)
A. Angle 1 and angle 3 are opposite vertex angles, and angle 3 and angle 2 are adjacent complementary angles;
B. They are the angles formed by the intersection of two straight lines;
C. They have a common vertex and a common edge, and the sum is 180 degrees;
D. They have a common point, and the sum is 180 degrees

Adjacent complementary angle: after two lines intersect, two corners or two corners with a common vertex and a common edge have a common fixed point, and the two sides of one corner are the opposite extension of the other called two sides, which is called adjacent complementary angle. There are two adjacent complementary angles of one corner. The sum of an angle and its adjacent complementary angle is equal to 180. So C is the correct answer