"Gravitation" topic 1 Solving the mass and density of celestial
bodies
Model 1 (orbiting method) assumes that the orbital radius of the satellite
orbiting the object is r, the period is T, the radius of the central object is
R, and the gravitational constant is G.
（1）Try to write an expression for the mass and average density of the central
object? When the satellite moves around the surface of the central object, its
period is T, then the expression for the average density of the central object
is?
（2）If the radius of the orbit around the object is unknown, what physical
quantity needs to be measured and the expression for the mass of the central
object is written?
Model 2 (gravitational acceleration method).Ignoring the rotation of the central
celestial body, it is known that the mass of an apple on the surface of the star
is m, the radius is R, the gravitational acceleration on the surface of the star
is g, and the gravitational constant is g.
(1) Calculate the mass and density of the star
(2) Find the gravitational acceleration g1 of the object at h distance from the
surface of the star
(3) Find the ratio of g to g1
(4) If the rotation of the star is not negligible, the gravitational acceleration
of the two stages of the star and the equator are g pole and g0 respectively,
the rotation period of the star is T, and the mass and density of the star are ?
Single-choice questions
1. Saturn's largest moon is called "Titan" (pictured), which orbits Saturn once
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, every 16 days, and its orbital radius is about 1.2 106 km , and if the
gravitational constant is known G = 6.67 10−11 N m2 / kg 2 , the mass of Saturn is
about ( ).
A． 5 1017 kg B． 5 1026 kg
C． 7 1033 kg D． 4 1036 kg
2. In April 2021, the core module of China's self-developed space station
"Tianhe" was successfully launched and put into orbit, and the operation of the
core module around the earth can be regarded as a uniform circular motion. The
gravitational constant is known, and the mass of the Earth can be calculated
from the following physical quantities ( )
A. Mass of the core module and radius around the ground
B. Mass of the core module and the period around the ground
C. Angular velocity and circum-earth period of the core module
D. Ground velocity and period around the core module
Multiple-choice questions
3. Two scientists were awarded the 2020 Nobel Prize in Physics for the
discovery of a supermassive compact object at the center of the Milky Way. They
continued to observe the position of a star near the center of the Milky Way
S 2 , and recorded S 2 an elliptical orbit as shown in the figure. O is a focal
point of an ellipse, and the eccentricity (eccentricity) of the ellipse is
about 0.87. P and Q are the far galactic and perigalactic points of the orbit,
respectively, and the distance between Q and O is about120AU (the distance
from the sun to the earth 1AU ), S 2 and the orbital period is about 16 years.
The hypothetical S 2 trajectory is mainly affected by the gravitational pull of
the compact object at the center of the Milky Way, and based on the above data
and daily astronomical knowledge, ( ) can be deduced
bodies
Model 1 (orbiting method) assumes that the orbital radius of the satellite
orbiting the object is r, the period is T, the radius of the central object is
R, and the gravitational constant is G.
（1）Try to write an expression for the mass and average density of the central
object? When the satellite moves around the surface of the central object, its
period is T, then the expression for the average density of the central object
is?
（2）If the radius of the orbit around the object is unknown, what physical
quantity needs to be measured and the expression for the mass of the central
object is written?
Model 2 (gravitational acceleration method).Ignoring the rotation of the central
celestial body, it is known that the mass of an apple on the surface of the star
is m, the radius is R, the gravitational acceleration on the surface of the star
is g, and the gravitational constant is g.
(1) Calculate the mass and density of the star
(2) Find the gravitational acceleration g1 of the object at h distance from the
surface of the star
(3) Find the ratio of g to g1
(4) If the rotation of the star is not negligible, the gravitational acceleration
of the two stages of the star and the equator are g pole and g0 respectively,
the rotation period of the star is T, and the mass and density of the star are ?
Single-choice questions
1. Saturn's largest moon is called "Titan" (pictured), which orbits Saturn once
Discipline Network (Beijing) Co ., Ltd
, every 16 days, and its orbital radius is about 1.2 106 km , and if the
gravitational constant is known G = 6.67 10−11 N m2 / kg 2 , the mass of Saturn is
about ( ).
A． 5 1017 kg B． 5 1026 kg
C． 7 1033 kg D． 4 1036 kg
2. In April 2021, the core module of China's self-developed space station
"Tianhe" was successfully launched and put into orbit, and the operation of the
core module around the earth can be regarded as a uniform circular motion. The
gravitational constant is known, and the mass of the Earth can be calculated
from the following physical quantities ( )
A. Mass of the core module and radius around the ground
B. Mass of the core module and the period around the ground
C. Angular velocity and circum-earth period of the core module
D. Ground velocity and period around the core module
Multiple-choice questions
3. Two scientists were awarded the 2020 Nobel Prize in Physics for the
discovery of a supermassive compact object at the center of the Milky Way. They
continued to observe the position of a star near the center of the Milky Way
S 2 , and recorded S 2 an elliptical orbit as shown in the figure. O is a focal
point of an ellipse, and the eccentricity (eccentricity) of the ellipse is
about 0.87. P and Q are the far galactic and perigalactic points of the orbit,
respectively, and the distance between Q and O is about120AU (the distance
from the sun to the earth 1AU ), S 2 and the orbital period is about 16 years.
The hypothetical S 2 trajectory is mainly affected by the gravitational pull of
the compact object at the center of the Milky Way, and based on the above data
and daily astronomical knowledge, ( ) can be deduced
